Actual source code: ex69.c

  1: static char help[] = "The variable-viscosity Stokes Problem in 2d with finite elements.\n\
  2: We solve the Stokes problem in a square domain\n\
  3: and compare against exact solutions from Mirko Velic.\n\n\n";

  5: /* We discretize the variable-viscosity Stokes problem using the finite element method on an unstructured mesh. The weak form equations are
  6: \begin{align*}
  7:   (\nabla v, \mu (\nabla u + {\nabla u}^T)) - (\nabla\cdot v, p) + (v, f) &= 0 \\
  8:   (q, \nabla\cdot u)                                                      &= 0
  9: \end{align*}
 10: Free slip conditions for velocity are enforced on every wall. The pressure is constrained to have zero integral over the domain.

 12: To produce nice output, use

 14:   -dm_refine 3 -show_error -dm_view hdf5:sol1.h5 -error_vec_view hdf5:sol1.h5::append -sol_vec_view hdf5:sol1.h5::append -exact_vec_view hdf5:sol1.h5::append
 15: */

 17: #include <petscdmplex.h>
 18: #include <petscsnes.h>
 19: #include <petscds.h>
 20: #include <petscbag.h>

 22: typedef enum {SOLKX, SOLCX, NUM_SOL_TYPES} SolutionType;
 23: const char *solTypes[NUM_SOL_TYPES+1] = {"solkx", "solcx", "unknown"};

 25: typedef struct {
 26:   PetscInt  n, m;       /* x- and y-wavelengths for variation across the domain */
 27:   /* SolKx */
 28:   PetscReal B;          /* Exponential scale for viscosity variation */
 29:   /* SolCx */
 30:   PetscReal etaA, etaB; /* Two viscosities for discontinuous change */
 31:   PetscReal xc;         /* The location of viscosity jump */
 32: } Parameter;

 34: typedef struct {
 35:   SolutionType solType; /* The type of exact solution */
 36:   PetscBag     bag;     /* Holds problem parameters */
 37: } AppCtx;

 39: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
 40: {
 41:   PetscInt c;
 42:   for (c = 0; c < Nc; ++c) u[c] = 0.0;
 43:   return 0;
 44: }
 45: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
 46: {
 47:   PetscInt c;
 48:   for (c = 0; c < Nc; ++c) u[c] = 1.0;
 49:   return 0;
 50: }

 52: static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 53:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 54:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 55:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 56: {
 57:   f0[0] = 0.0;
 58:   f0[1] = -PetscSinScalar(constants[1]*PETSC_PI*x[1])*PetscCosScalar(constants[0]*PETSC_PI*x[0]);
 59: }

 61: static void stokes_momentum_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 62:                                const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 63:                                const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 64:                                PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 65: {
 66:   const PetscReal mu = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]);
 67:   PetscInt        c, d;

 69:   for (c = 0; c < dim; ++c) {
 70:     for (d = 0; d < dim; ++d) {
 71:       f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]);
 72:     }
 73:     f1[c*dim+c] -= u[dim];
 74:   }
 75: }

 77: static void stokes_momentum_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 78:                                const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 79:                                const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 80:                                PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 81: {
 82:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
 83:   PetscInt        c, d;

 85:   for (c = 0; c < dim; ++c) {
 86:     for (d = 0; d < dim; ++d) {
 87:       f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]);
 88:     }
 89:     f1[c*dim+c] -= u[dim];
 90:   }
 91: }

 93: static void stokes_mass(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 94:                         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 95:                         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 96:                         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 97: {
 98:   PetscInt d;
 99:   f0[0] = 0.0;
100:   for (d = 0; d < dim; ++d) f0[0] -= u_x[d*dim+d];
101: }

103: static void f1_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux,
104:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
105:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
106:                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
107: {
108:   PetscInt d;
109:   for (d = 0; d < dim*dim; ++d) f1[d] = 0.0;
110: }

112: /* < q, \nabla\cdot u >, J_{pu} */
113: static void stokes_mass_J(PetscInt dim, PetscInt Nf, PetscInt NfAux,
114:                           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
115:                           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
116:                           PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
117: {
118:   PetscInt d;
119:   for (d = 0; d < dim; ++d) g1[d*dim+d] = -1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
120: }

122: /* -< \nabla\cdot v, p >, J_{up} */
123: static void stokes_momentum_pres_J(PetscInt dim, PetscInt Nf, PetscInt NfAux,
124:                                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
125:                                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
126:                                    PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
127: {
128:   PetscInt d;
129:   for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
130: }

132: /* < \nabla v, \nabla u + {\nabla u}^T >, J_{uu}
133:    This just gives \nabla u, give the perdiagonal for the transpose */
134: static void stokes_momentum_vel_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
135:                                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
136:                                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
137:                                      PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
138: {
139:   const PetscReal mu  = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]);
140:   PetscInt        cI, d;

142:   for (cI = 0; cI < dim; ++cI) {
143:     for (d = 0; d < dim; ++d) {
144:       g3[((cI*dim+cI)*dim+d)*dim+d] += mu; /*g3[cI, cI, d, d]*/
145:       g3[((cI*dim+d)*dim+d)*dim+cI] += mu; /*g3[cI, d, d, cI]*/
146:     }
147:   }
148: }
149: static void stokes_momentum_vel_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
150:                                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
151:                                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
152:                                      PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
153: {
154:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
155:   PetscInt        cI, d;

157:   for (cI = 0; cI < dim; ++cI) {
158:     for (d = 0; d < dim; ++d) {
159:       g3[((cI*dim+cI)*dim+d)*dim+d] += mu; /*g3[cI, cI, d, d]*/
160:       g3[((cI*dim+d)*dim+d)*dim+cI] += mu; /*g3[cI, d, d, cI]*/
161:     }
162:   }
163: }

165: /* 1/mu < q, I q >, Jp_{pp} */
166: static void stokes_identity_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
167:                                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
168:                                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
169:                                  PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
170: {
171:   const PetscReal mu = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]);
172:   g0[0] = 1.0/mu;
173: }

175: static void stokes_identity_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
176:                                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
177:                                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
178:                                  PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
179: {
180:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
181:   g0[0] = 1.0/mu;
182: }

184: /*
185:   SolKxSolution - Exact Stokes solutions for exponentially varying viscosity

187:  Input Parameters:
188: + pos   - The (x,z) coordinate at which to evaluate the solution
189: . n     - The constant defining the x-dependence of the forcing function
190: . m     - The constant defining the z-dependence of the forcing function
191: - B     - The viscosity coefficient

193:   Output Parameters:
194: + vel   - The (x,z)-velocity at (x,z), or NULL
195: . p     - The pressure at (x,z), or NULL
196: . s     - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
197: . gamma - The strain rate, or NULL
198: - mu    - The viscosity at (x,z), or NULL

200:   Note:
201: $  The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
202: $  conditions everywhere. The forcing term f is given by
203: $
204: $    fx = 0
205: $    fz = sigma*sin(km*z)*cos(kn*x)
206: $
207: $  where
208: $
209: $    km = m*Pi (m may be non-integral)
210: $    kn = n*Pi
211: $
212: $  meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
213: $  The viscosity eta is exp(2*B*x).
214: */
215: static PetscErrorCode SolKxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal B,
216:                                     PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
217: {
218:   PetscReal sigma = 1.0;
219:   PetscReal Z;
220:   PetscReal u1,u2,u3,u4,u5,u6;
221:   PetscReal sum1,sum2,sum3,sum4,sum5,sum6;
222:   PetscReal kn,km,x,z;
223:   PetscReal _PC1,_PC2,_PC3,_PC4;
224:   PetscReal Rp, UU, VV;
225:   PetscReal a,b,r,_aa,_bb,AA,BB,Rm;
226:   PetscReal num1,num2,num3,num4,den1;

228:   PetscReal t1,t2,t3,t4,t5,t6,t7,t8,t9,t10;
229:   PetscReal t11,t12,t13,t14,t15,t16,t17,t18,t19,t20;
230:   PetscReal t21,t22,t23,t24,t25,t26,t27,t28,t29,t30;
231:   PetscReal t31,t32,t33,t34,t35,t36,t37,t38,t39,t40;
232:   PetscReal t41,t42,t43,t44,t45,t46,t47,t49,t51,t53;
233:   PetscReal t56,t58,t61,t62,t63,t64,t65,t66,t67,t68;
234:   PetscReal t69,t70,t71,t72,t73,t74,t75,t76,t77,t78;
235:   PetscReal t79,t80,t81,t82,t83,t84,t85,t86,t87,t88;
236:   PetscReal t89,t90,t91,t92,t93,t94,t95,t96,t97,t99;
237:   PetscReal t100,t101,t103,t104,t105,t106,t107,t108,t109,t110;
238:   PetscReal t111,t112,t113,t114,t115,t116,t117,t118,t119,t120;
239:   PetscReal t121,t124,t125,t126,t127,t129,t130,t132,t133,t135;
240:   PetscReal t136,t138,t140,t141,t142,t143,t152,t160,t162;

243:   /*************************************************************************/
244:   /*************************************************************************/
245:   /* rho = -sin(km*z)*cos(kn*x) */
246:   x = pos[0];
247:   z = pos[1];
248:   Z = PetscExpReal( 2.0 * B * x);
249:   km = m*PETSC_PI; /* solution valid for km not zero -- should get trivial solution if km=0 */
250:   kn = (PetscReal) n*PETSC_PI;
251:   /*************************************************************************/
252:   /*************************************************************************/
253:   a = B*B + km*km;
254:   b = 2.0*km*B;
255:   r = PetscSqrtReal(a*a + b*b);
256:   Rp = PetscSqrtReal( (r+a)/2.0);
257:   Rm  = PetscSqrtReal( (r-a)/2.0);
258:   UU  = Rp - B;
259:   VV = Rp + B;

261:   sum1=0.0;
262:   sum2=0.0;
263:   sum3=0.0;
264:   sum4=0.0;
265:   sum5=0.0;
266:   sum6=0.0;
267:   /*sum7=0.0;*/

269:   /*******************************************/
270:   /*         calculate the constants         */
271:   /*******************************************/

273:   t1 = kn * kn;
274:   t4 = km * km;
275:   t5 = t4 + t1;
276:   t6 = t5 * t5;
277:   t8 = pow(km + kn, 0.2e1);
278:   t9 = B * B;
279:   t16 = pow(km - kn, 0.2e1);
280:   _aa = -0.4e1 * B * t1 * sigma * t5 / (t6 + 0.4e1 * t8 * t9) / (t6 + 0.4e1 * t16 * t9);

282:   t2 = km * km;
283:   t3 = kn * kn;
284:   t5 = pow(t2 + t3, 0.2e1);
285:   t6 = km - kn;
286:   t7 = km + kn;
287:   t9 = B * B;
288:   t13 = t7 * t7;
289:   t19 = t6 * t6;
290:   _bb = sigma * kn * (t5 + 0.4e1 * t6 * t7 * t9) / (t5 + 0.4e1 * t13 * t9) / (t5 + 0.4e1 * t19 * t9);

292:   AA = _aa;
293:   BB = _bb;

295:   /*******************************************/
296:   /*       calculate the velocities etc      */
297:   /*******************************************/
298:   t1 = Rm * Rm;
299:   t2 = B - Rp;
300:   t4 = Rp + B;
301:   t6 = UU * x;
302:   t9 = PetscExpReal(t6 - 0.4e1 * Rp);
303:   t13 = B * B;
304:   t16 = Rp * t1;
305:   t18 = Rp * Rp;
306:   t19 = B * t18;
307:   t20 = t13 * Rp;
308:   t22 = kn * kn;
309:   t24 = B * t1;
310:   t32 = 0.8e1 * t13 * BB * kn * Rp;
311:   t34 = 0.2e1 * Rm;
312:   t35 = PetscCosReal(t34);
313:   t37 = Rp * Rm;
314:   t49 = PetscSinReal(t34);
315:   t63 = PetscExpReal(t6 - 0.2e1 * Rp);
316:   t65 = Rm * t2;
317:   t67 = 0.2e1 * B * kn;
318:   t68 = B * Rm;
319:   t69 = t67 + t68 + t37;
320:   t73 = 0.3e1 * t13;
321:   t75 = 0.2e1 * B * Rp;
322:   t76 = t73 - t75 + t1 - t22 - t18;
323:   t78 = t65 * t76 * BB;
324:   t80 = Rm - kn;
325:   t81 = PetscCosReal(t80);
326:   t83 = -t67 + t68 + t37;
327:   t88 = Rm + kn;
328:   t89 = PetscCosReal(t88);
329:   t92 = t65 * t76 * AA;
330:   t97 = PetscSinReal(t80);
331:   t103 = PetscSinReal(t88);
332:   t108 = PetscExpReal(t6 - 0.3e1 * Rp - B);
333:   t110 = Rm * t4;
334:   t111 = t67 + t68 - t37;
335:   t115 = t73 + t75 + t1 - t22 - t18;
336:   t117 = t110 * t115 * BB;
337:   t120 = -t67 + t68 - t37;
338:   t127 = t110 * t115 * AA;
339:   t140 = PetscExpReal(t6 - Rp - B);
340:   num1 = -0.4e1 * t1 * t2 * t4 * AA * t9 + ((0.2e1 * Rp * (0.3e1 * t13 * B - 0.2e1 * t16 - t19 - 0.2e1 * t20 - B * t22 - t24) * AA - t32) * t35 + (0.2e1 * t37 * (t1 + 0.5e1 * t13 - t22 - t18) * AA - 0.8e1 * B * BB * kn * Rm * Rp) * t49 - 0.2e1 * B * (0.3e1 * t20 - Rp * t22 - t18 * Rp - 0.2e1 * t19 - t16 - 0.2e1 * t24) * AA + t32) * t63 + ((0.2e1 * t65 * t69 * AA + t78) * t81 + (0.2e1 * t65 * t83 * AA - t78) * t89 + (t92 - 0.2e1 * t65 * t69 * BB) * t97 + (t92 + 0.2e1 * t65 * t83 * BB) * t103) * t108 + ((-0.2e1 * t110 * t111 * AA - t117) * t81 + (-0.2e1 * t110 * t120 * AA + t117) * t89 + (-t127 + 0.2e1 * t110 * t111 * BB) * t97 + (-t127 - 0.2e1 * t110 * t120 * BB) * t103) * t140;

342:   t1 = Rp + B;
343:   t2 = Rm * t1;
344:   t3 = B * B;
345:   t4 = 0.3e1 * t3;
346:   t5 = B * Rp;
347:   t7 = Rm * Rm;
348:   t8 = kn * kn;
349:   t9 = Rp * Rp;
350:   t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9;
351:   t12 = t2 * t10 * AA;
352:   t14 = B * Rm;
353:   t20 = UU * x;
354:   t23 = PetscExpReal(t20 - 0.4e1 * Rp);
355:   t25 = Rp * Rm;
356:   t32 = Rm * kn;
357:   t37 = 0.2e1 * Rm;
358:   t38 = PetscCosReal(t37);
359:   t40 = t3 * B;
360:   t44 = B * t9;
361:   t45 = t3 * Rp;
362:   t53 = t3 * BB;
363:   t58 = PetscSinReal(t37);
364:   t69 = PetscExpReal(t20 - 0.2e1 * Rp);
365:   t72 = 0.3e1 * t40 * Rm;
366:   t73 = t9 * Rp;
367:   t74 = t73 * Rm;
368:   t75 = t7 * Rm;
369:   t76 = B * t75;
370:   t77 = t14 * t8;
371:   t78 = Rp * t75;
372:   t80 = 0.8e1 * t45 * kn;
373:   t81 = t25 * t8;
374:   t83 = 0.5e1 * t45 * Rm;
375:   t84 = t44 * Rm;
376:   t85 = t72 - t74 + t76 - t77 + t78 + t80 - t81 + t83 + t84;
377:   t88 = 0.2e1 * t9 * t3;
378:   t90 = 0.3e1 * t40 * Rp;
379:   t91 = t7 * t3;
380:   t93 = 0.2e1 * t5 * t32;
381:   t94 = t5 * t7;
382:   t95 = t5 * t8;
383:   t96 = B * t73;
384:   t97 = t7 * t9;
385:   t100 = 0.2e1 * t3 * Rm * kn;
386:   t101 = -t88 + t90 - t91 - t93 - t94 - t95 - t96 - t97 - t100;
387:   t105 = Rm - kn;
388:   t106 = PetscCosReal(t105);
389:   t108 = t72 - t80 + t83 + t76 + t84 - t81 - t74 + t78 - t77;
390:   t110 = -t97 - t96 - t88 + t100 + t90 - t95 + t93 - t91 - t94;
391:   t114 = Rm + kn;
392:   t115 = PetscCosReal(t114);
393:   t121 = PetscSinReal(t105);
394:   t127 = PetscSinReal(t114);
395:   t132 = PetscExpReal(t20 - 0.3e1 * Rp - B);
396:   t135 = 0.2e1 * B * kn;
397:   t136 = t135 + t14 - t25;
398:   t142 = -t135 + t14 - t25;
399:   t152 = t2 * t10 * BB;
400:   t162 = PetscExpReal(t20 - Rp - B);
401:   num2 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t23 + ((-0.2e1 * t25 * (t7 + 0.5e1 * t3 - t8 - t9) * AA + 0.8e1 * B * BB * t32 * Rp) * t38 + (0.2e1 * Rp * (0.3e1 * t40 - 0.2e1 * Rp * t7 - t44 - 0.2e1 * t45 - B * t8 - B * t7) * AA - 0.8e1 * t53 * kn * Rp) * t58 - 0.2e1 * t14 * (-t8 + t9 + t4 + t7) * AA + 0.8e1 * t53 * t32) * t69 + ((-t85 * AA - 0.2e1 * t101 * BB) * t106 + (-t108 * AA + 0.2e1 * t110 * BB) * t115 + (-0.2e1 * t101 * AA + t85 * BB) * t121 + (-0.2e1 * t110 * AA - t108 * BB) * t127) * t132 + ((t12 - 0.2e1 * t2 * t136 * BB) * t106 + (t12 + 0.2e1 * t2 * t142 * BB) * t115 + (-0.2e1 * t2 * t136 * AA - t152) * t121 + (-0.2e1 * t2 * t142 * AA + t152) * t127) * t162;

403:   t1 = Rm * Rm;
404:   t2 = B - Rp;
405:   t4 = Rp + B;
406:   t6 = VV * x;
407:   t7 = PetscExpReal(-t6);
408:   t11 = kn * kn;
409:   t13 = B * t1;
410:   t14 = Rp * Rp;
411:   t15 = B * t14;
412:   t16 = B * B;
413:   t17 = t16 * Rp;
414:   t21 = Rp * t1;
415:   t30 = 0.8e1 * t16 * BB * kn * Rp;
416:   t32 = 0.2e1 * Rm;
417:   t33 = PetscCosReal(t32);
418:   t35 = Rp * Rm;
419:   t47 = PetscSinReal(t32);
420:   t61 = PetscExpReal(-t6 - 0.2e1 * Rp);
421:   t63 = Rm * t2;
422:   t65 = 0.2e1 * B * kn;
423:   t66 = B * Rm;
424:   t67 = t65 + t66 + t35;
425:   t71 = 0.3e1 * t16;
426:   t73 = 0.2e1 * B * Rp;
427:   t74 = t71 - t73 + t1 - t11 - t14;
428:   t76 = t63 * t74 * BB;
429:   t78 = Rm - kn;
430:   t79 = PetscCosReal(t78);
431:   t81 = -t65 + t66 + t35;
432:   t86 = Rm + kn;
433:   t87 = PetscCosReal(t86);
434:   t90 = t63 * t74 * AA;
435:   t95 = PetscSinReal(t78);
436:   t101 = PetscSinReal(t86);
437:   t106 = PetscExpReal(-t6 - 0.3e1 * Rp - B);
438:   t108 = Rm * t4;
439:   t109 = t65 + t66 - t35;
440:   t113 = t71 + t73 + t1 - t11 - t14;
441:   t115 = t108 * t113 * BB;
442:   t118 = -t65 + t66 - t35;
443:   t125 = t108 * t113 * AA;
444:   t138 = PetscExpReal(-t6 - Rp - B);
445:   num3 = -0.4e1 * t1 * t2 * t4 * AA * t7 + ((-0.2e1 * Rp * (-B * t11 - t13 - t15 + 0.2e1 * t17 + 0.3e1 * t16 * B + 0.2e1 * t21) * AA + t30) * t33 + (-0.2e1 * t35 * (t1 + 0.5e1 * t16 - t11 - t14) * AA + 0.8e1 * B * BB * kn * Rm * Rp) * t47 + 0.2e1 * B * (0.3e1 * t17 - t21 + 0.2e1 * t15 + 0.2e1 * t13 - Rp * t11 - t14 * Rp) * AA - t30) * t61 + ((-0.2e1 * t63 * t67 * AA - t76) * t79 + (-0.2e1 * t63 * t81 * AA + t76) * t87 + (-t90 + 0.2e1 * t63 * t67 * BB) * t95 + (-t90 - 0.2e1 * t63 * t81 * BB) * t101) * t106 + ((0.2e1 * t108 * t109 * AA + t115) * t79 + (0.2e1 * t108 * t118 * AA - t115) * t87 + (t125 - 0.2e1 * t108 * t109 * BB) * t95 + (t125 + 0.2e1 * t108 * t118 * BB) * t101) * t138;

447:   t1 = B - Rp;
448:   t2 = Rm * t1;
449:   t3 = B * B;
450:   t4 = 0.3e1 * t3;
451:   t5 = B * Rp;
452:   t7 = Rm * Rm;
453:   t8 = kn * kn;
454:   t9 = Rp * Rp;
455:   t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9;
456:   t12 = t2 * t10 * AA;
457:   t14 = B * Rm;
458:   t20 = VV * x;
459:   t21 = PetscExpReal(-t20);
460:   t23 = Rp * Rm;
461:   t30 = Rm * kn;
462:   t35 = 0.2e1 * Rm;
463:   t36 = PetscCosReal(t35);
464:   t40 = B * t9;
465:   t41 = t3 * Rp;
466:   t43 = t3 * B;
467:   t51 = t3 * BB;
468:   t56 = PetscSinReal(t35);
469:   t67 = PetscExpReal(-t20 - 0.2e1 * Rp);
470:   t70 = 0.2e1 * B * kn;
471:   t71 = t70 + t14 + t23;
472:   t76 = Rm - kn;
473:   t77 = PetscCosReal(t76);
474:   t79 = -t70 + t14 + t23;
475:   t84 = Rm + kn;
476:   t85 = PetscCosReal(t84);
477:   t91 = t2 * t10 * BB;
478:   t93 = PetscSinReal(t76);
479:   t99 = PetscSinReal(t84);
480:   t104 = PetscExpReal(-t20 - 0.3e1 * Rp - B);
481:   t107 = 0.3e1 * t43 * Rm;
482:   t108 = t9 * Rp;
483:   t109 = t108 * Rm;
484:   t110 = t7 * Rm;
485:   t111 = B * t110;
486:   t112 = t14 * t8;
487:   t113 = Rp * t110;
488:   t115 = 0.8e1 * t41 * kn;
489:   t116 = t23 * t8;
490:   t118 = 0.5e1 * t41 * Rm;
491:   t119 = t40 * Rm;
492:   t120 = t107 + t109 + t111 - t112 - t113 - t115 + t116 - t118 + t119;
493:   t124 = 0.2e1 * t3 * Rm * kn;
494:   t125 = t5 * t8;
495:   t126 = B * t108;
496:   t127 = t7 * t9;
497:   t129 = 0.2e1 * t9 * t3;
498:   t130 = t5 * t7;
499:   t132 = 0.3e1 * t43 * Rp;
500:   t133 = t7 * t3;
501:   t135 = 0.2e1 * t5 * t30;
502:   t136 = t124 - t125 - t126 + t127 + t129 - t130 + t132 + t133 - t135;
503:   t141 = t107 + t115 - t118 + t111 + t119 + t116 + t109 - t113 - t112;
504:   t143 = t132 + t129 - t125 + t133 + t127 - t124 - t130 - t126 + t135;
505:   t160 = PetscExpReal(-t20 - Rp - B);
506:   num4 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t21 + ((0.2e1 * t23 * (t7 + 0.5e1 * t3 - t8 - t9) * AA - 0.8e1 * B * BB * t30 * Rp) * t36 + (-0.2e1 * Rp * (-B * t8 - B * t7 - t40 + 0.2e1 * t41 + 0.3e1 * t43 + 0.2e1 * Rp * t7) * AA + 0.8e1 * t51 * kn * Rp) * t56 - 0.2e1 * t14 * (-t8 + t9 + t4 + t7) * AA + 0.8e1 * t51 * t30) * t67 + ((t12 - 0.2e1 * t2 * t71 * BB) * t77 + (t12 + 0.2e1 * t2 * t79 * BB) * t85 + (-0.2e1 * t2 * t71 * AA - t91) * t93 + (-0.2e1 * t2 * t79 * AA + t91) * t99) * t104 + ((-t120 * AA + 0.2e1 * t136 * BB) * t77 + (-t141 * AA - 0.2e1 * t143 * BB) * t85 + (0.2e1 * t136 * AA + t120 * BB) * t93 + (0.2e1 * t143 * AA - t141 * BB) * t99) * t160;

508:   t1 = Rm * Rm;
509:   t2 = Rp * Rp;
510:   t3 = t1 * t2;
511:   t4 = B * B;
512:   t5 = t1 * t4;
513:   t9 = PetscExpReal(-0.4e1 * Rp);
514:   t15 = PetscCosReal(0.2e1 * Rm);
515:   t22 = PetscExpReal(-0.2e1 * Rp);
516:   den1 = (-0.4e1 * t3 + 0.4e1 * t5) * t9 + ((0.8e1 * t1 + 0.8e1 * t4) * t2 * t15 - 0.8e1 * t5 - 0.8e1 * t2 * t4) * t22 - 0.4e1 * t3 + 0.4e1 * t5;

518:   _PC1=num1/den1; _PC2=num2/den1; _PC3=num3/den1; _PC4=num4/den1;

520:   t1 = Rm * x;
521:   t2 = PetscCosReal(t1);
522:   t4 = PetscSinReal(t1);
523:   t10 = PetscExpReal(-0.2e1 * x * B);
524:   t12 = kn * x;
525:   t13 = PetscCosReal(t12);
526:   t16 = PetscSinReal(t12);
527:   u1 = -km * (_PC1 * t2 + _PC2 * t4 + _PC3 * t2 + _PC4 * t4 + t10 * AA * t13 + t10 * BB * t16);

529:   t2 = Rm * x;
530:   t3 = PetscCosReal(t2);
531:   t6 = PetscSinReal(t2);
532:   t22 = PetscExpReal(-0.2e1 * x * B);
533:   t23 = B * t22;
534:   t24 = kn * x;
535:   t25 = PetscCosReal(t24);
536:   t29 = PetscSinReal(t24);
537:   u2 = UU * _PC1 * t3 + UU * _PC2 * t6 - _PC1 * t6 * Rm + _PC2 * t3 * Rm - VV * _PC3 * t3 - VV * _PC4 * t6 - _PC3 * t6 * Rm + _PC4 * t3 * Rm - 0.2e1 * t23 * AA * t25 - 0.2e1 * t23 * BB * t29 - t22 * AA * t29 * kn + t22 * BB * t25 * kn;

539:   t3 = PetscExpReal(0.2e1 * x * B);
540:   t4 = t3 * B;
541:   t8 = km * km;
542:   t9 = t3 * t8;
543:   t11 = 0.3e1 * t9 * Rm;
544:   t12 = Rm * Rm;
545:   t14 = t3 * t12 * Rm;
546:   t15 = UU * UU;
547:   t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm;
548:   t20 = Rm * x;
549:   t21 = PetscSinReal(t20);
550:   t27 = 0.2e1 * B * t9;
551:   t33 = 0.2e1 * t4 * t12;
552:   t36 = 0.3e1 * t3 * UU * t12 - t27 - 0.2e1 * t4 * t15 + 0.3e1 * t9 * UU + t33 - t3 * t15 * UU;
553:   t37 = PetscCosReal(t20);
554:   t49 = VV * VV;
555:   t53 = -0.4e1 * t4 * VV * Rm - t11 + 0.3e1 * t3 * t49 * Rm - t14;
556:   t64 = t3 * t49 * VV + t33 - 0.3e1 * t9 * VV - 0.2e1 * t4 * t49 - t27 - 0.3e1 * t3 * VV * t12;
557:   t76 = B * t8;
558:   t80 = kn * kn;
559:   t83 = B * B;
560:   t87 = t80 * kn;
561:   t90 = kn * x;
562:   t91 = PetscSinReal(t90);
563:   t106 = PetscCosReal(t90);
564:   u3 = -((t19 * t21 + t36 * t37) * _PC1 + (t36 * t21 - t19 * t37) * _PC2 + (t53 * t21 + t64 * t37) * _PC3 + (t64 * t21 - t53 * t37) * _PC4 + (-0.3e1 * t8 * AA * kn - 0.8e1 * t76 * BB - 0.4e1 * BB * B * t80 + 0.4e1 * AA * t83 * kn - AA * t87) * t91 + (-0.4e1 * AA * t80 * B - 0.4e1 * t83 * BB * kn + 0.3e1 * t8 * BB * kn - sigma + BB * t87 - 0.8e1 * t76 * AA) * t106) / km;

566:   t3 = PetscExpReal(0.2e1 * x * B);
567:   t4 = km * km;
568:   t5 = t3 * t4;
569:   t6 = Rm * x;
570:   t7 = PetscCosReal(t6);
571:   t8 = _PC1 * t7;
572:   t10 = PetscSinReal(t6);
573:   t11 = _PC2 * t10;
574:   t13 = _PC3 * t7;
575:   t15 = _PC4 * t10;
576:   t18 = kn * x;
577:   t19 = PetscCosReal(t18);
578:   t22 = PetscSinReal(t18);
579:   t24 = UU * UU;
580:   t25 = t3 * t24;
581:   t28 = t3 * UU;
582:   t38 = Rm * Rm;
583:   t39 = t7 * t38;
584:   t42 = t10 * t38;
585:   t44 = t5 * t8 + t5 * t11 + t5 * t13 + t5 * t15 + t4 * AA * t19 + t4 * BB * t22 + t25 * t8 + t25 * t11 - 0.2e1 * t28 * _PC1 * t10 * Rm + 0.2e1 * t28 * _PC2 * t7 * Rm - t3 * _PC1 * t39 - t3 * _PC2 * t42;
586:   t45 = VV * VV;
587:   t46 = t3 * t45;
588:   t49 = t3 * VV;
589:   t62 = B * B;
590:   t78 = kn * kn;
591:   t82 = t46 * t13 + t46 * t15 + 0.2e1 * t49 * _PC3 * t10 * Rm - 0.2e1 * t49 * _PC4 * t7 * Rm - t3 * _PC3 * t39 - t3 * _PC4 * t42 + 0.4e1 * t62 * AA * t19 + 0.4e1 * t62 * BB * t22 + 0.4e1 * B * AA * t22 * kn - 0.4e1 * B * BB * t19 * kn - AA * t19 * t78 - BB * t22 * t78;
592:   u4 = t44 + t82;

594:   t3 = PetscExpReal(0.2e1 * x * B);
595:   t4 = t3 * B;
596:   t8 = km * km;
597:   t9 = t3 * t8;
598:   t10 = t9 * Rm;
599:   t11 = Rm * Rm;
600:   t13 = t3 * t11 * Rm;
601:   t14 = UU * UU;
602:   t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm;
603:   t19 = Rm * x;
604:   t20 = PetscSinReal(t19);
605:   t26 = 0.2e1 * B * t9;
606:   t31 = 0.2e1 * t4 * t11;
607:   t34 = 0.3e1 * t3 * UU * t11 - t26 - 0.2e1 * t4 * t14 + t9 * UU + t31 - t3 * t14 * UU;
608:   t35 = PetscCosReal(t19);
609:   t47 = VV * VV;
610:   t51 = -0.4e1 * t4 * VV * Rm - t10 + 0.3e1 * t3 * t47 * Rm - t13;
611:   t61 = t3 * t47 * VV + t31 - t9 * VV - 0.2e1 * t4 * t47 - t26 - 0.3e1 * t3 * VV * t11;
612:   t72 = B * t8;
613:   t76 = kn * kn;
614:   t79 = B * B;
615:   t83 = t76 * kn;
616:   t86 = kn * x;
617:   t87 = PetscSinReal(t86);
618:   t101 = PetscCosReal(t86);
619:   u5 = ((t18 * t20 + t34 * t35) * _PC1 + (t34 * t20 - t18 * t35) * _PC2 + (t51 * t20 + t61 * t35) * _PC3 + (t61 * t20 - t51 * t35) * _PC4 + (-t8 * AA * kn - 0.4e1 * t72 * BB - 0.4e1 * BB * B * t76 + 0.4e1 * AA * t79 * kn - AA * t83) * t87 + (-0.4e1 * AA * t76 * B - 0.4e1 * t79 * BB * kn + t8 * BB * kn - sigma + BB * t83 - 0.4e1 * t72 * AA) * t101) / km;

621:   t3 = PetscExpReal(0.2e1 * x * B);
622:   t4 = UU * UU;
623:   t8 = km * km;
624:   t9 = t3 * t8;
625:   t10 = t9 * Rm;
626:   t11 = Rm * Rm;
627:   t13 = t3 * t11 * Rm;
628:   t14 = t3 * B;
629:   t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm;
630:   t19 = Rm * x;
631:   t20 = PetscSinReal(t19);
632:   t28 = 0.2e1 * B * t9;
633:   t33 = 0.2e1 * t14 * t11;
634:   t34 = -0.2e1 * t4 * t14 + 0.3e1 * t3 * UU * t11 - t28 - t3 * t4 * UU - t9 * UU + t33;
635:   t35 = PetscCosReal(t19);
636:   t47 = VV * VV;
637:   t51 = -0.4e1 * t14 * VV * Rm - t13 + t10 + 0.3e1 * t3 * t47 * Rm;
638:   t61 = -0.3e1 * t3 * VV * t11 + t33 + t3 * t47 * VV + t9 * VV - 0.2e1 * t14 * t47 - t28;
639:   t71 = kn * kn;
640:   t74 = B * B;
641:   t80 = t71 * kn;
642:   t83 = kn * x;
643:   t84 = PetscSinReal(t83);
644:   t96 = PetscCosReal(t83);
645:   u6 = -((t18 * t20 + t34 * t35) * _PC1 + (t34 * t20 - t18 * t35) * _PC2 + (t51 * t20 + t61 * t35) * _PC3 + (t61 * t20 - t51 * t35) * _PC4 + (-0.4e1 * BB * B * t71 + 0.4e1 * AA * t74 * kn + t8 * AA * kn - AA * t80) * t84 + (-0.4e1 * AA * t71 * B - t8 * BB * kn - 0.4e1 * t74 * BB * kn - sigma + BB * t80) * t96) / km;

647:   /*SS = sin(km*z)*(exp(UU*x)*(_PC1*cos(Rm*x)+_PC2*sin(Rm*x)) + exp(-VV*x)*(_PC3*cos(Rm*x)+_PC4*sin(Rm*x)) + exp(-2*x*B)*(AA*cos(kn*x)+BB*sin(kn*x)));*/

649:   /* u1 = Vx, u2 = Vz, u3 = txx, u4 = tzx, u5 = pressure, u6 = tzz */

651:   sum5 += u5*PetscCosReal(km*z);  /* pressure */
652:   sum6 += u6*PetscCosReal(km*z);  /* zz total stress */

654:   u1 *= PetscCosReal(km*z); /* x velocity */
655:   sum1 += u1;
656:   u2 *= PetscSinReal(km*z); /* z velocity */
657:   sum2 += u2;

659:   u3 *= PetscCosReal(km*z); /* xx total stress */
660:   sum3 += u3;
661:   u4 *= PetscSinReal(km*z); /* zx stress */
662:   sum4 += u4;

664:   /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */
665:   /* sum7 += rho; */

667:   /* Output */
668:   if (mu) {
669:     *mu = Z;
670:   }
671:   if (vel) {
672:     vel[0] = sum1;
673:     vel[1] = sum2;
674:   }
675:   if (p) {
676:     (*p) = sum5;
677:   }
678:   if (s) {
679:     s[0] = sum3;
680:     s[1] = sum4;
681:     s[2] = sum6;
682:   }
683:   if (gamma) {
684:     /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
685:     gamma[0] = (sum3+sum5)/(2.0*Z);
686:     gamma[1] = (sum4)/(2.0*Z);
687:     gamma[2] = (sum6+sum5)/(2.0*Z);
688:   }
689:   return(0);
690: }

692: static PetscErrorCode SolKxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
693: {
694:   Parameter     *s = (Parameter *) ctx;

698:   SolKxSolution(x, s->m, s->n, s->B, v, NULL, NULL, NULL, NULL);
699:   return(0);
700: }

702: static PetscErrorCode SolKxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
703: {
704:   Parameter     *s = (Parameter *) ctx;

708:   SolKxSolution(x, s->m, s->n, s->B, NULL, p, NULL, NULL, NULL);
709:   return(0);
710: }

712: /*
713:   SolCxSolution - Exact Stokes solutions for discontinuous viscosity

715:  Input Parameters:
716: + pos   - The (x,z) coordinate at which to evaluate the solution
717: . n     - The constant defining the x-dependence of the forcing function
718: . m     - The constant defining the z-dependence of the forcing function
719: . xc    - The x coordinate at which the viscosity is discontinuous
720: . etaA  - The viscosity coefficient for x < xc
721: - etaB  - The viscosity coefficient for x > xc

723:   Output Parameters:
724: + vel   - The (x,z)-velocity at (x,z), or NULL
725: . p     - The pressure at (x,z), or NULL
726: . s     - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
727: . gamma - The strain rate, or NULL
728: - mu    - The viscosity at (x,z), or NULL

730:   Note:
731: $  The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
732: $  conditions everywhere. The forcing term f is given by
733: $
734: $    fx = 0
735: $    fz = sigma*sin(km*z)*cos(kn*x)
736: $
737: $  where
738: $
739: $    km = m*Pi (m may be non-integral)
740: $    kn = n*Pi
741: $
742: $  meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
743: $  The viscosity eta jumps from etaA to etaB at x = xc.
744: */
745: static PetscErrorCode SolCxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal xc, PetscReal etaA, PetscReal etaB,
746:                                     PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
747: {
748:   PetscReal _PC1A,_PC2A,_PC3A,_PC4A,_PC1B,_PC2B,_PC3B,_PC4B,_PC1,_PC2,_PC3,_PC4;
749:   PetscReal t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28,t29,t30,t31,t32,t33,t34,t35,t36,t37,t38,t39,t40;
750:   PetscReal t41,t42,t43,t44,t45,t46,t47,t48,t49,t50,t51,t52,t53,t54,t55,t56,t57,t58,t59,t60,t61,t62,t63,t64,t65,t66,t67,t68,t69,t70,t71,t72,t73,t74,t75,t76,t77,t78,t79,t80;
751:   PetscReal t81,t82,t83,t84,t85,t86,t87,t88,t89,t90,t91,t92,t93,t94,t95,t96,t97,t98,t99,t100,t101,t102,t103,t104,t105,t106,t107,t108,t109,t110,t111,t112,t113,t115,t116,t117,t118,t119,t120;
752:   PetscReal t121,t122,t123,t124,t125,t126,t127,t128,t129,t130,t131,t132,t133,t134,t135,t136,t137,t138,t139,t140,t141,t142,t143,t144,t145,t146,t147,t148,t149,t150,t151,t152,t153,t154,t155,t156,t157,t158,t159,t160;
753:   PetscReal t161,t162,t163,t164,t165,t166,t167,t168,t169,t170,t171,t172,t173,t174,t175,t176,t177,t178,t179,t180,t181,t182,t183,t184,t186,t187,t188,t189,t190,t191,t192,t193,t194,t195,t196,t197,t198,t199;
754:   PetscReal t201,t202,t203,t204,t206,t207,t208,t209,t210,t211,t212,t213,t215,t216,t217,t218,t219,t220,t221,t222,t223,t224,t225,t226,t227,t228,t229,t230,t231,t232,t233,t234,t235,t236,t237,t238,t239,t240;
755:   PetscReal t241,t242,t243,t244,t245,t246,t247,t248,t249,t250,t251,t252,t253,t254,t255,t256,t257,t258,t259,t260,t261,t262,t263,t264,t265,t267,t268,t269,t270,t272,t273,t274,t275,t276,t277,t278,t279,t280;
756:   PetscReal t281,t282,t283,t284,t285,t286,t288,t289,t290,t291,t292,t295,t296,t297,t298,t299,t300,t301,t303,t304,t305,t307,t308,t310,t311,t312,t313,t314,t315,t316,t317,t318,t319,t320;
757:   PetscReal t321,t322,t323,t324,t325,t326,t327,t328,t329,t330,t331,t332,t334,t335,t336,t337,t338,t339,t340,t341,t342,t344,t345,t346,t347,t348,t349,t350,t351,t352,t353,t354,t355,t356,t358,t359,t360;
758:   PetscReal t361,t362,t363,t364,t365,t366,t367,t368,t369,t370,t371,t372,t373,t374,t375,t376,t377,t378,t379,t380,t381,t382,t383,t384,t385,t386,t387,t389,t390,t391,t393,t394,t395,t396,t397,t398;
759:   PetscReal t401,t402,t403,t404,t405,t406,t407,t408,t409,t410,t411,t412,t413,t414,t415,t416,t417,t418,t419,t421,t422,t423,t424,t425,t426,t427,t428,t429,t430,t431,t432,t433,t434,t436,t437,t438,t439,t440;
760:   PetscReal t441,t442,t443,t444,t445,t446,t447,t448,t450,t451,t453,t454,t455,t456,t457,t458,t459,t461,t462,t463,t464,t465,t466,t468,t469,t470,t471,t474,t475,t478,t480;
761:   PetscReal t482,t483,t484,t485,t488,t489,t490,t492,t493,t495,t497,t498,t499,t501,t502,t503,t504,t505,t507,t508,t509,t510,t511,t512,t513,t515,t518,t520;
762:   PetscReal t522,t525,t527,t528,t529,t530,t532,t533,t534,t535,t536,t538,t539,t541,t542,t544,t545,t546,t547,t548,t549,t550,t551,t552,t553,t554,t555,t556,t557,t560;
763:   PetscReal t561,t562,t563,t564,t567,t568,t571,t573,t575,t576,t578,t579,t583,t590,t591,t594,t595,t596,t597,t598,t600;
764:   PetscReal t601,t602,t604,t606,t607,t608,t611,t613,t615,t616,t617,t619,t621,t623,t624,t625,t626,t627,t629,t630,t632,t633,t634,t638,t639,t640;
765:   PetscReal t641,t642,t643,t644,t645,t647,t648,t649,t650,t651,t652,t653,t654,t655,t656,t657,t658,t659,t660,t662,t663,t665,t666,t667,t668,t670,t671,t672,t673,t674,t675,t676,t679,t680;
766:   PetscReal t682,t683,t684,t685,t686,t688,t689,t690,t691,t693,t694,t695,t696,t697,t698,t699,t700,t701,t702,t704,t705,t708,t709,t711,t712,t713,t714,t717,t718,t719;
767:   PetscReal t721,t722,t723,t726,t727,t728,t730,t733,t734,t735,t736,t737,t738,t739,t740,t741,t744,t745,t746,t749,t750,t752,t753,t754,t755,t757,t758,t759,t760;
768:   PetscReal t761,t762,t763,t764,t766,t767,t768,t770,t771,t772,t773,t774,t775,t776,t777,t778,t780,t781,t782,t785,t786,t789,t790,t791,t792,t793,t794,t795,t796,t797,t798,t800;
769:   PetscReal t801,t806,t807,t808,t809,t811,t812,t817,t818,t819,t821,t822,t824,t827,t828,t830,t834,t835,t837,t840;
770:   PetscReal t842,t843,t844,t845,t846,t849,t850,t853,t854,t855,t857,t858,t859,t860,t863,t864,t867,t868,t869,t873,t874,t877,t878,t879,t880;
771:   PetscReal t884,t888,t891,t894,t900,t901,t903,t904,t907,t908,t909,t911,t914,t915,t916,t919,t920;
772:   PetscReal t923,t924,t925,t926,t927,t929,t932,t935,t937,t939,t942,t943,t944,t945,t947,t948,t949,t950,t952,t953,t954,t955,t956,t957;
773:   PetscReal t961,t964,t965,t966,t967,t968,t969,t971,t972,t974,t977,t978,t981,t983,t987,t988,t992,t993,t994,t997,t998;
774:   PetscReal t1001,t1003,t1005,t1006,t1009,t1010,t1012,t1013,t1015,t1016,t1017,t1018,t1020,t1021,t1029,t1031,t1032,t1033,t1040;
775:   PetscReal t1041,t1042,t1044,t1047,t1050,t1054,t1055,t1057,t1058,t1063,t1068,t1069,t1070,t1079,t1080;
776:   PetscReal t1088,t1089,t1091,t1092,t1094,t1096,t1101,t1102,t1103,t1104,t1105,t1108,t1112,t1113,t1118,t1119,t1120;
777:   PetscReal t1121,t1122,t1123,t1124,t1125,t1126,t1127,t1128,t1129,t1130,t1132,t1133,t1134,t1135,t1138,t1139,t1140,t1141,t1142,t1145,t1146,t1148,t1149,t1150,t1153,t1154,t1156,t1157,t1158,t1159;
778:   PetscReal t1161,t1162,t1165,t1166,t1170,t1171,t1172,t1173,t1175,t1176,t1178,t1180,t1181,t1182,t1185,t1189,t1192,t1193,t1195,t1196,t1199;
779:   PetscReal t1201,t1203,t1209,t1210,t1211,t1213,t1214,t1218,t1221,t1224,t1225,t1226,t1228,t1233,t1234,t1235,t1236,t1237,t1240;
780:   PetscReal t1241,t1242,t1243,t1244,t1245,t1248,t1251,t1252,t1257,t1258,t1259,t1260,t1263,t1268,t1269,t1272,t1280;
781:   PetscReal t1282,t1283,t1284,t1285,t1287,t1288,t1289,t1292,t1293,t1296,t1297,t1300,t1304,t1307,t1310,t1311,t1312,t1316,t1317,t1320;
782:   PetscReal t1321,t1323,t1328,t1330,t1331,t1332,t1333,t1336,t1338,t1343,t1344,t1346,t1349,t1350,t1354;
783:   PetscReal t1366,t1369,t1370,t1371,t1376,t1378,t1380,t1383,t1386,t1387,t1388,t1391,t1393,t1399;
784:   PetscReal t1411,t1412,t1420,t1427;
785:   PetscReal t1450,t1456,t1468,t1472,t1474,t1478;
786:   PetscReal t1504,t1511;
787:   PetscReal t1545;
788:   PetscReal t1564,t1583;

790:   PetscReal      sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, sum6 = 0.0;
791:   PetscReal      ZA = etaA, ZB = etaB;
792:   PetscInt       nz  = m,    nx = n;
793:   PetscReal      u1, u2, u3, u4, u5, u6, Z, x = pos[0], z = pos[1];

796:   /* Note that there is no Fourier sum here. */
797:   /****************************************************************************************/
798:   _PC1A = 0;
799:   /****************************************************************************************/
800:   t1 = nx * 0.3141592654e1;
801:   t2 = PetscSinReal(t1);
802:   t3 = nx * t2;
803:   t4 = nz * nz;
804:   t5 = t4 * t4;
805:   t6 = 0.3141592654e1 * 0.3141592654e1;
806:   t8 = t3 * t5 * t6;
807:   t9 = ZA * xc;
808:   t12 = PetscExpReal(xc * nz * 0.3141592654e1);
809:   t13 = t12 * t12;
810:   t15 = nz * 0.3141592654e1;
811:   t16 = PetscExpReal(t15);
812:   t17 = t16 * t16;
813:   t18 = t17 * t16;
814:   t19 = ZB * t13 * t18;
815:   t20 = t9 * t19;
816:   t23 = ZA * ZA;
817:   t24 = nx * nx;
818:   t25 = t24 * nx;
819:   t26 = t23 * t25;
820:   t28 = t13 * t13;
821:   t29 = t28 * t13;
822:   t33 = nx * ZB;
823:   t34 = t1 * xc;
824:   t35 = PetscSinReal(t34);
825:   t36 = t4 * nz;
826:   t37 = t35 * t36;
827:   t38 = t33 * t37;
828:   t39 = 0.3141592654e1 * ZA;
829:   t40 = t13 * t12;
830:   t41 = t17 * t40;
831:   t45 = ZB * ZB;
832:   t46 = t45 * t24;
833:   t47 = t46 * t4;
834:   t48 = 0.3141592654e1 * xc;
835:   t49 = t13 * t17;
836:   t53 = xc * xc;
837:   t54 = t36 * t53;
838:   t56 = t54 * t6 * t45;
839:   t57 = PetscCosReal(t34);
840:   t58 = t57 * t24;
841:   t59 = t28 * t12;
842:   t60 = t17 * t59;
843:   t61 = t58 * t60;
844:   t64 = t25 * t2;
845:   t65 = t64 * t15;
846:   t72 = nx * t23;
847:   t74 = t72 * t2 * t5;
848:   t75 = t6 * t53;
849:   t76 = t16 * t29;
850:   t80 = t23 * nz;
851:   t81 = t80 * 0.3141592654e1;
852:   t82 = t18 * t28;
853:   t86 = nx * t5;
854:   t87 = t23 * t6;
855:   t89 = xc * t2;
856:   t90 = t13 * t18;
857:   t91 = t89 * t90;
858:   t94 = t28 * t28;
859:   t96 = t24 * nz;
860:   t98 = t4 * t45;
861:   t99 = t98 * 0.3141592654e1;
862:   t100 = t58 * t41;
863:   t104 = 0.3141592654e1 * t25;
864:   t105 = ZA * nz * t104;
865:   t106 = t2 * ZB;
866:   t110 = t17 * t17;
867:   t111 = ZA * t110;
868:   t116 = nz * t28;
869:   t122 = t64 * t4 * t6;
870:   t126 = t23 * t29 * t4;
871:   t128 = t24 * xc;
872:   t132 = t36 * t23;
873:   t133 = t6 * t57;
874:   t135 = t128 * t41;
875:   t138 = t6 * xc;
876:   t142 = t72 * t2;
877:   t147 = 0.4e1 * t8 * t20 - 0.2e1 * t26 * t2 * t16 * t29 - 0.8e1 * t38 * t39 * t41 + 0.4e1 * t47 * t48 * t49 - 0.8e1 * t56 * t61 - 0.4e1 * t65 * t20 + 0.2e1 * t26 * t2 * t18 * t28 - 0.4e1 * t74 * t75 * t76 - 0.2e1 * t81 * t64 * t82 - 0.4e1 * t86 * t87 * t91 - t23 * t94 * t96 + 0.8e1 * t99 * t100 - 0.2e1 * t105 * t106 * t82 - 0.4e1 * t38 * t48 * t111 * t12 + 0.2e1 * t116 * ZB * t111 * t24 + 0.4e1 * t122 * t20 + 0.4e1 * t126 * 0.3141592654e1 * t17 * t128 + 0.8e1 * t132 * t133 * t135 + 0.4e1 * t74 * t138 * t76 - 0.2e1 * t142 * t4 * t18 * t28;
878:   t149 = ZA * t25 * t2;
879:   t150 = ZB * t28;
880:   t154 = t35 * t5;
881:   t155 = t72 * t154;
882:   t156 = t75 * t41;
883:   t159 = nx * ZA;
884:   t160 = t2 * t36;
885:   t161 = t159 * t160;
886:   t162 = 0.3141592654e1 * ZB;
887:   t163 = t28 * t16;
888:   t167 = t23 * t57;
889:   t168 = t167 * t24;
890:   t169 = nz * t110;
891:   t170 = t169 * t40;
892:   t173 = ZA * ZB;
893:   t174 = t173 * t90;
894:   t177 = t36 * 0.3141592654e1;
895:   t181 = t80 * t104;
896:   t184 = nz * t17;
897:   t188 = t17 * t29;
898:   t190 = t4 * 0.3141592654e1;
899:   t191 = t190 * t24;
900:   t206 = t138 * t60;
901:   t209 = t23 * t4;
902:   t211 = t209 * t6 * t25;
903:   t212 = t89 * t76;
904:   t216 = ZB * t16 * t29;
905:   t217 = t9 * t216;
906:   t220 = ZB * t110;
907:   t221 = ZA * t24;
908:   t222 = t221 * nz;
909:   t225 = t132 * t75;
910:   t232 = t45 * t28;
911:   t233 = t110 * t24;
912:   t234 = t233 * nz;
913:   t236 = t209 * 0.3141592654e1;
914:   t237 = t17 * xc;
915:   t239 = t237 * t13 * t24;
916:   t242 = -0.2e1 * t149 * t150 * t16 - 0.8e1 * t155 * t156 - 0.2e1 * t161 * t162 * t163 + 0.2e1 * t168 * t170 + 0.2e1 * t65 * t174 - 0.2e1 * t142 * t177 * t76 + 0.4e1 * t181 * t91 - 0.4e1 * t168 * t184 * t59 - 0.4e1 * t188 * t23 * t191 + 0.4e1 * t38 * t48 * ZA * t17 * t40 + 0.4e1 * t49 * t23 * t191 + 0.2e1 * t26 * t2 * t13 * t18 - 0.8e1 * t155 * t206 + 0.4e1 * t211 * t212 - 0.4e1 * t8 * t217 + 0.2e1 * t220 * t222 - 0.8e1 * t225 * t100 + 0.2e1 * t142 * t4 * t16 * t29 + t232 * t234 - 0.4e1 * t236 * t239;
917:   t244 = nx * t45;
918:   t245 = t244 * t37;
919:   t246 = t110 * t40;
920:   t251 = t237 * t59;
921:   t256 = t64 * t90;
922:   t260 = t36 * t45 * t133;
923:   t263 = t45 * t57;
924:   t264 = t263 * t24;
925:   t265 = t169 * t12;
926:   t269 = t6 * t36;
927:   t270 = t17 * t24;
928:   t274 = t110 * t13;
929:   t276 = t190 * t128;
930:   t279 = nx * t36;
931:   t281 = t28 * t40;
932:   t282 = t281 * t35;
933:   t286 = t138 * t41;
934:   t289 = t75 * t60;
935:   t296 = t190 * t173;
936:   t305 = t86 * t45 * t35;
937:   t312 = t33 * t154;
938:   t313 = t6 * ZA;
939:   t324 = t232 * t270;
940:   t327 = -0.2e1 * t245 * t48 * t246 + 0.4e1 * t159 * t37 * t162 * t251 + 0.4e1 * t209 * t75 * t256 + 0.8e1 * t260 * t135 + 0.2e1 * t264 * t265 + 0.32e2 * t9 * t150 * t269 * t270 + 0.4e1 * t274 * t23 * t276 + 0.2e1 * t279 * t45 * t282 * t48 + 0.8e1 * t155 * t286 + 0.8e1 * t155 * t289 - 0.8e1 * t150 * ZA * t96 * t17 + 0.8e1 * t296 * t61 - 0.2e1 * t105 * t106 * t163 - 0.2e1 * t81 * t256 - 0.8e1 * t305 * t156 - 0.4e1 * t33 * t282 * t177 * t9 - 0.16e2 * t312 * t313 * t237 * t40 - 0.4e1 * t168 * t184 * t40 + 0.2e1 * t168 * t265 + 0.16e2 * t269 * t53 * t324;
941:   t328 = t3 * t4;
942:   t331 = t72 * t37;
943:   t332 = t48 * t60;
944:   t335 = nz * t94;
945:   t345 = t72 * t35;
946:   t349 = t173 * t57;
947:   t355 = t53 * t17;
948:   t364 = t54 * t6 * ZB;
949:   t365 = t28 * t17;
950:   t369 = xc * ZB;
951:   t370 = t269 * t369;
952:   t371 = ZA * t57;
953:   t373 = t371 * t270 * t40;
954:   t385 = nx * t35;
955:   t396 = t4 * xc;
956:   t397 = t396 * t162;
957:   t415 = t37 * t48;
958:   t418 = -0.32e2 * t364 * t365 * t221 - 0.16e2 * t370 * t373 - 0.4e1 * t331 * t48 * t41 + 0.4e1 * t86 * t23 * t53 * t6 * t2 * t90 + 0.2e1 * t385 * t177 * t23 * xc * t246 + 0.16e2 * t132 * t53 * t6 * t28 * t270 - 0.4e1 * t397 * t371 * t233 * t12 - 0.12e2 * t173 * t58 * t190 * t251 + 0.2e1 * t385 * t36 * 0.3141592654e1 * t23 * xc * t59 - 0.8e1 * t99 * t61 - 0.2e1 * t244 * t59 * t415;
959:   t427 = t371 * t270 * t59;
960:   t439 = t209 * t48;
961:   t440 = t110 * t12;
962:   t441 = t58 * t440;
963:   t447 = t36 * xc;
964:   t455 = t48 * t440;
965:   t471 = ZB * t17;
966:   t492 = 0.12e2 * t397 * t373 - 0.4e1 * t122 * t217 + 0.16e2 * t364 * t427 + 0.16e2 * t312 * t313 * t355 * t40 - 0.8e1 * t279 * t39 * t35 * ZB * t60 + 0.2e1 * t439 * t441 - 0.2e1 * t81 * t64 * t163 + 0.8e1 * t447 * t87 * t61 + 0.2e1 * t23 * t59 * t57 * t276 + 0.2e1 * t245 * t455 - 0.4e1 * t349 * t96 * t440 - 0.16e2 * t370 * t427 + 0.4e1 * t181 * t212 - 0.16e2 * t365 * t23 * t269 * t128 + 0.16e2 * t86 * t138 * ZA * t35 * t471 * t59 + 0.8e1 * t305 * t289 - 0.4e1 * t439 * t100 + 0.2e1 * ZB * t25 * t2 * ZA * t18 * t28 + 0.2e1 * t142 * t4 * t28 * t16 - 0.8e1 * t56 * t100;
967:   t499 = ZA * t53 * t19;
968:   t505 = t396 * 0.3141592654e1;
969:   t518 = t173 * t53 * t16 * t29;
970:   t533 = t23 * t28;
971:   t535 = t188 * t45;
972:   t538 = t24 * t4;
973:   t545 = t3 * t177;
974:   t546 = t173 * t76;
975:   t555 = t45 * t110;
976:   t557 = t72 * t160;
977:   t561 = -0.8e1 * t225 * t61 - 0.2e1 * t161 * t162 * t82 + t533 * t234 + 0.4e1 * t535 * t191 + 0.4e1 * t167 * t538 * t332 + 0.4e1 * t349 * t96 * t60 + 0.2e1 * t545 * t546 - 0.2e1 * t264 * t170 + 0.4e1 * t397 * t281 * ZA * t58 - t555 * t96 - 0.4e1 * t557 * t48 * t76;
978:   t567 = t396 * 0.3141592654e1 * t45;
979:   t568 = t58 * t246;
980:   t597 = t58 * nz;
981:   t615 = t13 * t45;
982:   t616 = t615 * t233;
983:   t619 = t94 * t45;
984:   t621 = t45 * t59;
985:   t625 = 0.2e1 * t149 * t216 + 0.2e1 * t567 * t568 - 0.16e2 * t269 * xc * t324 - 0.2e1 * t236 * xc * t281 * t58 - 0.2e1 * t142 * t177 * t90 - 0.8e1 * t567 * t100 + 0.2e1 * t65 * t546 - 0.8e1 * t305 * t206 + 0.2e1 * nz * t45 * t281 * t57 * t24 - t23 * t110 * t96 - 0.8e1 * t296 * t100 + 0.2e1 * t23 * t281 * t597 + 0.4e1 * t545 * t20 + 0.2e1 * t159 * t2 * t4 * ZB * t163 - 0.4e1 * t557 * t48 * t90 + 0.4e1 * t122 * t518 + 0.8e1 * t263 * t538 * t332 - 0.4e1 * t505 * t616 - t619 * t96 - 0.2e1 * t621 * t57 * t276;
986:   t626 = t49 * t45;
987:   t660 = t29 * t45;
988:   t685 = 0.2e1 * t545 * t174 - 0.4e1 * t126 * 0.3141592654e1 * t24 * xc - 0.4e1 * t47 * t48 * t188 + 0.4e1 * t505 * t660 * t24 - 0.2e1 * t142 * t177 * t163 - 0.2e1 * t142 * t4 * t13 * t18 + 0.8e1 * t260 * t128 * t60 - 0.2e1 * t328 * t546 - 0.2e1 * t26 * t2 * t28 * t16 + 0.4e1 * t545 * t217 - 0.4e1 * t209 * t138 * t256;
989:   t690 = t6 * 0.3141592654e1;
990:   t691 = ZA * t690;
991:   t693 = t24 * t24;
992:   t694 = t693 * xc;
993:   t695 = t188 * t694;
994:   t698 = t23 * ZA;
995:   t699 = t698 * t690;
996:   t700 = t699 * t5;
997:   t704 = t5 * t4;
998:   t705 = t691 * t704;
999:   t709 = t691 * t5;
1000:   t713 = t5 * nz;
1001:   t714 = t713 * ZB;
1002:   t718 = t698 * t6;
1003:   t719 = t713 * t28;
1004:   t722 = t699 * t704;
1005:   t726 = t713 * t94;
1006:   t733 = t713 * t45;
1007:   t736 = t87 * t36;
1008:   t740 = -0.4e1 * t691 * t98 * t695 + 0.8e1 * t700 * t270 * t13 + 0.4e1 * t705 * t660 * xc + 0.8e1 * t709 * t660 * t128 + 0.2e1 * t87 * t714 * t110 + t718 * t719 * t110 - 0.4e1 * t722 * t237 * t13 - t313 * t726 * t45 - 0.4e1 * t699 * t704 * xc * t29 + t313 * t733 * t28 + 0.4e1 * t736 * t150 * t233;
1009:   t746 = t313 * t36;
1010:   t752 = t6 * t6;
1011:   t753 = t23 * t752;
1012:   t759 = t698 * t752;
1013:   t760 = t759 * t36;
1014:   t761 = t17 * t693;
1015:   t762 = xc * t28;
1016:   t763 = t761 * t762;
1017:   t766 = t87 * t713;
1018:   t773 = t699 * t4;
1019:   t774 = t110 * t693;
1020:   t775 = xc * t13;
1021:   t785 = t704 * t17;
1022:   t789 = -0.16e2 * t736 * t150 * t270 + t718 * t116 * t693 - 0.2e1 * t746 * t555 * t24 + 0.4e1 * t705 * t535 + 0.64e2 * t753 * t713 * t17 * t150 * t128 - 0.16e2 * t760 * t763 + 0.2e1 * t766 * t150 * t110 + 0.4e1 * t722 * t274 * xc + 0.4e1 * t773 * t774 * t775 - 0.8e1 * t766 * t150 * t17 + 0.8e1 * t700 * t233 * t775 + 0.4e1 * t699 * t785 * t13;
1023:   t791 = t691 * t4;
1024:   t792 = t45 * t693;
1025:   t793 = t49 * t792;
1026:   t796 = t759 * t713;
1027:   t797 = t53 * t28;
1028:   t798 = t270 * t797;
1029:   t801 = t87 * nz;
1030:   t818 = t5 * t36;
1031:   t819 = t753 * t818;
1032:   t827 = t753 * t36 * ZB;
1033:   t830 = xc * t45;
1034:   t834 = -0.4e1 * t791 * t793 + 0.32e2 * t796 * t798 + 0.2e1 * t801 * ZB * t693 * t110 + 0.2e1 * t718 * t36 * t28 * t24 - 0.8e1 * t700 * t128 * t29 - 0.8e1 * t700 * t239 - 0.8e1 * t801 * t150 * t761 + 0.32e2 * t819 * t365 * t369 - 0.64e2 * t753 * t714 * t798 + 0.32e2 * t827 * t763 + 0.4e1 * t705 * t830 * t49;
1035:   t842 = xc * t29;
1036:   t843 = t270 * t842;
1037:   t849 = t759 * t818;
1038:   t853 = t691 * t396;
1039:   t857 = t691 * t5 * t45;
1040:   t869 = t313 * nz;
1041:   t874 = -0.2e1 * t718 * t36 * t94 * t24 - 0.4e1 * t773 * t761 * t29 + 0.8e1 * t700 * t843 + 0.2e1 * t87 * t726 * ZB + 0.16e2 * t849 * t797 * t17 + 0.4e1 * t853 * t793 + 0.8e1 * t857 * t239 + 0.2e1 * t801 * t150 * t693 - 0.8e1 * t700 * t270 * t29 - 0.8e1 * t709 * t49 * t46 - t869 * t619 * t693 + t869 * t232 * t693;
1042:   t877 = ZA * t752;
1043:   t878 = t877 * t818;
1044:   t911 = 0.16e2 * t878 * t53 * t45 * t365 - 0.4e1 * t699 * t785 * t29 - 0.4e1 * t705 * t188 * t830 + 0.2e1 * t801 * t94 * t693 * ZB - 0.8e1 * t857 * t843 - t718 * t726 + 0.4e1 * t773 * t761 * t13 - 0.4e1 * t705 * t775 * t555 + 0.2e1 * t746 * t232 * t233 - 0.16e2 * t878 * t830 * t365 - 0.2e1 * t746 * t619 * t24;
1045:   t916 = t110 * t28;
1046:   t945 = t28 * t693 * t45 * t17;
1047:   t948 = 0.32e2 * t877 * t733 * t798 + 0.2e1 * t718 * t36 * t916 * t24 - 0.4e1 * t705 * t626 + t718 * nz * t916 * t693 - t869 * t792 * t110 - 0.4e1 * t773 * t761 * t775 + t718 * t719 + 0.2e1 * t746 * t232 * t24 - 0.16e2 * t849 * t365 * xc - t718 * t713 * t110 - 0.4e1 * t773 * t694 * t29 + 0.16e2 * t877 * t54 * t945;
1048:   t974 = t761 * t797;
1049:   t987 = 0.4e1 * t773 * t695 + 0.4e1 * t736 * t150 * t24 + 0.4e1 * t722 * t842 * t17 - 0.16e2 * t877 * t447 * t945 + 0.2e1 * t87 * t714 * t28 + t313 * t713 * t916 * t45 - 0.4e1 * t853 * t615 * t774 - 0.32e2 * t877 * t713 * xc * t324 + 0.16e2 * t760 * t974 + 0.4e1 * t736 * t94 * t24 * ZB + t869 * t792 * t916 - 0.8e1 * t691 * t5 * xc * t616;
1050:   t1021 = -t718 * t169 * t693 - 0.32e2 * t827 * t974 + 0.2e1 * t801 * t150 * t774 + 0.4e1 * t791 * t188 * t792 + 0.4e1 * t736 * t220 * t24 + 0.4e1 * t791 * t842 * t792 + 0.8e1 * t709 * t660 * t270 - t718 * t335 * t693 - 0.2e1 * t718 * t36 * t110 * t24 - 0.32e2 * t819 * t797 * t471 - t313 * t733 * t110 - 0.32e2 * t796 * t270 * t762;

1052:   _PC2A = (t147 - 0.4e1 * t65 * t217 + t418 + 0.2e1 * t150 * t222 + t327 - 0.2e1 * t149 * t19 + 0.2e1 * t335 * ZB * t24 * ZA - 0.16e2 * t312 * t313 * t355 * t59 - 0.4e1 * t281 * ZB * ZA * t597 - 0.2e1 * t505 * t45 * t281 * t58 - 0.4e1 * t211 * t2 * t53 * t76 + 0.8e1 * t305 * t286 - 0.4e1 * t122 * t499 - 0.4e1 * t331 * t332 + 0.8e1 * t345 * t177 * t60 - 0.2e1 * t142 * t177 * t82 + 0.2e1 * t72 * t281 * t415 + 0.4e1 * t349 * t96 * t41 - 0.2e1 * t81 * t64 * t76 + 0.2e1 * t58 * t80 * t59 + 0.8e1 * t345 * t177 * t41 - 0.4e1 * t8 * t499 + t242 + 0.4e1 * t8 * t518 + t625 + t685 + 0.2e1 * t328 * t174 + 0.2e1 * t331 * t455 - 0.2e1 * t33 * t2 * t4 * ZA * t82 - 0.4e1 * t626 * t191 + 0.16e2 * t364 * t373 - 0.2e1 * t621 * t597 - 0.2e1 * t439 * t568 + t492 + t533 * t96 + t232 * t96 + 0.2e1 * t567 * t441 + t561) / (t740 + t789 + t834 + t874 + t911 + t948 + t987 + t1021);
1053:   /****************************************************************************************/
1054:   t1 = nz * nz;
1055:   t2 = t1 * nz;
1056:   t3 = t2 * 0.3141592654e1;
1057:   t4 = t3 * xc;
1058:   t5 = ZB * ZB;
1059:   t7 = PetscExpReal(nz * 0.3141592654e1);
1060:   t8 = t7 * t7;
1061:   t9 = t5 * t8;
1062:   t12 = PetscExpReal(xc * nz * 0.3141592654e1);
1063:   t13 = t12 * t12;
1064:   t14 = t13 * t13;
1065:   t15 = t14 * t13;
1066:   t19 = nx * nx;
1067:   t21 = nx * 0.3141592654e1;
1068:   t22 = PetscSinReal(t21);
1069:   t23 = t19 * nx * t22;
1070:   t24 = t23 * 0.3141592654e1;
1071:   t25 = ZA * ZB;
1072:   t26 = t7 * t15;
1073:   t27 = t25 * t26;
1074:   t30 = t21 * xc;
1075:   t31 = PetscSinReal(t30);
1076:   t32 = t31 * nx;
1077:   t33 = t32 * nz;
1078:   t34 = ZA * ZA;
1079:   t35 = t8 * t8;
1080:   t36 = t34 * t35;
1081:   t40 = t2 * t34;
1082:   t41 = 0.3141592654e1 * t8;
1083:   t42 = t41 * t15;
1084:   t45 = t1 * t5;
1085:   t46 = t14 * t14;
1086:   t49 = t19 * t5;
1087:   t51 = t19 * t46;
1088:   t53 = t19 * t34;
1089:   t55 = t8 * t7;
1090:   t56 = t13 * t55;
1091:   t57 = t25 * t56;
1092:   t60 = t2 * nx;
1093:   t61 = 0.3141592654e1 * 0.3141592654e1;
1094:   t63 = t60 * t31 * t61;
1095:   t64 = xc * xc;
1096:   t65 = ZA * t64;
1097:   t66 = ZB * t8;
1098:   t67 = t14 * t12;
1099:   t68 = t66 * t67;
1100:   t69 = t65 * t68;
1101:   t72 = -0.4e1 * t4 * t9 * t15 + 0.4e1 * t24 * t27 + 0.4e1 * t33 * t36 * t12 - 0.4e1 * t40 * t42 - t45 * t46 + t45 * t14 - t49 * t14 + t51 * t5 - t53 * t14 + 0.4e1 * t24 * t57 + 0.32e2 * t63 * t69;
1102:   t73 = t1 * nx;
1103:   t75 = t73 * t31 * 0.3141592654e1;
1104:   t76 = t8 * t67;
1105:   t77 = t25 * t76;
1106:   t80 = t1 * t1;
1107:   t81 = t80 * t34;
1108:   t83 = t61 * t14;
1109:   t87 = t1 * t19;
1110:   t88 = PetscCosReal(t30);
1111:   t90 = t87 * t88 * t61;
1112:   t91 = t5 * t64;
1113:   t92 = t13 * t12;
1114:   t93 = t8 * t92;
1115:   t94 = t91 * t93;
1116:   t100 = ZB * t64 * ZA * t8 * t92;
1117:   t103 = nz * t19;
1118:   t105 = t103 * t88 * 0.3141592654e1;
1119:   t106 = ZA * xc;
1120:   t107 = ZB * t35;
1121:   t109 = t106 * t107 * t12;
1122:   t112 = t34 * xc;
1123:   t113 = t112 * t93;
1124:   t116 = t35 * t14;
1125:   t118 = t1 * ZA;
1126:   t119 = ZB * t14;
1127:   t122 = t1 * t46;
1128:   t125 = t19 * ZB;
1129:   t126 = t35 * ZA;
1130:   t127 = t125 * t126;
1131:   t129 = t1 * ZB;
1132:   t132 = -0.16e2 * t75 * t77 + 0.16e2 * t81 * t64 * t83 * t8 + 0.16e2 * t90 * t94 - 0.32e2 * t90 * t100 + 0.8e1 * t105 * t109 - 0.8e1 * t75 * t113 + t45 * t116 + 0.2e1 * t118 * t119 + 0.2e1 * t122 * t25 - 0.2e1 * t127 + 0.2e1 * t129 * t126;
1133:   t134 = t1 * t34;
1134:   t136 = t34 * t64;
1135:   t137 = t136 * t76;
1136:   t141 = t91 * t76;
1137:   t145 = t103 * t34;
1138:   t146 = 0.3141592654e1 * xc;
1139:   t147 = t8 * t13;
1140:   t153 = t14 * ZA;
1141:   t156 = xc * t5;
1142:   t157 = t156 * t93;
1143:   t160 = t103 * t5;
1144:   t162 = t146 * t8 * t15;
1145:   t166 = t34 * t7 * t15;
1146:   t169 = t134 * t116 - 0.16e2 * t63 * t137 - t49 * t116 - 0.16e2 * t63 * t141 - t53 * t116 + 0.4e1 * t145 * t146 * t147 - 0.2e1 * t51 * t25 - 0.2e1 * t125 * t153 - 0.16e2 * t75 * t157 + 0.4e1 * t160 * t162 - 0.4e1 * t24 * t166;
1147:   t170 = t106 * t68;
1148:   t177 = t35 * t92;
1149:   t178 = t112 * t177;
1150:   t181 = t156 * t76;
1151:   t186 = t35 * t12;
1152:   t187 = t112 * t186;
1153:   t193 = t5 * 0.3141592654e1;
1154:   t206 = t34 * t14;
1155:   t207 = t206 * t7;
1156:   t210 = -0.32e2 * t63 * t170 + 0.32e2 * t90 * t170 + 0.8e1 * t75 * t109 + 0.4e1 * t105 * t178 - 0.16e2 * t75 * t181 - 0.16e2 * t90 * t113 - 0.4e1 * t75 * t187 + 0.16e2 * t90 * t141 - 0.4e1 * t103 * t15 * t193 * xc + 0.16e2 * t73 * t22 * t34 * t146 * t26 + 0.4e1 * t32 * nz * t34 * t67 + 0.4e1 * t24 * t207;
1157:   t217 = t106 * t66 * t92;
1158:   t226 = t88 * t19 * nz;
1159:   t227 = 0.3141592654e1 * t34;
1160:   t229 = t227 * xc * t67;
1161:   t232 = t73 * t31;
1162:   t234 = t146 * t5 * t67;
1163:   t238 = t61 * ZB;
1164:   t239 = t14 * t8;
1165:   t240 = t238 * t239;
1166:   t243 = t136 * t93;
1167:   t246 = -0.8e1 * t33 * t25 * t186 + 0.32e2 * t90 * t217 - t45 * t35 + t53 * t35 - t134 * t35 - t134 * t46 + t134 * t14 - 0.4e1 * t226 * t229 + 0.4e1 * t232 * t234 + 0.32e2 * t87 * t65 * t240 + 0.16e2 * t63 * t243;
1168:   t247 = t14 * t92;
1169:   t249 = t227 * t247 * xc;
1170:   t254 = t73 * t22;
1171:   t259 = t60 * t22 * t61;
1172:   t260 = t112 * t26;
1173:   t264 = t146 * t247 * t5;
1174:   t268 = xc * t14;
1175:   t274 = t5 * t14;
1176:   t275 = t274 * t8;
1177:   t280 = nz * nx;
1178:   t281 = t280 * t22;
1179:   t282 = t55 * t14;
1180:   t283 = t25 * t282;
1181:   t290 = ZA * t247 * xc * ZB;
1182:   t295 = t22 * nx * t1 * 0.3141592654e1;
1183:   t298 = -0.4e1 * t232 * t249 + 0.8e1 * t105 * t217 - 0.4e1 * t254 * t227 * t26 - 0.8e1 * t259 * t260 - 0.4e1 * t232 * t264 - 0.16e2 * t81 * t61 * t268 * t8 + 0.16e2 * t80 * t64 * t61 * t275 - 0.4e1 * t232 * t229 + 0.8e1 * t281 * t283 - 0.4e1 * t105 * t187 + 0.8e1 * t75 * t290 + 0.4e1 * t295 * t27;
1184:   t301 = t61 * t5;
1185:   t307 = t87 * t34;
1186:   t312 = t61 * xc;
1187:   t313 = t312 * t239;
1188:   t317 = t34 * t55 * t14;
1189:   t329 = ZB * t13 * t55;
1190:   t330 = t65 * t329;
1191:   t337 = -0.16e2 * t87 * t64 * t301 * t239 - 0.32e2 * t90 * t69 - 0.16e2 * t307 * t64 * t61 * t239 + 0.16e2 * t307 * t313 + 0.4e1 * t24 * t317 + t53 * t46 + t49 * t35 - 0.32e2 * t63 * t100 - 0.4e1 * t280 * t31 * t34 * t247 + 0.8e1 * t259 * t330 - 0.4e1 * t280 * t31 * t247 * t5;
1192:   t340 = t5 * t35;
1193:   t344 = t25 * t93;
1194:   t356 = t41 * t13;
1195:   t360 = t23 * nz * t61;
1196:   t363 = t25 * t64 * t7 * t15;
1197:   t366 = t156 * t177;
1198:   t369 = t14 * t7;
1199:   t370 = t25 * t369;
1200:   t373 = t156 * t186;
1201:   t378 = 0.4e1 * t24 * t283 + 0.4e1 * t33 * t340 * t12 - 0.16e2 * t75 * t344 - 0.4e1 * t280 * t31 * t5 * t67 + 0.8e1 * t33 * t25 * t247 + 0.32e2 * t63 * t217 + 0.4e1 * t40 * t356 - 0.8e1 * t360 * t363 + 0.4e1 * t75 * t366 + 0.4e1 * t295 * t370 - 0.4e1 * t75 * t373 - 0.4e1 * t105 * t366;
1202:   t382 = t112 * t76;
1203:   t387 = t80 * t61;
1204:   t391 = t136 * t26;
1205:   t409 = 0.16e2 * t63 * t382 + 0.4e1 * t226 * t234 - 0.16e2 * t387 * xc * t275 + 0.8e1 * t259 * t391 - 0.16e2 * t105 * t344 + 0.4e1 * t226 * t264 - 0.8e1 * t105 * t170 + 0.16e2 * t232 * t193 * t76 + 0.8e1 * t360 * t330 - 0.8e1 * t105 * t290 + 0.16e2 * t90 * t243;
1206:   t423 = t153 * t8;
1207:   t426 = t34 * t13;
1208:   t427 = t426 * t55;
1209:   t430 = t34 * t8;
1210:   t437 = t80 * ZA;
1211:   t441 = 0.4e1 * t145 * t42 - 0.16e2 * t90 * t157 + 0.24e2 * t75 * t217 + 0.4e1 * t226 * t249 + 0.4e1 * t254 * t227 * t282 + 0.4e1 * t160 * t356 - 0.8e1 * t129 * t423 - 0.8e1 * t281 * t427 - 0.8e1 * t33 * t430 * t67 + 0.8e1 * t33 * t430 * t92 + 0.32e2 * t437 * ZB * t313;
1212:   t453 = t106 * ZB * t7 * t15;
1213:   t456 = t2 * t5;
1214:   t459 = t112 * t56;
1215:   t462 = t126 * t14;
1216:   t474 = t40 * 0.3141592654e1;
1217:   t475 = xc * t8;
1218:   t480 = t146 * t13 * t35;
1219:   t483 = -0.4e1 * t103 * xc * t193 * t147 + 0.16e2 * t87 * t61 * t156 * t239 + 0.8e1 * t259 * t453 - 0.4e1 * t456 * t356 + 0.8e1 * t259 * t459 - 0.2e1 * t125 * t462 - 0.8e1 * t281 * t207 + 0.16e2 * t295 * t459 - 0.8e1 * t60 * t22 * ZA * t312 * t329 + 0.4e1 * t474 * t475 * t15 + 0.4e1 * t160 * t480;
1220:   t497 = t136 * t56;
1221:   t504 = t9 * t13;
1222:   t509 = t475 * t13;
1223:   t512 = -0.8e1 * t105 * t113 - 0.4e1 * t254 * t227 * t56 + 0.8e1 * t281 * t57 + 0.4e1 * t295 * t283 + 0.2e1 * t129 * t462 + 0.4e1 * t24 * t370 - 0.8e1 * t360 * t497 - 0.4e1 * t24 * t427 - 0.4e1 * t145 * t162 + 0.4e1 * t4 * t504 - 0.8e1 * t281 * t370 - 0.4e1 * t474 * t509;
1224:   t528 = t5 * t13;
1225:   t529 = t528 * t35;
1226:   t532 = t106 * t329;
1227:   t542 = -0.16e2 * t295 * t453 - 0.32e2 * t437 * t64 * t240 + 0.8e1 * t281 * t317 + 0.24e2 * t75 * t170 - 0.4e1 * t75 * t178 + 0.8e1 * t360 * t453 - 0.4e1 * t4 * t529 - 0.16e2 * t295 * t532 - 0.8e1 * t33 * t344 - 0.16e2 * t90 * t181 + 0.4e1 * t33 * t340 * t92;
1228:   t557 = t146 * t15;
1229:   t562 = xc * t15;
1230:   t563 = t562 * t5;
1231:   t573 = 0.16e2 * t232 * t193 * t93 - 0.8e1 * t259 * t363 - 0.8e1 * t259 * t497 + 0.8e1 * t33 * t77 + 0.8e1 * t360 * t391 + 0.4e1 * t254 * t227 * t369 + 0.4e1 * t145 * t557 + 0.8e1 * t281 * t166 + 0.4e1 * t3 * t563 + 0.8e1 * t105 * t382 - 0.4e1 * t145 * t480 - 0.4e1 * t33 * t36 * t92;
1232:   t600 = 0.4e1 * t456 * t42 - 0.8e1 * t360 * t260 - 0.4e1 * t40 * t557 - 0.4e1 * t105 * t373 + 0.16e2 * t226 * t227 * t93 - 0.16e2 * t90 * t382 - 0.4e1 * t145 * t356 - 0.16e2 * t63 * t157 - 0.32e2 * t87 * t25 * t313 - 0.16e2 * t226 * t227 * t76 - 0.16e2 * t63 * t113;
1233:   t623 = xc * t13;
1234:   t627 = 0.8e1 * t125 * t423 - 0.8e1 * t360 * t532 + 0.16e2 * t90 * t137 - 0.4e1 * t160 * t42 + 0.16e2 * t63 * t94 + 0.16e2 * t63 * t181 - 0.8e1 * t281 * t27 - 0.8e1 * t75 * t382 + 0.8e1 * t360 * t459 + 0.4e1 * t295 * t57 + 0.16e2 * t105 * t77 + 0.4e1 * t474 * t623 * t35;
1235:   t632 = t61 * 0.3141592654e1;
1236:   t633 = t632 * t8;
1237:   t634 = t80 * nz;
1238:   t638 = t632 * t634;
1239:   t639 = t638 * xc;
1240:   t642 = t61 * t34;
1241:   t643 = t122 * t19;
1242:   t649 = t61 * t61;
1243:   t650 = t649 * t1;
1244:   t652 = t19 * t19;
1245:   t653 = t14 * t652;
1246:   t654 = t653 * t9;
1247:   t657 = t14 * t1;
1248:   t658 = t657 * t19;
1249:   t665 = t632 * t34;
1250:   t666 = t665 * t2;
1251:   t667 = t8 * t19;
1252:   t668 = t667 * t623;
1253:   t674 = t665 * nz;
1254:   t675 = t652 * xc;
1255:   t682 = 0.8e1 * t633 * t426 * t634 - 0.8e1 * t639 * t529 - 0.4e1 * t642 * t643 + 0.2e1 * t642 * t116 * t80 + 0.32e2 * t650 * t64 * t654 + 0.4e1 * t301 * t658 + 0.4e1 * t387 * t46 * ZA * ZB - 0.16e2 * t666 * t668 - 0.16e2 * t666 * t667 * t15 - 0.8e1 * t674 * t675 * t15 + 0.4e1 * t238 * t153 * t80;
1256:   t683 = t46 * t652;
1257:   t686 = t633 * t15;
1258:   t691 = t35 * t80;
1259:   t698 = t35 * t652;
1260:   t705 = t14 * t80;
1261:   t708 = t61 * t35;
1262:   t717 = -0.2e1 * t642 * t683 - 0.8e1 * t686 * t5 * t634 * xc - 0.2e1 * t301 * t691 + 0.8e1 * t638 * t563 - 0.2e1 * t642 * t691 - 0.2e1 * t642 * t698 - 0.2e1 * t301 * t698 - 0.2e1 * t301 * t683 + 0.2e1 * t642 * t705 + 0.2e1 * t708 * t274 * t80 + 0.2e1 * t301 * t653 - 0.2e1 * t642 * t80 * t46;
1263:   t727 = t61 * t46;
1264:   t737 = t649 * t34;
1265:   t738 = t737 * t1;
1266:   t739 = t8 * t652;
1267:   t740 = t739 * t268;
1268:   t746 = t61 * ZA;
1269:   t754 = t632 * nz * xc;
1270:   t758 = 0.2e1 * t301 * t705 + 0.2e1 * t642 * t653 - 0.8e1 * t665 * xc * t634 * t15 - 0.2e1 * t727 * t5 * t80 - 0.32e2 * t650 * xc * t654 + 0.2e1 * t301 * t698 * t14 - 0.32e2 * t738 * t740 + 0.8e1 * t674 * t739 * t562 + 0.4e1 * t746 * t119 * t652 + 0.8e1 * t674 * t698 * t623 - 0.8e1 * t754 * t528 * t698;
1271:   t762 = t633 * t13;
1272:   t764 = t5 * nz * t652;
1273:   t767 = t80 * t1;
1274:   t768 = t649 * t767;
1275:   t772 = t649 * ZA;
1276:   t773 = t772 * t129;
1277:   t777 = t35 * t1 * t19;
1278:   t780 = t632 * t5;
1279:   t781 = t780 * t15;
1280:   t786 = t698 * ZA;
1281:   t790 = t64 * t14;
1282:   t800 = t649 * t8;
1283:   t809 = 0.4e1 * t238 * t126 * t80 - 0.8e1 * t762 * t764 - 0.32e2 * t768 * xc * t275 + 0.64e2 * t773 * t740 - 0.4e1 * t301 * t777 - 0.8e1 * t781 * nz * t8 * t675 + 0.4e1 * t238 * t786 + 0.32e2 * t768 * t34 * t790 * t8 - 0.8e1 * t633 * t528 * t634 + 0.8e1 * t754 * t528 * t739 + 0.128e3 * t800 * t119 * t80 * t19 * t106 + 0.8e1 * t674 * t739 * t13;
1284:   t812 = t649 * t80;
1285:   t817 = t83 * ZB;
1286:   t824 = t746 * ZB;
1287:   t828 = t800 * t14;
1288:   t855 = -0.64e2 * t812 * xc * t274 * t667 + 0.4e1 * t817 * t786 + 0.4e1 * t727 * ZA * t652 * ZB - 0.32e2 * t824 * t657 * t667 - 0.32e2 * t828 * t34 * t767 * xc - 0.8e1 * t633 * t15 * t34 * t634 - 0.8e1 * t674 * t739 * t15 + 0.32e2 * t768 * t64 * t275 + 0.4e1 * t708 * t14 * t307 + 0.2e1 * t708 * t206 * t652 + 0.8e1 * t632 * t35 * t13 * t34 * t634 * xc;
1289:   t858 = t35 * t19;
1290:   t873 = t2 * t8;
1291:   t878 = t61 * t1;
1292:   t901 = -0.16e2 * t632 * t2 * xc * t528 * t858 + 0.8e1 * t824 * t658 + 0.4e1 * t301 * t14 * t777 - 0.8e1 * t665 * t634 * t509 - 0.8e1 * t674 * t739 * t623 - 0.16e2 * t781 * t873 * t19 * xc + 0.8e1 * t878 * t14 * t127 + 0.8e1 * t878 * ZA * t51 * ZB + 0.8e1 * t686 * t764 + 0.8e1 * t665 * xc * t634 * t15 * t8 + 0.8e1 * t633 * t15 * t5 * t634 + 0.4e1 * t387 * t14 * t107 * ZA;
1293:   t903 = t739 * t790;
1294:   t923 = t737 * t80;
1295:   t924 = t667 * t790;
1296:   t927 = t780 * t2;
1297:   t937 = t15 * t19 * xc;
1298:   t943 = 0.32e2 * t738 * t903 + 0.16e2 * t781 * t873 * t19 + 0.8e1 * t754 * t15 * t652 * t5 + 0.16e2 * t666 * t858 * t623 + 0.64e2 * t828 * t25 * t767 * xc - 0.16e2 * t762 * t456 * t19 + 0.64e2 * t923 * t924 + 0.16e2 * t927 * t668 - 0.64e2 * t768 * ZA * t790 * t66 - 0.64e2 * t773 * t903 + 0.16e2 * t927 * t937 + 0.16e2 * t666 * t667 * t562;
1299:   t977 = 0.64e2 * t812 * t5 * t924 + 0.8e1 * t639 * t504 + 0.8e1 * t238 * t35 * t118 * t19 + 0.4e1 * t642 * t658 - 0.16e2 * t817 * t437 * t8 - 0.128e3 * t772 * ZB * t80 * t924 + 0.16e2 * t666 * t667 * t13 - 0.4e1 * t301 * t643 - 0.16e2 * t824 * t653 * t8 - 0.4e1 * t642 * t777 - 0.64e2 * t923 * t667 * t268 - 0.16e2 * t666 * t937;

1301:   _PC3A = (t72 + t132 + t169 + t210 + t246 + t298 + t337 + t378 + t409 + t441 + t483 + t512 + t542 + t573 + t600 + t627) / (t682 + t717 + t758 + t809 + t855 + t901 + t943 + t977);
1302:   /****************************************************************************************/
1303:   _PC4A = 0;
1304:   /****************************************************************************************/
1305:   t1 = nx * 0.3141592654e1;
1306:   t2 = t1 * xc;
1307:   t3 = PetscCosReal(t2);
1308:   t4 = nx * nx;
1309:   t6 = nz * 0.3141592654e1;
1310:   t7 = t3 * t4 * t6;
1311:   t8 = ZA * ZB;
1312:   t9 = PetscExpReal(t6);
1313:   t10 = t9 * t9;
1314:   t11 = xc * nz;
1315:   t13 = PetscExpReal(t11 * 0.3141592654e1);
1316:   t14 = t13 * t13;
1317:   t15 = t14 * t13;
1318:   t16 = t14 * t14;
1319:   t17 = t16 * t15;
1320:   t18 = t10 * t17;
1321:   t19 = t8 * t18;
1322:   t22 = PetscSinReal(t2);
1323:   t23 = nx * t22;
1324:   t24 = t23 * nz;
1325:   t25 = ZB * ZB;
1326:   t30 = nz * nz;
1327:   t31 = t30 * nz;
1328:   t32 = t31 * nx;
1329:   t33 = 0.3141592654e1 * 0.3141592654e1;
1330:   t35 = t32 * t22 * t33;
1331:   t36 = ZA * ZA;
1332:   t37 = t36 * xc;
1333:   t38 = t16 * t13;
1334:   t39 = t10 * t38;
1335:   t40 = t37 * t39;
1336:   t43 = PetscSinReal(t1);
1337:   t44 = nx * t43;
1338:   t45 = t30 * 0.3141592654e1;
1339:   t46 = t44 * t45;
1340:   t47 = ZA * xc;
1341:   t49 = ZB * t16 * t9;
1342:   t54 = t4 * nx * t43;
1343:   t55 = xc * xc;
1344:   t57 = t54 * t30 * t55;
1345:   t58 = t33 * 0.3141592654e1;
1346:   t59 = t58 * t25;
1347:   t60 = t16 * t9;
1348:   t61 = t59 * t60;
1349:   t64 = xc * t25;
1350:   t65 = t14 * t9;
1351:   t66 = t64 * t65;
1352:   t70 = t44 * t31 * t33;
1353:   t71 = t37 * t65;
1354:   t74 = t10 * t15;
1355:   t75 = t64 * t74;
1356:   t78 = t25 * t10;
1357:   t83 = t54 * nz * t33;
1358:   t84 = t55 * t25;
1359:   t85 = t10 * t9;
1360:   t86 = t14 * t85;
1361:   t87 = t84 * t86;
1362:   t90 = t30 * t30;
1363:   t92 = t44 * t90 * t58;
1364:   t93 = t55 * xc;
1365:   t94 = t93 * t25;
1366:   t95 = t85 * t16;
1367:   t96 = t94 * t95;
1368:   t102 = t23 * t45;
1369:   t103 = t10 * t10;
1370:   t104 = ZB * t103;
1371:   t106 = t47 * t104 * t15;
1372:   t111 = t54 * 0.3141592654e1;
1373:   t112 = t25 * t85;
1374:   t113 = t112 * t16;
1375:   t115 = t8 * t39;
1376:   t118 = t16 * t14;
1377:   t119 = t85 * t118;
1378:   t120 = t37 * t119;
1379:   t123 = t16 * t16;
1380:   t124 = t36 * t123;
1381:   t125 = t124 * t9;
1382:   t127 = -0.8e1 * t7 * t19 + 0.2e1 * t24 * t25 * t13 * t10 - 0.16e2 * t35 * t40 - 0.16e2 * t46 * t47 * t49 - 0.8e1 * t57 * t61 + 0.4e1 * t46 * t66 + 0.2e1 * t70 * t71 - 0.16e2 * t35 * t75 + 0.6e1 * t24 * t78 * t38 - 0.2e1 * t83 * t87 - 0.8e1 * t92 * t96 - 0.8e1 * t46 * t37 * t95 - 0.12e2 * t102 * t106 + 0.2e1 * t83 * t71 + t111 * t113 + 0.8e1 * t7 * t115 + 0.2e1 * t83 * t120 + t111 * t125;
1383:   t128 = t37 * t74;
1384:   t131 = t44 * nz;
1385:   t133 = t25 * t9 * t118;
1386:   t136 = t36 * t14;
1387:   t137 = t136 * t9;
1388:   t140 = t30 * t4;
1389:   t142 = t140 * t3 * t33;
1390:   t143 = t64 * t39;
1391:   t147 = t30 * nx * t43;
1392:   t148 = 0.3141592654e1 * t36;
1393:   t149 = t9 * t118;
1394:   t153 = t44 * t31 * ZA;
1395:   t154 = t33 * xc;
1396:   t155 = t154 * t49;
1397:   t160 = ZA * t17 * xc * ZB;
1398:   t163 = t103 * t13;
1399:   t164 = t64 * t163;
1400:   t170 = t44 * t90 * t55;
1401:   t171 = t58 * ZB;
1402:   t172 = ZA * t16;
1403:   t174 = t171 * t172 * t9;
1404:   t177 = t36 * t55;
1405:   t178 = t177 * t149;
1406:   t181 = t54 * t11;
1407:   t182 = t33 * t25;
1408:   t186 = t25 * t14;
1409:   t187 = t186 * t9;
1410:   t193 = t186 * t85;
1411:   t198 = ZB * t55;
1412:   t199 = ZA * t103;
1413:   t201 = t198 * t199 * t15;
1414:   t204 = 0.2e1 * t7 * t128 - 0.2e1 * t131 * t133 - 0.2e1 * t131 * t137 + 0.16e2 * t142 * t143 - t147 * t148 * t149 + 0.8e1 * t153 * t155 - 0.4e1 * t7 * t160 + 0.2e1 * t7 * t164 + 0.10e2 * t102 * t40 + 0.16e2 * t170 * t174 + 0.2e1 * t83 * t178 - 0.2e1 * t181 * t182 * t65 - t111 * t187 - 0.2e1 * t70 * t87 + 0.4e1 * t102 * t160 - 0.2e1 * t131 * t193 - 0.16e2 * t142 * t75 + 0.16e2 * t35 * t201;
1415:   t210 = t32 * t22;
1416:   t211 = t33 * t55;
1417:   t212 = t25 * t38;
1418:   t213 = t211 * t212;
1419:   t216 = nz * nx;
1420:   t217 = t22 * t25;
1421:   t222 = ZB * t85 * t16;
1422:   t226 = t23 * t30;
1423:   t227 = t13 * t10;
1424:   t228 = t148 * t227;
1425:   t233 = t37 * t163;
1426:   t237 = nz * t4 * t3;
1427:   t238 = t148 * t74;
1428:   t241 = t64 * t86;
1429:   t245 = t148 * xc * t15;
1430:   t248 = t112 * t118;
1431:   t250 = t22 * t36;
1432:   t256 = 0.3141592654e1 * t25;
1433:   t257 = t256 * t39;
1434:   t262 = t38 * t103;
1435:   t263 = t37 * t262;
1436:   t267 = t148 * t17 * xc;
1437:   t270 = -0.6e1 * t7 * t143 - 0.4e1 * t24 * t19 - 0.8e1 * t210 * t213 - 0.2e1 * t216 * t217 * t15 - 0.32e2 * t153 * t211 * t222 + 0.4e1 * t226 * t228 + 0.16e2 * t142 * t201 + 0.2e1 * t7 * t233 - 0.4e1 * t237 * t238 - 0.2e1 * t83 * t241 - 0.2e1 * t237 * t245 + t111 * t248 + 0.2e1 * t216 * t250 * t15 - 0.2e1 * t131 * t125 - 0.4e1 * t226 * t257 + t147 * t148 * t95 - 0.2e1 * t102 * t263 + 0.2e1 * t237 * t267;
1438:   t273 = t37 * t149;
1439:   t277 = t47 * t104 * t13;
1440:   t285 = t31 * t36;
1441:   t286 = t44 * t285;
1442:   t291 = t25 * t123 * t9;
1443:   t304 = 0.3141592654e1 * xc;
1444:   t305 = t304 * t212;
1445:   t312 = t256 * t18;
1446:   t315 = t8 * t60;
1447:   t319 = t54 * t30 * t58;
1448:   t323 = t90 * t36;
1449:   t324 = t44 * t323;
1450:   t325 = t55 * t58;
1451:   t326 = t325 * t60;
1452:   t329 = 0.2e1 * t102 * t164 + 0.2e1 * t83 * t273 - 0.4e1 * t102 * t277 - 0.2e1 * t7 * t263 + 0.4e1 * t24 * t8 * t17 - 0.4e1 * t286 * t154 * t60 - 0.2e1 * t131 * t291 - t147 * t148 * t119 + 0.2e1 * t24 * t78 * t17 + 0.2e1 * t54 * t85 * 0.3141592654e1 * ZA * ZB - 0.4e1 * t226 * t305 - 0.2e1 * t70 * t66 + t147 * t256 * t95 + 0.4e1 * t237 * t312 + 0.2e1 * t111 * t315 - 0.8e1 * t319 * t96 - t111 * t193 - 0.8e1 * t324 * t326;
1453:   t332 = t8 * t95;
1454:   t335 = t136 * t85;
1455:   t337 = t256 * t227;
1456:   t340 = t177 * t119;
1457:   t346 = t37 * t86;
1458:   t351 = t103 * t15;
1459:   t352 = t177 * t351;
1460:   t355 = t64 * t119;
1461:   t358 = t8 * t227;
1462:   t361 = t85 * 0.3141592654e1;
1463:   t365 = t84 * t39;
1464:   t372 = ZB * t10;
1465:   t373 = t372 * t38;
1466:   t374 = t47 * t373;
1467:   t379 = t177 * t39;
1468:   t384 = -0.2e1 * t46 * t332 + t111 * t335 + 0.4e1 * t237 * t337 - 0.2e1 * t83 * t340 + 0.16e2 * t286 * t211 * t95 + 0.2e1 * t70 * t346 - 0.8e1 * t170 * t61 - 0.8e1 * t142 * t352 - 0.2e1 * t83 * t355 - 0.4e1 * t24 * t358 + 0.2e1 * t147 * t361 * t8 + 0.8e1 * t35 * t365 - 0.2e1 * t226 * t267 + 0.8e1 * t102 * t115 - 0.12e2 * t102 * t374 + 0.16e2 * t142 * t40 - 0.8e1 * t142 * t379 + 0.4e1 * t237 * t228;
1469:   t386 = t54 * t30 * t93;
1470:   t387 = ZA * t85;
1471:   t389 = t171 * t387 * t16;
1472:   t394 = t64 * t60;
1473:   t398 = t304 * t25 * t15;
1474:   t401 = t361 * t25;
1475:   t405 = t84 * t65;
1476:   t410 = t148 * t18;
1477:   t414 = t25 * t16 * t9;
1478:   t417 = t84 * t74;
1479:   t422 = t177 * t86;
1480:   t428 = ZB * t38;
1481:   t429 = t47 * t428;
1482:   t432 = t148 * t39;
1483:   t439 = 0.16e2 * t386 * t389 - 0.16e2 * t386 * t174 + 0.8e1 * t46 * t394 + 0.2e1 * t237 * t398 - t147 * t401 + 0.4e1 * t7 * t374 + 0.2e1 * t83 * t405 - 0.4e1 * t46 * t241 - 0.4e1 * t226 * t410 + 0.2e1 * t131 * t414 + 0.8e1 * t35 * t417 - 0.8e1 * t142 * t365 + 0.2e1 * t70 * t422 - 0.4e1 * t181 * t182 * t60 + 0.12e2 * t102 * t429 - 0.4e1 * t226 * t432 + 0.32e2 * t35 * t374 - 0.4e1 * t7 * t106;
1484:   t442 = t36 * t9 * t118;
1485:   t444 = t123 * t9;
1486:   t445 = t8 * t444;
1487:   t448 = t361 * t36;
1488:   t451 = t47 * t372 * t17;
1489:   t454 = t94 * t60;
1490:   t457 = t25 * t103;
1491:   t465 = t47 * t372 * t15;
1492:   t468 = t36 * t85;
1493:   t469 = t468 * t16;
1494:   t474 = t43 * t85;
1495:   t478 = t8 * t74;
1496:   t484 = t256 * t74;
1497:   t489 = t198 * ZA * t10 * t15;
1498:   t501 = -t111 * t442 + 0.4e1 * t131 * t445 - t147 * t448 + 0.4e1 * t7 * t451 + 0.8e1 * t92 * t454 - 0.2e1 * t24 * t457 * t13 - 0.2e1 * t286 * t211 * t65 + 0.4e1 * t7 * t465 + t111 * t469 - 0.2e1 * t216 * t250 * t17 - 0.2e1 * t216 * t474 * t25 - 0.4e1 * t24 * t478 + 0.4e1 * t24 * t8 * t38 + 0.4e1 * t226 * t484 - 0.16e2 * t142 * t489 - 0.2e1 * t24 * t212 * t103 - 0.2e1 * t216 * t22 * t17 * t25 + 0.2e1 * t70 * t120;
1499:   t504 = t33 * t36 * t55 * t38;
1500:   t507 = t37 * t18;
1501:   t512 = t47 * ZB * t13 * t10;
1502:   t518 = t59 * t95;
1503:   t530 = t84 * t351;
1504:   t534 = t37 * t227;
1505:   t549 = -0.8e1 * t210 * t504 + 0.2e1 * t102 * t507 + 0.4e1 * t7 * t512 + t111 * t133 - 0.16e2 * t35 * t489 + 0.8e1 * t170 * t518 + 0.2e1 * t24 * t36 * t13 * t10 + 0.4e1 * t131 * t387 * ZB + 0.12e2 * t102 * t465 - 0.8e1 * t142 * t530 + t111 * t291 - 0.2e1 * t102 * t534 - 0.4e1 * t70 * t394 - 0.10e2 * t102 * t128 + 0.4e1 * t237 * t305 + 0.8e1 * t102 * t19 + 0.2e1 * t83 * t346 - 0.16e2 * t35 * t128;
1506:   t557 = t468 * t118;
1507:   t562 = t93 * t58;
1508:   t563 = t562 * t60;
1509:   t567 = t44 * t90 * t93;
1510:   t575 = ZA * t55;
1511:   t576 = t575 * t428;
1512:   t583 = t37 * t60;
1513:   t590 = t140 * t3;
1514:   t601 = -0.2e1 * t226 * t398 - 0.2e1 * t70 * t340 - 0.2e1 * t131 * t557 - 0.4e1 * t24 * t115 + 0.8e1 * t324 * t563 + 0.16e2 * t567 * t389 + 0.16e2 * t70 * t84 * t95 + 0.2e1 * t70 * t178 - 0.16e2 * t142 * t576 - 0.4e1 * t237 * t257 - 0.4e1 * t226 * t312 + 0.8e1 * t46 * t583 + 0.2e1 * t24 * t36 * t38 * t103 + 0.8e1 * t590 * t213 + 0.2e1 * t102 * t143 - 0.16e2 * t35 * t143 + 0.2e1 * t131 * t248 + 0.4e1 * t46 * t346;
1515:   t604 = nz * t36;
1516:   t606 = t154 * t95;
1517:   t625 = t36 * t103;
1518:   t640 = t30 * t36;
1519:   t641 = t54 * t640;
1520:   t642 = t325 * t95;
1521:   t647 = -0.4e1 * t131 * t315 - 0.4e1 * t54 * t604 * t606 - t147 * t148 * t60 + 0.16e2 * t35 * t576 - 0.8e1 * t102 * t478 + 0.32e2 * t142 * t465 - 0.4e1 * t237 * t484 - 0.2e1 * t70 * t355 + 0.2e1 * t70 * t273 + 0.2e1 * t102 * t233 - 0.2e1 * t24 * t625 * t13 - 0.8e1 * t7 * t358 - 0.2e1 * t111 * t445 - 0.4e1 * t7 * t429 + 0.16e2 * t46 * t47 * t222 + 0.2e1 * t131 * t113 + 0.8e1 * t641 * t642 - 0.2e1 * t7 * t534;
1522:   t652 = t36 * t16;
1523:   t653 = t652 * t9;
1524:   t655 = t64 * t227;
1525:   t658 = t182 * t95;
1526:   t663 = t562 * t95;
1527:   t684 = t64 * t351;
1528:   t689 = t36 * t10;
1529:   t695 = t154 * t222;
1530:   t698 = -0.4e1 * t216 * t217 * t38 - t111 * t653 - 0.2e1 * t7 * t655 - 0.4e1 * t181 * t658 + 0.2e1 * t131 * t469 - 0.8e1 * t641 * t663 - 0.4e1 * t83 * t583 - 0.2e1 * t83 * t177 * t65 - 0.4e1 * t24 * t457 * t15 + 0.16e2 * t70 * t84 * t60 + 0.8e1 * t57 * t518 - 0.32e2 * t142 * t374 + 0.4e1 * t24 * t8 * t351 + 0.4e1 * t102 * t684 - t147 * t256 * t86 - 0.2e1 * t24 * t689 * t15 - 0.2e1 * t70 * t241 + 0.8e1 * t153 * t695;
1531:   t711 = t575 * t373;
1532:   t717 = t304 * t17 * t25;
1533:   t736 = t177 * t74;
1534:   t739 = 0.2e1 * t226 * t245 - 0.8e1 * t102 * t358 - 0.16e2 * t57 * t389 - 0.2e1 * t102 * t655 + 0.8e1 * t590 * t504 - 0.8e1 * t641 * t326 - 0.16e2 * t35 * t711 - t111 * t557 + t111 * t137 - 0.2e1 * t226 * t717 + 0.8e1 * t102 * t37 * t351 + 0.2e1 * t131 * t335 - 0.4e1 * t131 * t332 - 0.2e1 * t216 * t474 * t36 - 0.2e1 * t111 * t332 + 0.16e2 * t142 * t711 - t147 * t256 * t60 + 0.8e1 * t142 * t736;
1535:   t750 = t64 * t262;
1536:   t763 = t44 * t640;
1537:   t770 = t84 * t119;
1538:   t782 = 0.4e1 * t102 * t512 + 0.8e1 * t142 * t417 + 0.8e1 * t641 * t563 - 0.2e1 * t7 * t507 + 0.2e1 * t7 * t750 - 0.8e1 * t35 * t352 + 0.4e1 * t237 * t410 + 0.4e1 * t7 * t684 - 0.2e1 * t46 * t445 + t147 * t148 * t65 + 0.4e1 * t763 * t304 * t119 + 0.16e2 * t70 * t177 * t60 + 0.2e1 * t70 * t770 - t111 * t414 - 0.16e2 * t567 * t174 - 0.4e1 * t46 * t71 - 0.4e1 * t46 * t355 - 0.4e1 * t7 * t277;
1539:   t797 = t64 * t149;
1540:   t821 = -t54 * t448 + 0.2e1 * t131 * t442 + 0.8e1 * t7 * t478 + 0.8e1 * t35 * t379 - 0.2e1 * t181 * t182 * t149 + 0.2e1 * t70 * t405 + 0.2e1 * t83 * t770 - 0.2e1 * t70 * t797 - 0.6e1 * t7 * t75 - 0.4e1 * t286 * t606 - 0.4e1 * t237 * t432 + t147 * t256 * t149 - 0.4e1 * t763 * t304 * t149 - 0.2e1 * t102 * t75 + 0.2e1 * t237 * t717 + 0.8e1 * t324 * t642 - 0.16e2 * t170 * t389 + 0.2e1 * t83 * t422;
1541:   t827 = t84 * t149;
1542:   t846 = t54 * nz * ZA;
1543:   t854 = t64 * t18;
1544:   t867 = -0.16e2 * t142 * t128 + 0.32e2 * t35 * t465 - 0.2e1 * t83 * t827 + 0.2e1 * t46 * t315 + t147 * t148 * t86 - 0.4e1 * t102 * t451 - 0.8e1 * t226 * t148 * xc * t38 - 0.2e1 * t24 * t689 * t38 + 0.2e1 * t131 * t187 + 0.8e1 * t846 * t155 + 0.8e1 * t35 * t736 + 0.2e1 * t24 * t689 * t17 - 0.2e1 * t7 * t854 + t147 * t256 * t119 + 0.2e1 * t102 * t854 - 0.8e1 * t35 * t530 + 0.4e1 * t46 * t797 + 0.2e1 * t102 * t750;
1545:   t909 = -0.8e1 * t324 * t663 + t147 * t256 * t444 - t147 * t256 * t65 + 0.4e1 * t226 * t238 + 0.2e1 * t7 * t40 - t54 * t401 + 0.16e2 * t57 * t174 + 0.4e1 * t226 * t337 + 0.4e1 * t24 * t8 * t163 + 0.8e1 * t846 * t695 + 0.8e1 * t319 * t454 + 0.2e1 * t131 * t653 - 0.8e1 * t46 * t64 * t95 + 0.6e1 * t24 * t78 * t15 - 0.4e1 * t44 * t31 * xc * t658 - 0.32e2 * t153 * t211 * t49 - 0.2e1 * t70 * t827 + t147 * t148 * t444;
1546:   t914 = t25 * ZB;
1547:   t915 = t33 * t914;
1548:   t919 = t4 * t4;
1549:   t920 = t16 * t919;
1550:   t929 = t123 * t90;
1551:   t932 = t919 * t103;
1552:   t935 = t33 * ZB;
1553:   t939 = t652 * t919;
1554:   t942 = t16 * t30;
1555:   t943 = t942 * t4;
1556:   t949 = t103 * t16;
1557:   t950 = t949 * t90;
1558:   t953 = -0.2e1 * t915 * t103 * t90 + 0.2e1 * t915 * t920 - 0.2e1 * t915 * t123 * t919 + 0.2e1 * t915 * t16 * t90 - 0.2e1 * t915 * t929 - 0.2e1 * t915 * t932 - 0.2e1 * t935 * t323 * t123 + 0.2e1 * t935 * t939 + 0.4e1 * t915 * t943 + 0.4e1 * t182 * t172 * t90 + 0.2e1 * t915 * t950;
1559:   t954 = t171 * t36;
1560:   t955 = t90 * nz;
1561:   t956 = xc * t955;
1562:   t957 = t118 * t10;
1563:   t964 = t33 * t33;
1564:   t965 = t964 * ZB;
1565:   t966 = t965 * t640;
1566:   t967 = t10 * t919;
1567:   t968 = t55 * t16;
1568:   t969 = t967 * t968;
1569:   t972 = t935 * t36;
1570:   t974 = t103 * t30 * t4;
1571:   t977 = xc * t16;
1572:   t978 = t967 * t977;
1573:   t981 = t90 * t30;
1574:   t983 = t16 * t10;
1575:   t987 = t182 * ZA;
1576:   t988 = t4 * t10;
1577:   t992 = t171 * t604;
1578:   t993 = xc * t14;
1579:   t994 = t932 * t993;
1580:   t997 = t182 * t30;
1581:   t1005 = t171 * t285;
1582:   t1006 = t988 * t993;
1583:   t1009 = t58 * t914;
1584:   t1010 = t1009 * t31;
1585:   t1013 = 0.8e1 * t954 * t956 * t957 + 0.2e1 * t915 * t932 * t16 + 0.32e2 * t966 * t969 - 0.4e1 * t972 * t974 - 0.32e2 * t966 * t978 + 0.32e2 * t965 * t981 * t177 * t983 - 0.32e2 * t987 * t942 * t988 + 0.8e1 * t992 * t994 + 0.8e1 * t997 * t949 * ZA * t4 - 0.2e1 * t935 * t124 * t919 - 0.16e2 * t1005 * t1006 + 0.16e2 * t1010 * t1006;
1586:   t1015 = t964 * t25;
1587:   t1016 = ZA * t30;
1588:   t1017 = t1015 * t1016;
1589:   t1020 = t967 * t993;
1590:   t1031 = t1009 * t118;
1591:   t1032 = t31 * t10;
1592:   t1040 = t964 * t914;
1593:   t1041 = t1040 * t90;
1594:   t1044 = t55 * t10 * t4 * t16;
1595:   t1047 = t1040 * t30;
1596:   t1050 = t123 * ZA;
1597:   t1054 = t977 * t988;
1598:   t1057 = 0.64e2 * t1017 * t978 - 0.8e1 * t992 * t1020 + 0.2e1 * t972 * t950 + 0.4e1 * t182 * t929 * ZA + 0.4e1 * t182 * t199 * t90 - 0.16e2 * t1031 * t1032 * t4 * xc + 0.4e1 * t182 * t172 * t919 + 0.64e2 * t1041 * t1044 + 0.32e2 * t1047 * t969 + 0.4e1 * t182 * t1050 * t919 - 0.64e2 * t1041 * t1054;
1599:   t1058 = t1009 * nz;
1600:   t1063 = t932 * ZA;
1601:   t1069 = t123 * t30 * t4;
1602:   t1080 = t993 * t103 * t4;
1603:   t1088 = t935 * t103;
1604:   t1094 = -0.8e1 * t1058 * t994 - 0.32e2 * t1047 * t978 + 0.4e1 * t182 * t1063 - 0.4e1 * t915 * t974 - 0.4e1 * t915 * t1069 - 0.2e1 * t935 * t625 * t90 - 0.8e1 * t1009 * t10 * t14 * t955 - 0.16e2 * t1010 * t1080 - 0.2e1 * t935 * t625 * t919 - 0.64e2 * t1017 * t969 + 0.2e1 * t1088 * t939 + 0.8e1 * t1009 * t957 * t955;
1605:   t1113 = t955 * t118 * xc;
1606:   t1120 = t4 * t118;
1607:   t1125 = t981 * xc;
1608:   t1133 = nz * t10;
1609:   t1140 = -0.8e1 * t954 * t955 * t10 * t993 + 0.2e1 * t935 * t652 * t90 - 0.64e2 * t1015 * t981 * t575 * t983 + 0.8e1 * t182 * t103 * t1016 * t4 + 0.8e1 * t1009 * t1113 + 0.16e2 * t954 * t1032 * t4 * t14 - 0.16e2 * t954 * t1032 * t1120 + 0.64e2 * t1015 * t10 * t172 * t1125 + 0.8e1 * t171 * t103 * t136 * t956 - 0.8e1 * t1031 * t1133 * t919 * xc + 0.8e1 * t1058 * t1020;
1610:   t1153 = xc * t118;
1611:   t1165 = t182 * t16;
1612:   t1170 = t171 * t10;
1613:   t1178 = ZA * t90;
1614:   t1182 = 0.4e1 * t1088 * t652 * t140 + 0.8e1 * t954 * t1133 * t919 * t14 + 0.4e1 * t972 * t943 - 0.4e1 * t972 * t1069 - 0.16e2 * t954 * t31 * t4 * t1153 - 0.8e1 * t954 * nz * t919 * t1153 - 0.8e1 * t954 * t1133 * t919 * t118 + 0.4e1 * t1165 * t1063 + 0.16e2 * t1005 * t1080 - 0.8e1 * t1170 * t118 * t36 * t955 - 0.16e2 * t987 * t920 * t10 - 0.16e2 * t1165 * t1178 * t10;
1615:   t1195 = t1040 * t981;
1616:   t1199 = t1009 * t955;
1617:   t1203 = t1009 * t10;
1618:   t1211 = t965 * t323;
1619:   t1225 = -0.32e2 * t965 * t10 * t652 * t1125 + 0.4e1 * t915 * t16 * t974 + 0.4e1 * t182 * t90 * t949 * ZA + 0.32e2 * t1195 * t968 * t10 - 0.8e1 * t1199 * t993 * t103 + 0.8e1 * t1203 * t118 * nz * t919 + 0.8e1 * t1170 * t136 * t955 + 0.64e2 * t1211 * t1044 + 0.16e2 * t1031 * t1032 * t4 + 0.8e1 * t987 * t943 + 0.8e1 * t1199 * t993 * t10 + 0.8e1 * t997 * t1050 * t4;
1620:   t1263 = -0.128e3 * t1015 * t1178 * t1044 + 0.16e2 * t1005 * t988 * t1153 + 0.8e1 * t1058 * t1153 * t919 + 0.16e2 * t1010 * t1120 * xc - 0.8e1 * t954 * t1113 - 0.8e1 * t1203 * t14 * nz * t919 - 0.16e2 * t1203 * t14 * t31 * t4 - 0.8e1 * t1203 * t1113 - 0.32e2 * t1195 * t977 * t10 - 0.64e2 * t1211 * t1054 + 0.8e1 * t992 * t967 * t1153 + 0.128e3 * t1015 * t983 * t90 * t4 * t47;

1622:   _PC1B = (t127 + t204 + t270 + t329 + t384 + t439 + t501 + t549 + t601 + t647 + t698 + t739 + t782 + t821 + t867 + t909) / (t953 + t1013 + t1057 + t1094 + t1140 + t1182 + t1225 + t1263);
1623:   /****************************************************************************************/
1624:   t1 = nz * nz;
1625:   t2 = t1 * nz;
1626:   t3 = nx * t2;
1627:   t4 = 0.3141592654e1 * ZA;
1628:   t5 = t3 * t4;
1629:   t6 = nx * 0.3141592654e1;
1630:   t7 = t6 * xc;
1631:   t8 = PetscSinReal(t7);
1632:   t9 = t8 * ZB;
1633:   t10 = nz * 0.3141592654e1;
1634:   t11 = PetscExpReal(t10);
1635:   t12 = t11 * t11;
1636:   t15 = PetscExpReal(xc * nz * 0.3141592654e1);
1637:   t16 = t15 * t15;
1638:   t17 = t16 * t16;
1639:   t18 = t17 * t15;
1640:   t19 = t12 * t18;
1641:   t23 = t1 * t1;
1642:   t24 = nx * t23;
1643:   t25 = ZB * ZB;
1644:   t27 = t18 * t8;
1645:   t28 = 0.3141592654e1 * 0.3141592654e1;
1646:   t29 = xc * xc;
1647:   t30 = t28 * t29;
1648:   t34 = t1 * xc;
1649:   t35 = 0.3141592654e1 * ZB;
1650:   t36 = t34 * t35;
1651:   t37 = PetscCosReal(t7);
1652:   t38 = ZA * t37;
1653:   t39 = nx * nx;
1654:   t40 = t39 * t12;
1655:   t41 = t16 * t15;
1656:   t43 = t38 * t40 * t41;
1657:   t46 = t25 * nz;
1658:   t47 = t46 * 0.3141592654e1;
1659:   t48 = t39 * nx;
1660:   t49 = PetscSinReal(t6);
1661:   t50 = t48 * t49;
1662:   t51 = t12 * t11;
1663:   t52 = t51 * t17;
1664:   t53 = t50 * t52;
1665:   t56 = t34 * 0.3141592654e1 * t25;
1666:   t57 = t37 * t39;
1667:   t58 = t17 * t41;
1668:   t59 = t12 * t58;
1669:   t60 = t57 * t59;
1670:   t63 = t25 * t18;
1671:   t64 = t57 * nz;
1672:   t67 = ZA * ZA;
1673:   t68 = t67 * nz;
1674:   t69 = 0.3141592654e1 * t48;
1675:   t70 = t68 * t69;
1676:   t71 = t49 * xc;
1677:   t72 = t17 * t16;
1678:   t73 = t11 * t72;
1679:   t74 = t71 * t73;
1680:   t77 = t1 * t67;
1681:   t78 = t77 * 0.3141592654e1;
1682:   t81 = nx * t25;
1683:   t82 = t81 * t49;
1684:   t83 = t17 * t17;
1685:   t85 = t1 * t83 * t11;
1686:   t87 = nx * ZB;
1687:   t88 = t8 * t2;
1688:   t89 = t87 * t88;
1689:   t90 = 0.3141592654e1 * xc;
1690:   t91 = t12 * t12;
1691:   t92 = ZA * t91;
1692:   t97 = ZB * ZA;
1693:   t98 = t97 * t37;
1694:   t99 = t39 * nz;
1695:   t100 = t12 * t41;
1696:   t104 = 0.8e1 * t5 * t9 * t19 + 0.8e1 * t24 * t25 * t27 * t30 + 0.12e2 * t36 * t43 - t47 * t53 - 0.2e1 * t56 * t60 - 0.4e1 * t63 * t64 + 0.6e1 * t70 * t74 + 0.4e1 * t78 * t60 - t82 * t85 + 0.4e1 * t89 * t90 * t92 * t41 + 0.4e1 * t98 * t99 * t100;
1697:   t105 = t67 * t48;
1698:   t106 = t49 * t51;
1699:   t107 = t106 * t72;
1700:   t109 = t1 * 0.3141592654e1;
1701:   t110 = t109 * xc;
1702:   t115 = nx * t67;
1703:   t116 = t115 * t49;
1704:   t117 = t1 * t16;
1705:   t118 = t117 * t11;
1706:   t120 = t2 * t25;
1707:   t121 = t28 * 0.3141592654e1;
1708:   t122 = t121 * t29;
1709:   t123 = t120 * t122;
1710:   t129 = t1 * ZB;
1711:   t130 = t129 * t4;
1712:   t131 = t57 * t100;
1713:   t134 = t12 * t16;
1714:   t136 = t109 * t39;
1715:   t139 = ZB * t18;
1716:   t141 = t39 * t1;
1717:   t142 = t141 * t90;
1718:   t145 = t77 * t90;
1719:   t146 = t91 * t41;
1720:   t147 = t57 * t146;
1721:   t151 = t25 * t39 * t1;
1722:   t152 = t72 * t12;
1723:   t156 = t49 * t2;
1724:   t158 = t83 * t11;
1725:   t162 = -t105 * t107 + 0.8e1 * t110 * t72 * t25 * t39 - t116 * t118 + 0.8e1 * t123 * t53 + 0.8e1 * t5 * t9 * t59 - 0.8e1 * t130 * t131 - 0.8e1 * t134 * t25 * t136 - 0.12e2 * t139 * t38 * t142 - 0.8e1 * t145 * t147 - 0.8e1 * t151 * t90 * t152 - 0.2e1 * t87 * t156 * t4 * t158;
1726:   t164 = t115 * t88;
1727:   t165 = t90 * t19;
1728:   t168 = t25 * t48;
1729:   t169 = t49 * t16;
1730:   t170 = t169 * t11;
1731:   t174 = ZA * nz * t69;
1732:   t175 = ZB * t51;
1733:   t176 = t175 * t17;
1734:   t177 = t71 * t176;
1735:   t180 = t1 * t29;
1736:   t181 = t28 * t25;
1737:   t182 = t180 * t181;
1738:   t183 = t50 * t73;
1739:   t186 = ZA * t1;
1740:   t187 = t28 * t48;
1741:   t188 = t186 * t187;
1742:   t189 = ZB * t17;
1743:   t190 = t189 * t11;
1744:   t191 = t71 * t190;
1745:   t194 = t50 * t158;
1746:   t196 = t115 * t156;
1747:   t197 = t90 * t73;
1748:   t201 = t49 * t17 * t11;
1749:   t204 = t88 * t90;
1750:   t207 = t68 * 0.3141592654e1;
1751:   t208 = t17 * t11;
1752:   t209 = t50 * t208;
1753:   t211 = -0.2e1 * t164 * t165 - t168 * t170 + t168 * t107 + 0.8e1 * t174 * t177 + 0.2e1 * t182 * t183 + 0.8e1 * t188 * t191 + t47 * t194 - 0.6e1 * t196 * t197 - t168 * t201 - 0.4e1 * t81 * t18 * t204 - t207 * t209;
1754:   t212 = t2 * 0.3141592654e1;
1755:   t213 = t212 * t52;
1756:   t215 = t81 * t8;
1757:   t216 = t212 * t59;
1758:   t219 = t3 * t90;
1759:   t220 = t25 * t8;
1760:   t221 = t18 * t91;
1761:   t225 = t71 * t52;
1762:   t231 = t16 * t51;
1763:   t232 = t50 * t231;
1764:   t237 = ZA * t12;
1765:   t243 = t67 * t28;
1766:   t244 = t24 * t243;
1767:   t245 = t71 * t231;
1768:   t249 = -t116 * t213 - 0.4e1 * t215 * t216 + 0.2e1 * t219 * t220 * t221 - 0.4e1 * t70 * t225 + 0.4e1 * t98 * t99 * t146 + t47 * t232 - 0.2e1 * t145 * t57 * t221 + 0.4e1 * t89 * t90 * t237 * t41 - t105 * t201 - 0.6e1 * t244 * t245 + t105 * t170;
1769:   t252 = t25 * t37;
1770:   t253 = t252 * t39;
1771:   t255 = nz * t15 * t12;
1772:   t258 = t2 * t29;
1773:   t259 = ZB * t28;
1774:   t260 = t258 * t259;
1775:   t263 = t106 * t17;
1776:   t265 = xc * t25;
1777:   t269 = t25 * t49;
1778:   t270 = t269 * t52;
1779:   t273 = t1 * t25;
1780:   t274 = t273 * 0.3141592654e1;
1781:   t275 = t57 * t19;
1782:   t278 = t24 * t30;
1783:   t288 = t1 * t11 * t72;
1784:   t290 = t212 * t208;
1785:   t292 = t2 * xc;
1786:   t296 = 0.2e1 * t253 * t255 + 0.16e2 * t260 * t43 + t105 * t263 - 0.4e1 * t10 * t265 * t53 + 0.4e1 * t219 * t270 - 0.12e2 * t274 * t275 + 0.8e1 * t278 * t270 - 0.2e1 * ZB * nz * t69 * t49 * ZA * t158 - t82 * t288 - t116 * t290 + 0.16e2 * t292 * t243 * t275;
1787:   t301 = t50 * t176;
1788:   t304 = t51 * t72;
1789:   t305 = t71 * t304;
1790:   t308 = t25 * t41;
1791:   t311 = ZA * t48;
1792:   t312 = t311 * t49;
1793:   t317 = t91 * t15;
1794:   t318 = t57 * t317;
1795:   t321 = t81 * t88;
1796:   t322 = t90 * t59;
1797:   t325 = t212 * t231;
1798:   t327 = t15 * t12;
1799:   t328 = t57 * t327;
1800:   t331 = t77 * t187;
1801:   t334 = t2 * ZA;
1802:   t335 = t334 * t122;
1803:   t336 = t50 * t190;
1804:   t339 = 0.8e1 * t151 * t90 * t134 + 0.16e2 * t186 * t30 * t301 - 0.2e1 * t70 * t305 + 0.2e1 * t308 * t64 - 0.2e1 * t312 * ZB * t83 * t11 + 0.2e1 * t56 * t318 + 0.2e1 * t321 * t322 - t116 * t325 - 0.4e1 * t274 * t328 + 0.2e1 * t331 * t305 - 0.16e2 * t335 * t336;
1805:   t341 = t169 * t51;
1806:   t344 = t49 * t11 * t72;
1807:   t346 = t77 * t30;
1808:   t347 = t50 * t304;
1809:   t350 = t25 * t51;
1810:   t352 = nx * ZA;
1811:   t353 = t49 * t23;
1812:   t354 = t352 * t353;
1813:   t355 = t28 * xc;
1814:   t362 = t25 * t91;
1815:   t365 = t23 * nz;
1816:   t366 = nx * t365;
1817:   t367 = t366 * t122;
1818:   t368 = ZB * t49;
1819:   t369 = ZA * t51;
1820:   t370 = t369 * t17;
1821:   t371 = t368 * t370;
1822:   t374 = t115 * t353;
1823:   t375 = t355 * t73;
1824:   t381 = t105 * t341 - t105 * t344 - 0.2e1 * t346 * t347 - t350 * t50 - 0.8e1 * t354 * t355 * t176 - 0.4e1 * t98 * t99 * t317 - 0.2e1 * t362 * t99 - 0.16e2 * t367 * t371 + 0.6e1 * t374 * t375 - 0.8e1 * t182 * t53 - t82 * t290;
1825:   t382 = t71 * t208;
1826:   t394 = t2 * t67;
1827:   t395 = t394 * t122;
1828:   t398 = t352 * t156;
1829:   t402 = t17 * t12;
1830:   t403 = t39 * ZA;
1831:   t404 = t402 * t403;
1832:   t407 = t269 * t208;
1833:   t411 = t49 * t83 * t11;
1834:   t413 = t46 * t69;
1835:   t419 = -0.4e1 * t331 * t382 + 0.2e1 * t115 * t58 * t204 - 0.2e1 * t145 * t60 + 0.12e2 * t274 * t131 + 0.2e1 * t346 * t232 + 0.8e1 * t395 * t53 - 0.8e1 * t398 * t90 * t176 - 0.64e2 * t260 * t404 + 0.4e1 * t219 * t407 + t168 * t411 - 0.6e1 * t413 * t74 - 0.2e1 * t110 * t308 * t57;
1836:   t424 = t16 * t11;
1837:   t425 = t212 * t424;
1838:   t427 = t258 * t181;
1839:   t430 = t67 * t29;
1840:   t431 = t366 * t430;
1841:   t432 = t121 * t49;
1842:   t433 = t432 * t52;
1843:   t436 = nz * t12;
1844:   t437 = t436 * t18;
1845:   t440 = t29 * xc;
1846:   t441 = t440 * t121;
1847:   t442 = t394 * t441;
1848:   t445 = t67 * t37;
1849:   t446 = t445 * t39;
1850:   t448 = nz * t18 * t91;
1851:   t453 = t352 * t49;
1852:   t458 = t8 * t23;
1853:   t462 = t81 * t458;
1854:   t463 = t30 * t19;
1855:   t466 = -t47 * t209 + t116 * t425 - 0.8e1 * t427 * t275 + 0.8e1 * t431 * t433 - 0.2e1 * t253 * t437 - 0.8e1 * t442 * t53 - 0.2e1 * t446 * t448 + 0.2e1 * t175 * t312 + 0.6e1 * t453 * t129 * t208 + 0.8e1 * t115 * t18 * t458 * t30 + 0.8e1 * t462 * t463;
1856:   t470 = t436 * t58;
1857:   t475 = t2 * t121 * t440 * t25;
1858:   t485 = t212 * t73;
1859:   t488 = t67 * t72 * t1;
1860:   t490 = t39 * xc;
1861:   t501 = 0.4e1 * t374 * t355 * t52 + 0.2e1 * t446 * t470 - 0.8e1 * t475 * t53 - 0.2e1 * t446 * t437 - 0.4e1 * t36 * t38 * t39 * t15 * t12 - t116 * t485 + 0.8e1 * t488 * 0.3141592654e1 * t12 * t490 - t207 * t183 - 0.2e1 * t182 * t232 - 0.6e1 * t413 * t245 - 0.4e1 * t413 * t382;
1862:   t503 = t115 * t8;
1863:   t510 = t355 * t19;
1864:   t513 = t432 * t208;
1865:   t525 = t38 * t40 * t18;
1866:   t533 = -0.4e1 * t503 * t216 - 0.4e1 * t89 * t90 * t92 * t15 - 0.16e2 * t462 * t510 + 0.8e1 * t431 * t513 - 0.4e1 * t78 * t131 + t47 * t183 - 0.2e1 * t67 * t83 * t99 + 0.4e1 * t331 * t225 + 0.16e2 * t260 * t525 - 0.4e1 * t89 * t90 * t237 * t58 - t207 * t53;
1867:   t536 = t28 * t37;
1868:   t538 = t490 * t100;
1869:   t541 = t334 * t441;
1870:   t547 = t394 * t30;
1871:   t550 = t212 * t19;
1872:   t553 = t366 * t441;
1873:   t556 = nz * t17;
1874:   t571 = -0.8e1 * t427 * t131 + 0.16e2 * t394 * t536 * t538 + 0.16e2 * t541 * t336 + 0.2e1 * t453 * t129 * t158 - 0.8e1 * t547 * t147 + 0.4e1 * t503 * t550 - 0.8e1 * t553 * t270 + 0.4e1 * t556 * ZB * t92 * t39 - 0.2e1 * t67 * t91 * t99 - t82 * t425 + 0.4e1 * t78 * t275 + 0.2e1 * t78 * xc * t41 * t57;
1875:   t583 = t90 * t317;
1876:   t594 = t212 * t158;
1877:   t596 = t152 * t67;
1878:   t602 = t67 * t17;
1879:   t607 = 0.8e1 * t367 * t407 - 0.4e1 * t98 * t99 * t59 + 0.16e2 * t260 * t18 * ZA * t57 + 0.2e1 * t321 * t583 - 0.6e1 * t174 * t368 * t52 - 0.4e1 * t89 * t90 * ZA * t15 * t12 + t116 * t594 - 0.8e1 * t596 * t136 - 0.4e1 * t98 * t99 * t327 + 0.2e1 * t602 * t99 + 0.2e1 * t164 * t583;
1880:   t613 = t83 * t25;
1881:   t616 = t81 * t156;
1882:   t627 = t90 * t231;
1883:   t630 = t91 * t16;
1884:   t638 = 0.4e1 * t196 * t90 * t208 - 0.8e1 * t130 * t60 - 0.2e1 * t613 * t99 + 0.6e1 * t616 * t197 - 0.8e1 * t547 * t131 + 0.8e1 * t67 * t18 * t37 * t142 + 0.2e1 * t145 * t328 - 0.6e1 * t196 * t627 + 0.8e1 * t630 * t67 * t142 - 0.8e1 * t547 * t275 + 0.8e1 * t395 * t209;
1885:   t643 = t77 * t355;
1886:   t648 = t115 * t458;
1887:   t651 = t134 * t67;
1888:   t657 = t30 * t304;
1889:   t660 = t30 * t146;
1890:   t665 = t25 * t17;
1891:   t668 = t50 * t424;
1892:   t671 = -0.4e1 * t321 * t90 * t146 - 0.6e1 * t643 * t232 + 0.8e1 * t182 * t209 - 0.16e2 * t648 * t510 + 0.8e1 * t651 * t136 + 0.8e1 * t89 * t4 * t100 - 0.2e1 * t374 * t657 - 0.8e1 * t648 * t660 + 0.8e1 * t130 * t328 + 0.2e1 * t665 * t99 + 0.2e1 * t346 * t668;
1893:   t672 = t90 * t424;
1894:   t676 = t120 * t536;
1895:   t680 = t436 * t41;
1896:   t688 = t366 * t67 * t440;
1897:   t696 = xc * t12;
1898:   t697 = t696 * t18;
1899:   t701 = t252 * t141;
1900:   t702 = t90 * t221;
1901:   t705 = 0.2e1 * t196 * t672 - t47 * t347 + 0.16e2 * t676 * t538 - t116 * t85 - 0.2e1 * t253 * t680 + t207 * t194 + 0.4e1 * t98 * t99 * t19 - 0.8e1 * t688 * t433 + 0.16e2 * t541 * t301 - 0.6e1 * t312 * t190 + 0.4e1 * t352 * t88 * t35 * t697 + 0.2e1 * t701 * t702;
1902:   t712 = t24 * t430;
1903:   t713 = t28 * t49;
1904:   t721 = t1 * t17 * t11;
1905:   t726 = ZB * xc;
1906:   t737 = nz * t91;
1907:   t741 = 0.8e1 * t346 * t209 + 0.2e1 * t712 * t713 * t424 + 0.8e1 * t130 * t275 - t47 * t668 + t116 * t721 - 0.8e1 * t688 * t513 + 0.4e1 * t352 * t27 * t212 * t726 + 0.8e1 * t648 * t463 + 0.4e1 * t274 * t60 - 0.4e1 * t374 * t355 * t208 - 0.4e1 * t253 * t737 * t41;
1908:   t745 = t269 * t231;
1909:   t749 = t1 * t28 * t265;
1910:   t757 = t16 * t39;
1911:   t758 = t696 * t757;
1912:   t762 = t69 * t49;
1913:   t772 = t355 * t100;
1914:   t775 = t81 * t353;
1915:   t778 = -0.8e1 * t398 * t90 * t190 - 0.2e1 * t278 * t745 + 0.4e1 * t749 * t53 + 0.32e2 * t394 * t29 * t28 * t17 * t40 - 0.8e1 * t78 * t758 + t350 * nz * t762 - 0.6e1 * t87 * t49 * t186 * t52 - 0.8e1 * t553 * t407 - 0.4e1 * t749 * t209 + 0.16e2 * t648 * t772 - 0.6e1 * t775 * t375;
1916:   t790 = t212 * t304;
1917:   t793 = t156 * 0.3141592654e1;
1918:   t795 = t355 * t304;
1919:   t800 = t91 * t39;
1920:   t801 = t800 * nz;
1921:   t807 = t2 * t28;
1922:   t808 = t807 * t726;
1923:   t811 = -0.2e1 * t616 * t672 - 0.2e1 * t446 * t680 - 0.2e1 * t78 * xc * t58 * t57 + 0.8e1 * t367 * t270 - t82 * t790 + t115 * t51 * t793 - 0.2e1 * t775 * t795 + 0.8e1 * t123 * t209 + 0.2e1 * t665 * t801 - 0.2e1 * t67 * t41 * t64 - 0.32e2 * t808 * t43;
1924:   t812 = t117 * t51;
1925:   t821 = t24 * t355;
1926:   t827 = t90 * t304;
1927:   t840 = t800 * t41;
1928:   t844 = -t116 * t812 - 0.2e1 * t110 * t25 * t58 * t57 - 0.4e1 * t78 * t328 + t82 * t485 - 0.4e1 * t821 * t407 + 0.4e1 * t196 * t90 * t52 + 0.2e1 * t196 * t827 + t82 * t325 + 0.2e1 * t253 * t448 - 0.32e2 * t402 * t67 * t807 * t490 - t207 * t232 + 0.12e2 * t186 * t90 * ZB * t37 * t840;
1929:   t849 = t1 * t51;
1930:   t850 = t849 * t17;
1931:   t860 = t269 * t424;
1932:   t863 = t273 * t187;
1933:   t874 = 0.16e2 * t462 * t772 - t116 * t850 + 0.16e2 * t553 * t371 + t116 * t288 - 0.12e2 * t97 * t57 * t109 * t697 + t82 * t594 - 0.2e1 * t278 * t860 - 0.2e1 * t863 * t305 - 0.16e2 * t180 * t259 * t311 * t201 - 0.6e1 * t863 * t74 + 0.8e1 * t174 * t191;
1934:   t879 = xc * ZA;
1935:   t888 = t67 * t51;
1936:   t901 = ZA * t17;
1937:   t903 = t368 * t901 * t11;
1938:   t908 = -0.2e1 * t352 * t51 * t156 * t35 + 0.64e2 * t879 * t189 * t807 * t40 + 0.2e1 * t46 * t58 * t37 * t39 - t888 * t50 + t105 * t411 - 0.16e2 * t335 * t301 + 0.8e1 * t152 * t25 * t136 - 0.8e1 * t278 * t407 + 0.2e1 * t712 * t713 * t231 - 0.16e2 * t367 * t903 + 0.2e1 * t145 * t318;
1939:   t923 = t71 * t424;
1940:   t926 = t87 * t458;
1941:   t927 = t28 * ZA;
1942:   t944 = 0.8e1 * t354 * t355 * t190 - 0.8e1 * t110 * t16 * t25 * t800 - 0.2e1 * t374 * t30 * t73 - 0.16e2 * t354 * t30 * t176 - 0.2e1 * t244 * t923 - 0.32e2 * t926 * t927 * t696 * t41 - 0.32e2 * t808 * t525 + 0.6e1 * t749 * t232 - 0.8e1 * t188 * t177 + 0.4e1 * t36 * t58 * ZA * t57 + 0.4e1 * t821 * t270;
1943:   t948 = t90 * t327;
1944:   t961 = t30 * t100;
1945:   t964 = t29 * t49;
1946:   t981 = t106 * t1;
1947:   t983 = -0.2e1 * t219 * t220 * t100 + 0.2e1 * t321 * t948 - 0.16e2 * t189 * ZA * t99 * t12 - 0.2e1 * t369 * nz * t69 * t368 + 0.2e1 * t374 * t795 - 0.8e1 * t462 * t961 - 0.8e1 * t244 * t964 * t208 + 0.2e1 * t413 * t923 + 0.4e1 * t36 * t38 * t40 * t58 - 0.2e1 * t87 * t51 * t49 * t1 * ZA + t888 * nz * t762 + t115 * t981;
1948:   t1012 = 0.6e1 * t616 * t627 - t82 * t213 + 0.2e1 * t775 * t657 - 0.12e2 * t215 * t550 - 0.6e1 * t145 * t131 + 0.2e1 * t81 * t41 * t204 + 0.6e1 * ZB * t48 * t49 * t370 - 0.4e1 * t70 * t382 + 0.2e1 * t446 * t255 + 0.8e1 * t89 * t4 * t327 - 0.4e1 * t56 * t147;
1949:   t1018 = t212 * t100;
1950:   t1029 = t212 * t327;
1951:   t1040 = 0.6e1 * t70 * t245 + 0.2e1 * t56 * t328 + t207 * t668 + 0.4e1 * t503 * t1018 + 0.2e1 * t253 * t470 - 0.6e1 * t398 * t35 * t208 - 0.8e1 * t331 * t964 * t52 - 0.4e1 * t503 * t1029 + 0.6e1 * t821 * t745 + 0.4e1 * t63 * t37 * t142 + 0.16e2 * t260 * t38 * t840;
1952:   t1068 = t207 * t347 - 0.2e1 * t164 * t702 - 0.2e1 * t331 * t964 * t73 + 0.8e1 * t374 * t30 * t52 + 0.16e2 * t278 * t903 + 0.2e1 * t863 * t923 + 0.6e1 * t445 * t141 * t165 - 0.2e1 * t164 * t90 * t100 + 0.6e1 * t331 * t74 - 0.2e1 * t182 * t668 - 0.2e1 * t115 * t41 * t204;
1953:   t1079 = t58 * t8;
1954:   t1091 = t807 * t29;
1955:   t1092 = t665 * t40;
1956:   t1101 = ZB * t91;
1957:   t1102 = t403 * nz;
1958:   t1105 = -0.4e1 * t58 * ZB * ZA * t64 - t82 * t850 + 0.2e1 * t821 * t860 + t81 * t51 * t793 + 0.2e1 * t3 * t25 * t1079 * t90 + t82 * t721 - 0.2e1 * t643 * t668 + 0.16e2 * t926 * t927 * t29 * t91 * t41 + 0.32e2 * t1091 * t1092 - 0.2e1 * t219 * t220 * t19 + 0.4e1 * t139 * ZA * t64 + 0.4e1 * t1101 * t1102;
1959:   t1108 = t849 * t72;
1960:   t1121 = t737 * t15;
1961:   t1124 = t29 * t12;
1962:   t1133 = t116 * t1108 - 0.8e1 * t475 * t209 - 0.32e2 * t807 * xc * t1092 + 0.2e1 * t278 * t269 * t73 + t82 * t812 - 0.6e1 * t56 * t131 + 0.2e1 * t253 * t1121 + 0.16e2 * t926 * t927 * t1124 * t41 + t168 * t263 - 0.2e1 * t616 * t827 + t81 * t981;
1963:   t1134 = t394 * t28;
1964:   t1159 = -0.8e1 * t1134 * t29 * t18 * t57 + t82 * t118 - 0.12e2 * t215 * t1018 + 0.2e1 * t602 * t801 - t168 * t341 + 0.2e1 * t67 * t58 * t64 + t168 * t344 - 0.6e1 * t174 * t368 * t208 + 0.16e2 * t553 * t903 + t116 * t790 - 0.4e1 * t36 * t38 * t800 * t15;
1965:   t1161 = nz * t83;
1966:   t1173 = ZB * t12;
1967:   t1196 = 0.4e1 * t1161 * ZB * t39 * ZA - 0.4e1 * t215 * t1029 - 0.8e1 * t488 * 0.3141592654e1 * t39 * xc + 0.32e2 * t821 * ZA * t8 * t1173 * t18 - 0.8e1 * t427 * t147 + 0.6e1 * t701 * t165 - 0.16e2 * t926 * t927 * t1124 * t18 - 0.8e1 * t1091 * t63 * t57 - 0.8e1 * t442 * t209 - 0.8e1 * t462 * t660 - 0.6e1 * t398 * t35 * t52;
1968:   t1228 = 0.2e1 * t413 * t305 - 0.8e1 * t648 * t961 - 0.16e2 * t87 * t27 * t23 * t28 * ZA * t29 + 0.4e1 * t189 * t1102 - 0.4e1 * t87 * t1079 * t212 * t879 + 0.2e1 * t164 * t948 - 0.2e1 * t70 * t923 + 0.2e1 * t164 * t322 + 0.2e1 * t446 * t1121 + 0.2e1 * t863 * t964 * t304 - t82 * t1108 + 0.16e2 * t676 * t490 * t19;
1969:   t1234 = t25 * ZB;
1970:   t1235 = t1234 * t28;
1971:   t1236 = t365 * t91;
1972:   t1240 = ZB * t121;
1973:   t1241 = t1240 * t77;
1974:   t1242 = t39 * t39;
1975:   t1243 = t12 * t1242;
1976:   t1244 = xc * t72;
1977:   t1245 = t1243 * t1244;
1978:   t1248 = t365 * t25;
1979:   t1252 = t243 * nz;
1980:   t1257 = t23 * t1;
1981:   t1258 = t1240 * t1257;
1982:   t1259 = t67 * t12;
1983:   t1260 = xc * t16;
1984:   t1268 = t1234 * t121;
1985:   t1269 = t1268 * t23;
1986:   t1272 = t1242 * t91;
1987:   t1280 = t67 * xc;
1988:   t1284 = t28 * t28;
1989:   t1285 = t67 * t1284;
1990:   t1287 = t1285 * t2 * ZB;
1991:   t1288 = t17 * xc;
1992:   t1289 = t1243 * t1288;
1993:   t1292 = 0.2e1 * t1235 * t1236 * t17 + 0.8e1 * t1241 * t1245 + 0.4e1 * t927 * t1248 * t91 - 0.2e1 * t1252 * ZB * t1242 * t91 - 0.8e1 * t1258 * t1259 * t1260 - 0.4e1 * t1235 * t2 * t83 * t39 + 0.16e2 * t1269 * t758 + 0.2e1 * t1252 * t189 * t1272 - 0.2e1 * t1252 * t83 * t1242 * ZB + 0.8e1 * t1258 * t630 * t1280 - 0.32e2 * t1287 * t1289;
1994:   t1293 = t365 * t83;
1995:   t1300 = ZA * t1284;
1996:   t1304 = t17 * t1242 * t25 * t12;
1997:   t1307 = t927 * t2;
1998:   t1311 = t23 * t2;
1999:   t1312 = t1300 * t1311;
2000:   t1316 = t1234 * t1284;
2001:   t1317 = t1316 * t1311;
2002:   t1321 = t1240 * t23;
2003:   t1331 = t1240 * t23 * t67;
2004:   t1332 = t40 * t1244;
2005:   t1338 = t1243 * t1260;
2006:   t1344 = -0.2e1 * t1235 * t1293 - 0.16e2 * t181 * t365 * t901 * t12 - 0.64e2 * t1300 * t258 * t1304 + 0.8e1 * t1307 * t613 * t39 + 0.64e2 * t1312 * t265 * t402 - 0.32e2 * t1317 * t1288 * t12 - 0.16e2 * t1321 * t67 * t39 * t1244 + 0.2e1 * t1235 * nz * t1272 * t17 + 0.16e2 * t1331 * t1332 + 0.64e2 * t1300 * t292 * t1304 - 0.8e1 * t1241 * t1338 - 0.2e1 * t243 * t1293 * ZB;
2007:   t1346 = t1316 * t2;
2008:   t1349 = t927 * nz;
2009:   t1350 = t25 * t1242;
2010:   t1354 = t1268 * t1257;
2011:   t1366 = t1268 * t1;
2012:   t1370 = t29 * t17;
2013:   t1371 = t1243 * t1370;
2014:   t1386 = -0.32e2 * t1346 * t1289 + 0.4e1 * t1349 * t1350 * t91 + 0.8e1 * t1354 * t1260 * t12 - 0.16e2 * t181 * nz * t901 * t1243 - 0.4e1 * t1235 * t2 * t91 * t39 + 0.8e1 * t1366 * t152 * t1242 + 0.32e2 * t1287 * t1371 + 0.8e1 * t1258 * t1280 * t152 - 0.8e1 * t1354 * t1260 * t91 + 0.128e3 * t1300 * t365 * xc * t1092 + 0.8e1 * t1366 * t1338;
2015:   t1387 = t1257 * t12;
2016:   t1391 = t1240 * t1;
2017:   t1399 = t1272 * t1260;
2018:   t1412 = t1285 * t1311;
2019:   t1427 = -0.8e1 * t1268 * t1387 * t16 - 0.8e1 * t1391 * t67 * t1242 * t1244 - 0.4e1 * t1134 * t1101 * t39 + 0.8e1 * t1241 * t1399 - 0.8e1 * t1258 * t596 + 0.4e1 * t927 * t1293 * t25 - 0.16e2 * t1331 * t758 + 0.8e1 * t1307 * t665 * t39 + 0.32e2 * t1412 * t1370 * t1173 + 0.8e1 * t1307 * t665 * t800 + 0.8e1 * t1391 * t1259 * t1242 * t16 - 0.8e1 * t1391 * t1259 * t1242 * t72;
2020:   t1456 = t365 * ZB;
2021:   t1468 = 0.4e1 * t927 * t1248 * t17 - 0.2e1 * t1235 * nz * t1242 * t91 + 0.8e1 * t1366 * t1244 * t1242 - 0.16e2 * t1269 * t134 * t39 + 0.8e1 * t1268 * t1257 * t72 * xc + 0.16e2 * t1321 * t1259 * t757 + 0.32e2 * t1317 * t1370 * t12 + 0.4e1 * t1349 * t613 * t1242 + 0.2e1 * t243 * t1456 * t17 - 0.64e2 * t1285 * t365 * t12 * t189 * t490 - 0.8e1 * t1354 * t152 * xc;
2022:   t1472 = t1316 * t365;
2023:   t1474 = t1124 * t39 * t17;
2024:   t1478 = t17 * t91;
2025:   t1504 = t72 * t39;
2026:   t1511 = 0.4e1 * t1134 * t189 * t800 + 0.64e2 * t1472 * t1474 + 0.4e1 * t1235 * t2 * t1478 * t39 + 0.4e1 * t1349 * t665 * t1242 - 0.8e1 * t1258 * t1280 * t72 + 0.2e1 * t1252 * t189 * t1242 + 0.2e1 * t243 * t365 * t189 * t91 + 0.4e1 * t927 * t365 * t1478 * t25 - 0.128e3 * t1300 * t1248 * t1474 - 0.2e1 * t1235 * t1236 + 0.16e2 * t1269 * t1504 * xc + 0.2e1 * t1235 * t365 * t17;
2027:   t1545 = -0.2e1 * t1235 * t1161 * t1242 + 0.4e1 * t1349 * t1350 * t1478 - 0.8e1 * t1366 * t1245 + 0.2e1 * t1235 * t556 * t1242 - 0.32e2 * t1412 * t402 * t726 - 0.8e1 * t1366 * t1399 + 0.8e1 * t1258 * t651 - 0.2e1 * t243 * t1456 * t91 + 0.8e1 * t1268 * t1387 * t72 - 0.16e2 * t1269 * t1332 + 0.4e1 * t1134 * t189 * t39 + 0.16e2 * t1269 * t152 * t39;
2028:   t1564 = t1260 * t800;
2029:   t1583 = 0.64e2 * t1285 * t1456 * t1474 - 0.64e2 * t1472 * t1288 * t40 - 0.8e1 * t1366 * t134 * t1242 + 0.8e1 * t1307 * t362 * t39 + 0.4e1 * t1235 * t2 * t17 * t39 + 0.32e2 * t1346 * t1371 - 0.16e2 * t1269 * t1564 - 0.16e2 * t1321 * t1259 * t1504 + 0.16e2 * t1331 * t1564 - 0.64e2 * t1312 * t29 * t25 * t402 - 0.4e1 * t1134 * t83 * t39 * ZB - 0.32e2 * t181 * t2 * t404;

2031:   _PC2B = (t1133 + t1196 + t1068 + t811 + t466 + t1012 + t381 + t162 + t249 + t533 + t844 + t104 + t1159 + t571 + t211 + t874 + t607 + t339 + t296 + t638 + t908 + t671 + t419 + t983 + t705 + t1105 + t501 + t778 + t1040 + t1228 + t741 + t944) / (t1292 + t1344 + t1386 + t1427 + t1468 + t1511 + t1545 + t1583);
2032:   /****************************************************************************************/
2033:   t1 = nz * nz;
2034:   t2 = t1 * nz;
2035:   t3 = t2 * nx;
2036:   t4 = nx * 0.3141592654e1;
2037:   t5 = t4 * xc;
2038:   t6 = PetscSinReal(t5);
2039:   t7 = 0.3141592654e1 * 0.3141592654e1;
2040:   t9 = t3 * t6 * t7;
2041:   t10 = xc * xc;
2042:   t11 = ZA * ZA;
2043:   t12 = t10 * t11;
2044:   t13 = nz * 0.3141592654e1;
2045:   t14 = PetscExpReal(t13);
2046:   t15 = t14 * t14;
2047:   t16 = xc * nz;
2048:   t18 = PetscExpReal(t16 * 0.3141592654e1);
2049:   t19 = t18 * t18;
2050:   t20 = t19 * t18;
2051:   t21 = t15 * t20;
2052:   t22 = t12 * t21;
2053:   t25 = nx * t6;
2054:   t26 = t1 * 0.3141592654e1;
2055:   t27 = t25 * t26;
2056:   t28 = ZA * ZB;
2057:   t29 = t18 * t15;
2058:   t30 = t28 * t29;
2059:   t33 = t25 * nz;
2060:   t34 = t11 * t15;
2061:   t35 = t19 * t19;
2062:   t36 = t35 * t18;
2063:   t40 = t25 * t1;
2064:   t41 = 0.3141592654e1 * t11;
2065:   t42 = t15 * t36;
2066:   t43 = t41 * t42;
2067:   t46 = nx * nx;
2068:   t47 = t1 * t46;
2069:   t48 = t47 * t11;
2070:   t49 = t7 * xc;
2071:   t50 = t35 * t15;
2072:   t51 = t49 * t50;
2073:   t55 = PetscSinReal(t4);
2074:   t56 = t46 * nx * t55;
2075:   t58 = t56 * nz * t7;
2076:   t59 = ZB * ZB;
2077:   t60 = t10 * t59;
2078:   t61 = t15 * t14;
2079:   t62 = t19 * t61;
2080:   t63 = t60 * t62;
2081:   t66 = t19 * t14;
2082:   t67 = t60 * t66;
2083:   t70 = t28 * t42;
2084:   t73 = PetscCosReal(t5);
2085:   t74 = t47 * t73;
2086:   t75 = t7 * t11;
2087:   t77 = t75 * t10 * t36;
2088:   t80 = t73 * t46;
2089:   t81 = t80 * nz;
2090:   t82 = 0.3141592654e1 * t59;
2091:   t83 = t82 * t42;
2092:   t87 = xc * t11;
2093:   t88 = t87 * t62;
2094:   t91 = nz * nx;
2095:   t92 = t55 * t61;
2096:   t96 = nx * t55;
2097:   t98 = t96 * t2 * t7;
2098:   t101 = xc * t59;
2099:   t102 = t101 * t62;
2100:   t108 = t1 * t1;
2101:   t109 = t108 * t7;
2102:   t111 = t59 * t35;
2103:   t112 = t111 * t15;
2104:   t115 = t35 * t20;
2105:   t123 = t1 * nx * t55;
2106:   t124 = t61 * t35;
2107:   t127 = t35 * t19;
2108:   t128 = t61 * t127;
2109:   t129 = t60 * t128;
2110:   t132 = t56 * t16;
2111:   t133 = t7 * t59;
2112:   t134 = t133 * t124;
2113:   t137 = 0.6e1 * t58 * t88 - 0.2e1 * t91 * t92 * t11 + 0.2e1 * t98 * t63 - 0.6e1 * t58 * t102 - 0.2e1 * t91 * t92 * t59 - 0.16e2 * t109 * xc * t112 - 0.2e1 * t91 * t6 * t115 * t59 + 0.12e2 * t40 * t83 + t123 * t41 * t124 - 0.2e1 * t58 * t129 + 0.4e1 * t132 * t134;
2114:   t139 = t56 * 0.3141592654e1;
2115:   t140 = t111 * t14;
2116:   t144 = t49 * t124;
2117:   t147 = t91 * t55;
2118:   t148 = t61 * ZA;
2119:   t154 = ZA * t115 * xc * ZB;
2120:   t157 = t7 * 0.3141592654e1;
2121:   t159 = t96 * t108 * t157;
2122:   t160 = t10 * xc;
2123:   t161 = t160 * t59;
2124:   t162 = t35 * t14;
2125:   t163 = t161 * t162;
2126:   t166 = t28 * t162;
2127:   t169 = t80 * t13;
2128:   t170 = t101 * t42;
2129:   t173 = t2 * t11;
2130:   t174 = t96 * t173;
2131:   t175 = t7 * t10;
2132:   t179 = t59 * t15;
2133:   t184 = t15 * t15;
2134:   t193 = t139 * t140 + 0.4e1 * t56 * nz * t11 * t144 + 0.4e1 * t147 * t148 * ZB + 0.4e1 * t27 * t154 + 0.8e1 * t159 * t163 - 0.12e2 * t147 * t166 + 0.2e1 * t169 * t170 - 0.16e2 * t174 * t175 * t124 + 0.2e1 * t33 * t179 * t20 - 0.2e1 * t33 * t11 * t36 * t184 + 0.2e1 * t56 * t61 * 0.3141592654e1 * ZA * ZB;
2135:   t194 = t173 * 0.3141592654e1;
2136:   t195 = xc * t15;
2137:   t196 = t195 * t19;
2138:   t202 = t15 * t115;
2139:   t203 = t28 * t202;
2140:   t206 = t96 * t26;
2141:   t207 = t14 * t127;
2142:   t208 = t101 * t207;
2143:   t211 = t12 * t128;
2144:   t218 = t11 * t61;
2145:   t219 = t218 * t35;
2146:   t221 = t108 * ZA;
2147:   t223 = t7 * ZB;
2148:   t224 = t223 * t50;
2149:   t227 = ZA * xc;
2150:   t228 = ZB * t15;
2151:   t229 = t228 * t36;
2152:   t230 = t227 * t229;
2153:   t233 = t87 * t207;
2154:   t236 = t6 * t11;
2155:   t240 = -0.4e1 * t194 * t196 + 0.4e1 * t194 * t195 * t127 + 0.4e1 * t33 * t203 - 0.12e2 * t206 * t208 + 0.2e1 * t58 * t211 - 0.16e2 * t47 * t10 * t133 * t50 + t139 * t219 - 0.32e2 * t221 * t10 * t224 - 0.4e1 * t169 * t230 - 0.6e1 * t98 * t233 + 0.2e1 * t91 * t236 * t20;
2156:   t244 = t227 * t228 * t20;
2157:   t252 = t184 * t18;
2158:   t253 = t101 * t252;
2159:   t256 = t35 * t35;
2160:   t257 = t256 * t14;
2161:   t258 = t28 * t257;
2162:   t261 = t108 * t11;
2163:   t263 = t7 * t35;
2164:   t268 = ZB * t61 * t35;
2165:   t273 = t96 * t108 * t160;
2166:   t274 = t157 * ZB;
2167:   t276 = t274 * t148 * t35;
2168:   t279 = t101 * t21;
2169:   t282 = 0.3141592654e1 * xc;
2170:   t283 = t59 * t36;
2171:   t284 = t282 * t283;
2172:   t289 = 0.4e1 * t169 * t244 - 0.4e1 * t132 * t133 * t162 - 0.2e1 * t147 * t140 - 0.2e1 * t27 * t253 + 0.2e1 * t139 * t258 + 0.16e2 * t261 * t10 * t263 * t15 - 0.16e2 * t206 * t227 * t268 - 0.16e2 * t273 * t276 - 0.6e1 * t27 * t279 - 0.4e1 * t40 * t284 - 0.32e2 * t9 * t230;
2173:   t290 = t1 * t11;
2174:   t291 = t96 * t290;
2175:   t297 = t59 * t61;
2176:   t298 = t297 * t127;
2177:   t300 = ZB * t36;
2178:   t301 = t227 * t300;
2179:   t304 = t1 * t59;
2180:   t305 = t184 * t35;
2181:   t310 = t46 * ZB;
2182:   t311 = t184 * ZA;
2183:   t312 = t310 * t311;
2184:   t314 = t60 * t21;
2185:   t317 = t1 * ZA;
2186:   t318 = ZB * t35;
2187:   t321 = t1 * t256;
2188:   t324 = t96 * t261;
2189:   t325 = t10 * t157;
2190:   t326 = t325 * t124;
2191:   t329 = -0.4e1 * t291 * t282 * t128 + t123 * t82 * t62 - t139 * t298 + 0.12e2 * t27 * t301 + t304 * t305 - 0.2e1 * t58 * t12 * t66 - 0.2e1 * t312 + 0.8e1 * t9 * t314 + 0.2e1 * t317 * t318 + 0.2e1 * t321 * t28 - 0.8e1 * t324 * t326;
2192:   t331 = t28 * t124;
2193:   t334 = 0.3141592654e1 * t15;
2194:   t335 = t334 * t127;
2195:   t338 = t35 * ZA;
2196:   t341 = t46 * t256;
2197:   t344 = t46 * t11;
2198:   t346 = t46 * t59;
2199:   t348 = t297 * t35;
2200:   t351 = ZA * t10;
2201:   t352 = t351 * t300;
2202:   t355 = t1 * ZB;
2203:   t362 = 0.12e2 * t147 * t331 - 0.4e1 * t173 * t335 - 0.2e1 * t310 * t338 - 0.2e1 * t341 * t28 - t344 * t305 - t346 * t305 + 0.2e1 * t147 * t348 + 0.16e2 * t9 * t352 + 0.2e1 * t355 * t311 + t290 * t305 + 0.2e1 * t33 * t34 * t20;
2204:   t363 = t36 * t184;
2205:   t364 = t87 * t363;
2206:   t368 = t47 * t73 * t7;
2207:   t373 = t160 * t157;
2208:   t374 = t373 * t124;
2209:   t377 = t311 * t35;
2210:   t380 = t12 * t62;
2211:   t386 = ZB * t10 * ZA * t15 * t20;
2212:   t389 = t87 * t66;
2213:   t393 = t56 * t1 * t10;
2214:   t401 = 0.2e1 * t27 * t364 - 0.16e2 * t368 * t279 - t123 * t41 * t257 + 0.8e1 * t324 * t374 + 0.2e1 * t355 * t377 - 0.2e1 * t98 * t380 - 0.16e2 * t9 * t386 + 0.2e1 * t58 * t389 + 0.16e2 * t393 * t276 + t123 * t82 * t162 - 0.2e1 * t33 * t179 * t36;
2215:   t412 = t11 * t14 * t127;
2216:   t416 = t11 * t19;
2217:   t417 = t416 * t61;
2218:   t421 = t96 * t2 * ZA;
2219:   t426 = t56 * nz * ZA;
2220:   t427 = t318 * t14;
2221:   t428 = t49 * t427;
2222:   t431 = t82 * t29;
2223:   t434 = t87 * t21;
2224:   t442 = 0.2e1 * t33 * t11 * t184 * t18 + 0.4e1 * t81 * t284 - t139 * t412 + 0.2e1 * t147 * t219 - 0.2e1 * t147 * t417 + 0.32e2 * t421 * t175 * t268 + 0.8e1 * t426 * t428 + 0.4e1 * t81 * t431 - 0.2e1 * t169 * t434 - 0.2e1 * t98 * t129 - 0.32e2 * t47 * t28 * t51;
2225:   t443 = t184 * t20;
2226:   t447 = t61 * 0.3141592654e1;
2227:   t448 = t447 * t11;
2228:   t450 = t49 * t268;
2229:   t453 = t60 * t42;
2230:   t456 = t41 * t202;
2231:   t463 = t101 * t443;
2232:   t469 = t41 * xc * t20;
2233:   t474 = -0.8e1 * t27 * t87 * t443 - t56 * t448 - 0.8e1 * t426 * t450 + 0.8e1 * t368 * t453 + 0.4e1 * t40 * t456 + 0.4e1 * t40 * t431 - 0.4e1 * t81 * t456 - 0.4e1 * t27 * t463 + 0.6e1 * t139 * t331 + 0.2e1 * t40 * t469 - 0.16e2 * t9 * t434;
2234:   t482 = t108 * t10;
2235:   t492 = nz * t46;
2236:   t493 = t492 * t11;
2237:   t495 = t282 * t19 * t184;
2238:   t498 = t56 * t290;
2239:   t499 = t325 * t162;
2240:   t502 = t416 * t14;
2241:   t504 = t60 * t207;
2242:   t507 = -t123 * t82 * t257 - 0.4e1 * t169 * t301 + t123 * t41 * t162 + 0.16e2 * t482 * t7 * t112 - 0.12e2 * t206 * t102 - t123 * t82 * t66 - 0.4e1 * t147 * t258 - 0.4e1 * t493 * t495 - 0.8e1 * t498 * t499 + t139 * t502 - 0.2e1 * t98 * t504;
2243:   t508 = t101 * t162;
2244:   t512 = t41 * t115 * xc;
2245:   t515 = t87 * t42;
2246:   t520 = ZB * t184;
2247:   t522 = t227 * t520 * t18;
2248:   t525 = t492 * t59;
2249:   t528 = t6 * t59;
2250:   t532 = t520 * t20;
2251:   t533 = t351 * t532;
2252:   t539 = t447 * t59;
2253:   t544 = 0.8e1 * t206 * t508 - 0.2e1 * t40 * t512 - 0.16e2 * t368 * t515 + 0.12e2 * t206 * t88 + 0.4e1 * t27 * t522 + 0.4e1 * t525 * t495 - 0.4e1 * t91 * t528 * t36 - 0.16e2 * t368 * t533 - 0.16e2 * t206 * t227 * t427 - t56 * t539 - 0.2e1 * t132 * t133 * t66;
2254:   t551 = t87 * t162;
2255:   t554 = t351 * t229;
2256:   t560 = t59 * t19;
2257:   t561 = t560 * t14;
2258:   t564 = t101 * t202;
2259:   t567 = t87 * t252;
2260:   t573 = t227 * t228 * t115;
2261:   t578 = 0.4e1 * t33 * t70 + 0.4e1 * t493 * t335 - 0.4e1 * t58 * t551 + 0.16e2 * t9 * t554 - 0.4e1 * t33 * t28 * t252 + 0.2e1 * t147 * t561 + 0.2e1 * t169 * t564 - 0.2e1 * t27 * t567 - 0.8e1 * t324 * t499 - 0.4e1 * t169 * t573 + 0.12e2 * t27 * t244;
2262:   t579 = t82 * t202;
2263:   t591 = t282 * t115 * t59;
2264:   t598 = t101 * t66;
2265:   t606 = -0.4e1 * t81 * t579 - 0.2e1 * t169 * t567 - 0.6e1 * t27 * t170 + 0.8e1 * t169 * t203 + 0.2e1 * t98 * t67 + 0.2e1 * t81 * t591 + 0.32e2 * t368 * t244 - 0.2e1 * t27 * t564 + 0.4e1 * t206 * t598 + 0.16e2 * t9 * t170 + 0.2e1 * t33 * t283 * t184;
2266:   t608 = t373 * t162;
2267:   t611 = t59 * t184;
2268:   t617 = t101 * t29;
2269:   t624 = t227 * ZB * t18 * t15;
2270:   t629 = t157 * t59;
2271:   t630 = t629 * t124;
2272:   t633 = t3 * t6;
2273:   t634 = t175 * t283;
2274:   t644 = 0.8e1 * t498 * t608 + 0.2e1 * t33 * t611 * t18 - 0.4e1 * t206 * t389 - 0.2e1 * t27 * t617 - 0.4e1 * t169 * t154 + 0.4e1 * t27 * t624 + 0.12e2 * t27 * t230 - 0.8e1 * t393 * t630 - 0.8e1 * t633 * t634 + 0.16e2 * t47 * t7 * t101 * t50 + 0.2e1 * t123 * t447 * t28;
2275:   t645 = t41 * t29;
2276:   t648 = t2 * 0.3141592654e1;
2277:   t649 = t648 * xc;
2278:   t650 = t560 * t184;
2279:   t656 = t56 * t1 * t157;
2280:   t659 = t87 * t128;
2281:   t662 = t96 * t482;
2282:   t663 = t629 * t162;
2283:   t671 = t161 * t124;
2284:   t674 = t218 * t127;
2285:   t679 = 0.4e1 * t81 * t645 - 0.4e1 * t649 * t650 - 0.8e1 * t169 * t70 + 0.8e1 * t656 * t163 - 0.2e1 * t98 * t659 - 0.8e1 * t662 * t663 - 0.32e2 * t421 * t175 * t427 - 0.2e1 * t147 * t502 + 0.8e1 * t656 * t671 + 0.2e1 * t147 * t674 - 0.16e2 * t368 * t386;
2286:   t714 = t334 * t19;
2287:   t719 = t12 * t42;
2288:   t722 = t304 * t35 - t346 * t35 + t341 * t59 - t344 * t35 + t344 * t256 + t346 * t184 - 0.16e2 * t368 * t554 - 0.16e2 * t48 * t175 * t50 + 0.4e1 * t525 * t714 - 0.2e1 * t58 * t659 + 0.8e1 * t368 * t719;
2289:   t730 = xc * t19;
2290:   t735 = t59 * t256 * t14;
2291:   t752 = 0.4e1 * t173 * t714 - 0.6e1 * t27 * t515 - 0.16e2 * t9 * t279 + 0.4e1 * t194 * t730 * t184 - t139 * t735 - 0.4e1 * t492 * t127 * t82 * xc - 0.4e1 * t98 * t508 - t123 * t41 * t207 - 0.2e1 * t147 * t298 + 0.8e1 * t368 * t314 + 0.6e1 * t132 * t133 * t207;
2292:   t755 = t28 * t21;
2293:   t759 = t274 * t338 * t14;
2294:   t767 = t11 * t35;
2295:   t768 = t767 * t14;
2296:   t778 = t560 * t61;
2297:   t781 = -0.2e1 * t58 * t504 - 0.8e1 * t27 * t755 + 0.16e2 * t662 * t759 + 0.12e2 * t291 * t282 * t207 - 0.6e1 * t27 * t434 + t139 * t768 - 0.8e1 * t498 * t326 + 0.4e1 * t33 * t611 * t20 + 0.2e1 * t81 * t512 - t139 * t561 + 0.2e1 * t147 * t778;
2298:   t786 = t12 * t443;
2299:   t790 = t282 * t59 * t20;
2300:   t796 = t59 * t14 * t127;
2301:   t806 = t41 * t21;
2302:   t811 = -0.8e1 * t393 * t663 + 0.8e1 * t368 * t786 + 0.2e1 * t81 * t790 + 0.4e1 * t169 * t624 + t139 * t796 + 0.2e1 * t206 * t258 - 0.2e1 * t40 * t591 - 0.8e1 * t662 * t630 - 0.4e1 * t33 * t30 - 0.4e1 * t40 * t806 + 0.8e1 * t9 * t786;
2303:   t819 = t282 * t15 * t127;
2304:   t822 = t101 * t363;
2305:   t830 = t11 * t256 * t14;
2306:   t835 = t227 * t532;
2307:   t842 = 0.2e1 * t33 * t11 * t18 * t15 + t123 * t41 * t66 - 0.4e1 * t493 * t819 - 0.2e1 * t27 * t822 - 0.16e2 * t368 * t170 - 0.4e1 * t169 * t463 - t139 * t830 - 0.4e1 * t649 * t179 * t127 + 0.12e2 * t27 * t835 - 0.16e2 * t368 * t434 - 0.2e1 * t40 * t790;
2308:   t845 = t87 * t202;
2309:   t854 = t338 * t15;
2310:   t859 = t12 * t207;
2311:   t868 = t139 * t348 - 0.2e1 * t27 * t845 + 0.8e1 * t169 * t755 - 0.2e1 * t58 * t380 + 0.6e1 * t206 * t331 + 0.8e1 * t310 * t854 - 0.2e1 * t169 * t822 + 0.2e1 * t98 * t859 + 0.8e1 * t159 * t671 + 0.8e1 * t74 * t634 - 0.2e1 * t169 * t253;
2312:   t880 = t60 * t443;
2313:   t891 = t101 * t128;
2314:   t894 = -t123 * t539 - 0.2e1 * t147 * t796 + 0.32e2 * t368 * t230 + t139 * t674 - 0.16e2 * t98 * t60 * t124 + 0.32e2 * t9 * t244 + 0.8e1 * t368 * t880 - 0.8e1 * t40 * t41 * xc * t36 - t123 * t82 * t128 - 0.6e1 * t58 * t233 + 0.2e1 * t58 * t891;
2315:   t903 = t179 * t19;
2316:   t920 = t56 * t1 * t160;
2317:   t925 = -0.2e1 * t174 * t175 * t66 - 0.4e1 * t493 * t714 + 0.4e1 * t649 * t903 - 0.4e1 * t81 * t43 + t123 * t82 * t207 + 0.4e1 * t206 * t891 - 0.16e2 * t273 * t759 - 0.8e1 * t27 * t203 + 0.32e2 * t221 * ZB * t51 - 0.16e2 * t920 * t759 - 0.8e1 * t9 * t453;
2318:   t932 = t87 * t29;
2319:   t945 = t82 * t21;
2320:   t953 = -0.16e2 * t920 * t276 - 0.8e1 * t169 * t30 - 0.8e1 * t633 * t77 - 0.2e1 * t27 * t932 - 0.4e1 * t174 * t49 * t162 + 0.8e1 * t206 * t87 * t124 - 0.2e1 * t147 * t768 + 0.4e1 * t169 * t522 - 0.12e2 * t81 * t945 + 0.4e1 * t33 * t28 * t115 + 0.4e1 * t525 * t819;
2321:   t971 = t282 * t127;
2322:   t978 = -0.6e1 * t98 * t102 + 0.2e1 * t169 * t515 - 0.2e1 * t310 * t377 + 0.2e1 * t147 * t830 + 0.8e1 * t368 * t22 - 0.2e1 * t169 * t617 + 0.16e2 * t662 * t276 - 0.8e1 * t355 * t854 + 0.4e1 * t493 * t971 - 0.16e2 * t9 * t533 - 0.2e1 * t169 * t279;
2323:   t997 = xc * t127;
2324:   t998 = t997 * t59;
2325:   t1003 = 0.4e1 * t40 * t579 + 0.2e1 * t169 * t845 + 0.16e2 * t9 * t515 + 0.8e1 * t206 * t551 + t123 * t41 * t128 + 0.16e2 * t98 * t60 * t162 + 0.2e1 * t169 * t364 - 0.2e1 * t169 * t932 + t139 * t778 + 0.4e1 * t648 * t998 + 0.2e1 * t147 * t412;
2326:   t1006 = t2 * t59;
2327:   t1017 = xc * t35;
2328:   t1033 = 0.4e1 * t1006 * t335 + 0.4e1 * t81 * t806 - 0.2e1 * t33 * t34 * t115 + 0.8e1 * t498 * t374 - 0.16e2 * t261 * t7 * t1017 * t15 + 0.8e1 * t206 * t101 * t124 - t123 * t448 + 0.2e1 * t147 * t735 + 0.6e1 * t98 * t208 + 0.6e1 * t98 * t88 - 0.4e1 * t33 * t755;
2329:   t1055 = -0.4e1 * t173 * t971 + 0.2e1 * t98 * t891 + 0.8e1 * t9 * t880 + 0.4e1 * t169 * t835 - t304 * t184 + t344 * t184 - t123 * t41 * t62 - 0.2e1 * t98 * t598 + 0.2e1 * t58 * t859 + 0.32e2 * t47 * t351 * t224 + 0.2e1 * t98 * t389;
2330:   t1070 = t15 * t19;
2331:   t1089 = -0.16e2 * t368 * t352 - 0.8e1 * t9 * t719 + 0.4e1 * t96 * t2 * xc * t134 - 0.2e1 * t91 * t236 * t115 + 0.4e1 * t27 * t573 + 0.4e1 * t493 * t282 * t1070 + 0.2e1 * t33 * t59 * t18 * t15 + 0.12e2 * t40 * t945 - 0.4e1 * t492 * xc * t82 * t1070 - 0.2e1 * t91 * t528 * t20 + 0.8e1 * t324 * t608;
2332:   t1113 = t123 * t82 * t124 + 0.8e1 * t421 * t428 - t139 * t417 + 0.4e1 * t40 * t645 + 0.16e2 * t393 * t759 - 0.2e1 * t33 * t179 * t115 - 0.4e1 * t525 * t335 + 0.4e1 * t33 * t28 * t36 - 0.4e1 * t1006 * t714 + 0.6e1 * t206 * t166 - 0.8e1 * t421 * t450;
2333:   t1119 = t321 * t46;
2334:   t1122 = t157 * t11;
2335:   t1123 = t1122 * t2;
2336:   t1124 = t184 * t46;
2337:   t1128 = t108 * nz;
2338:   t1132 = t7 * t7;
2339:   t1133 = t1132 * t11;
2340:   t1134 = t1133 * t108;
2341:   t1135 = t15 * t46;
2342:   t1139 = t7 * ZA;
2343:   t1140 = t1139 * ZB;
2344:   t1141 = t1 * t35;
2345:   t1145 = t629 * t2;
2346:   t1146 = t1135 * t730;
2347:   t1149 = t157 * t1128;
2348:   t1150 = t1149 * xc;
2349:   t1153 = t46 * xc;
2350:   t1154 = t1153 * t127;
2351:   t1158 = t184 * t1 * t46;
2352:   t1161 = t46 * t46;
2353:   t1162 = t35 * t1161;
2354:   t1166 = t7 * t1;
2355:   t1170 = -0.4e1 * t133 * t1119 + 0.16e2 * t1123 * t1124 * t730 - 0.8e1 * t1122 * t1128 * t196 - 0.64e2 * t1134 * t1135 * t1017 - 0.32e2 * t1140 * t1141 * t1135 + 0.16e2 * t1145 * t1146 - 0.8e1 * t1150 * t650 - 0.16e2 * t1123 * t1154 - 0.4e1 * t133 * t1158 - 0.16e2 * t1140 * t1162 * t15 + 0.8e1 * t1166 * t35 * t312;
2356:   t1171 = t1161 * t184;
2357:   t1175 = t1122 * nz;
2358:   t1176 = t15 * t1161;
2359:   t1180 = t1132 * ZA;
2360:   t1181 = t1180 * t355;
2361:   t1182 = t1176 * t1017;
2362:   t1185 = t1161 * xc;
2363:   t1189 = t1133 * t1;
2364:   t1192 = t108 * t1;
2365:   t1193 = t1132 * t1192;
2366:   t1195 = t10 * t35;
2367:   t1199 = t157 * t15;
2368:   t1203 = t1141 * t46;
2369:   t1211 = t184 * t108;
2370:   t1218 = 0.2e1 * t133 * t1171 * t35 + 0.8e1 * t1175 * t1176 * t997 + 0.64e2 * t1181 * t1182 - 0.8e1 * t1175 * t1185 * t127 - 0.32e2 * t1189 * t1182 - 0.64e2 * t1193 * ZA * t1195 * t228 + 0.8e1 * t1199 * t416 * t1128 + 0.8e1 * t1140 * t1203 - 0.4e1 * t75 * t1158 - 0.8e1 * t1199 * t560 * t1128 - 0.2e1 * t133 * t1211 - 0.8e1 * t1199 * t127 * t11 * t1128;
2371:   t1221 = t256 * t1161;
2372:   t1224 = t35 * t108;
2373:   t1233 = t7 * t256;
2374:   t1236 = -t75 * t1211 - t75 * t1221 - t133 * t1221 + t75 * t1224 - t75 * t1171 - t133 * t1171 + t133 * t1224 + t75 * t1162 - t75 * t108 * t256 + t133 * t1162 - t1233 * t59 * t108;
2375:   t1240 = t1135 * t1195;
2376:   t1252 = t629 * t127;
2377:   t1263 = t1171 * ZA;
2378:   t1280 = -0.128e3 * t1180 * ZB * t108 * t1240 + 0.32e2 * t1193 * t10 * t112 + 0.4e1 * t133 * t1203 + 0.4e1 * t109 * t256 * ZA * ZB - 0.8e1 * t1252 * nz * t15 * t1185 + 0.8e1 * t1175 * t1171 * t730 - 0.8e1 * t1175 * t1176 * t127 + 0.4e1 * t223 * t1263 - 0.8e1 * t1175 * t1176 * t730 + 0.8e1 * t1166 * ZA * t341 * ZB + 0.64e2 * t1134 * t1240 + 0.8e1 * t1122 * xc * t1128 * t127 * t15;
2379:   t1283 = t1199 * t19;
2380:   t1287 = t1199 * t127;
2381:   t1289 = t59 * nz * t1161;
2382:   t1293 = t157 * nz * xc;
2383:   t1304 = t1132 * t108;
2384:   t1310 = t263 * ZB;
2385:   t1316 = t2 * t15;
2386:   t1323 = -0.16e2 * t1283 * t1006 * t46 + 0.8e1 * t1287 * t1289 + 0.8e1 * t1293 * t127 * t1161 * t59 + 0.16e2 * t1123 * t1135 * t19 + 0.8e1 * t1293 * t560 * t1176 + 0.64e2 * t1304 * t59 * t1240 + 0.4e1 * t75 * t1203 + 0.4e1 * t1310 * t1263 + 0.4e1 * t223 * t338 * t108 - 0.16e2 * t1252 * t1316 * t1153 - 0.16e2 * t1310 * t221 * t15;
2387:   t1330 = t1132 * t15;
2388:   t1336 = t1132 * t1;
2389:   t1338 = t1162 * t179;
2390:   t1370 = 0.8e1 * t1175 * t1176 * t19 + 0.4e1 * t1139 * t318 * t1161 + 0.128e3 * t1330 * t318 * t108 * t46 * t227 - 0.32e2 * t1336 * xc * t1338 + 0.4e1 * t1233 * ZA * t1161 * ZB - 0.8e1 * t1287 * t59 * t1128 * xc + 0.2e1 * t75 * t305 * t108 + 0.8e1 * t1199 * t127 * t59 * t1128 - 0.8e1 * t1283 * t1289 - 0.8e1 * t1293 * t560 * t1171 + 0.4e1 * t133 * t35 * t1158 + 0.8e1 * t157 * t184 * t19 * t11 * t1128 * xc;
2391:   t1376 = t7 * t184;
2392:   t1380 = t1176 * t1195;
2393:   t1393 = t1330 * t35;
2394:   t1411 = 0.16e2 * t1145 * t1154 + 0.8e1 * t1149 * t998 + 0.4e1 * t1376 * t35 * t48 + 0.32e2 * t1189 * t1380 + 0.32e2 * t1193 * t11 * t1195 * t15 - 0.64e2 * t1304 * xc * t111 * t1135 - 0.16e2 * t1123 * t1146 + 0.64e2 * t1393 * t28 * t1192 * xc - 0.16e2 * t1123 * t1135 * t127 - 0.8e1 * t1122 * xc * t1128 * t127 - 0.32e2 * t1193 * xc * t112 + 0.16e2 * t1252 * t1316 * t46;
2395:   t1450 = 0.2e1 * t1376 * t767 * t1161 + 0.2e1 * t1376 * t111 * t108 + 0.4e1 * t223 * t311 * t108 + 0.4e1 * t109 * t35 * t520 * ZA + 0.16e2 * t1123 * t1135 * t997 - 0.64e2 * t1181 * t1380 + 0.8e1 * t1150 * t903 - 0.32e2 * t1393 * t11 * t1192 * xc - 0.16e2 * t157 * t2 * xc * t560 * t1124 + 0.8e1 * t223 * t184 * t317 * t46 + 0.32e2 * t1336 * t10 * t1338 - 0.4e1 * t75 * t1119;
2396:   _PC3B = (t606 + t722 + t1089 + t781 + 0.16e2 * t48 * t51 + t978 + t868 + t507 - t304 * t256 + 0.8e1 * t9 * t22 + t752 + 0.4e1 * t174 * t144 - 0.2e1 * t81 * t469 + 0.6e1 * t139 * t166 + t362 + 0.2e1 * t98 * t211 + t925 + t137 - t290 * t184 + 0.12e2 * t81 * t83 + t842 + 0.8e1 * t74 * t77 + 0.16e2 * t98 * t12 * t162 - 0.4e1 * t33 * t28 * t443 - 0.8e1 * t27 * t70 - 0.2e1 * t33 * t34 * t36 - 0.8e1 * t27 * t30 + 0.2e1 * t58 * t67 - 0.4e1 * t40 * t43 + 0.2e1 * t58 * t63 + t1033 - t290 * t256 + t290 * t35 + t193 + t1113 + t578 + t442 + t474 + t544 + t329 + t679 + t401 + t953 + t811 + t644 + t894 + t289 + t240 + t1055 + t1003) / (t1170 + t1218 + 0.2e1 * t1236 + t1280 + t1323 + t1370 + t1411 + t1450);
2397:   /****************************************************************************************/
2398:   t1 = nz * nz;
2399:   t2 = t1 * xc;
2400:   t3 = ZB * ZB;
2401:   t5 = t2 * 0.3141592654e1 * t3;
2402:   t6 = nx * 0.3141592654e1;
2403:   t7 = t6 * xc;
2404:   t8 = PetscCosReal(t7);
2405:   t9 = nx * nx;
2406:   t10 = t8 * t9;
2407:   t11 = nz * 0.3141592654e1;
2408:   t12 = PetscExpReal(t11);
2409:   t13 = t12 * t12;
2410:   t16 = PetscExpReal(xc * nz * 0.3141592654e1);
2411:   t17 = t16 * t16;
2412:   t18 = t17 * t16;
2413:   t19 = t17 * t17;
2414:   t20 = t19 * t18;
2415:   t21 = t13 * t20;
2416:   t22 = t10 * t21;
2417:   t25 = ZA * ZA;
2418:   t26 = t1 * t25;
2419:   t27 = xc * 0.3141592654e1;
2420:   t28 = t26 * t27;
2421:   t29 = t19 * t16;
2422:   t30 = t13 * t13;
2423:   t31 = t29 * t30;
2424:   t35 = t9 * nx;
2425:   t36 = t3 * t35;
2426:   t37 = PetscSinReal(t6);
2427:   t38 = t13 * t12;
2428:   t39 = t37 * t38;
2429:   t40 = t39 * t19;
2430:   t42 = t1 * t1;
2431:   t43 = nx * t42;
2432:   t44 = xc * xc;
2433:   t45 = t25 * t44;
2434:   t46 = t43 * t45;
2435:   t47 = 0.3141592654e1 * 0.3141592654e1;
2436:   t48 = t47 * t37;
2437:   t49 = t17 * t38;
2438:   t54 = 0.3141592654e1 * t35;
2439:   t55 = ZA * nz * t54;
2440:   t56 = t37 * ZB;
2441:   t57 = t19 * t12;
2442:   t61 = t25 * t8;
2443:   t62 = t61 * t9;
2444:   t63 = nz * t30;
2445:   t64 = t63 * t16;
2446:   t67 = t1 * nz;
2447:   t69 = t47 * ZB;
2448:   t70 = t67 * t44 * t69;
2449:   t75 = nx * t3;
2450:   t76 = t75 * t37;
2451:   t77 = t67 * 0.3141592654e1;
2452:   t78 = t19 * t19;
2453:   t79 = t78 * t12;
2454:   t80 = t77 * t79;
2455:   t82 = t3 * t38;
2456:   t84 = t54 * t37;
2457:   t87 = PetscSinReal(t7);
2458:   t88 = t29 * t87;
2459:   t89 = t47 * t44;
2460:   t93 = nx * t25;
2461:   t94 = t87 * t42;
2462:   t95 = t93 * t94;
2463:   t96 = t47 * xc;
2464:   t97 = t13 * t29;
2465:   t98 = t96 * t97;
2466:   t101 = t87 * t67;
2467:   t102 = t93 * t101;
2468:   t103 = t13 * t18;
2469:   t107 = t47 * t35;
2470:   t108 = t26 * t107;
2471:   t109 = t37 * t44;
2472:   t110 = t19 * t17;
2473:   t111 = t12 * t110;
2474:   t116 = t37 * t19 * t12;
2475:   t118 = t37 * xc;
2476:   t119 = ZB * t19;
2477:   t120 = t119 * t12;
2478:   t121 = t118 * t120;
2479:   t125 = xc * t3;
2480:   t126 = t1 * t47 * t125;
2481:   t127 = t35 * t37;
2482:   t128 = t38 * t19;
2483:   t129 = t127 * t128;
2484:   t132 = t26 * 0.3141592654e1;
2485:   t133 = t16 * t13;
2486:   t134 = t10 * t133;
2487:   t137 = 0.3141592654e1 * ZB;
2488:   t138 = t2 * t137;
2489:   t139 = ZA * t8;
2490:   t140 = t9 * t13;
2491:   t145 = t30 * t18;
2492:   t146 = t10 * t145;
2493:   t149 = t3 * t8;
2494:   t150 = t149 * t9;
2495:   t153 = 0.2e1 * t5 * t22 + 0.2e1 * t28 * t10 * t31 + t36 * t40 - 0.2e1 * t46 * t48 * t49 - 0.2e1 * t55 * t56 * t57 - 0.2e1 * t62 * t64 + 0.16e2 * t70 * t29 * ZA * t10 - t76 * t80 + t82 * nz * t84 + 0.8e1 * t43 * t3 * t88 * t89 + 0.16e2 * t95 * t98 + 0.2e1 * t102 * t27 * t103 - 0.2e1 * t108 * t109 * t111 + t36 * t116 + 0.8e1 * t55 * t121 - 0.4e1 * t126 * t129 - 0.4e1 * t132 * t134 - 0.4e1 * t138 * t139 * t140 * t20 + 0.8e1 * t28 * t146 - 0.2e1 * t150 * t64;
2496:   t154 = t42 * nz;
2497:   t155 = nx * t154;
2498:   t156 = t44 * xc;
2499:   t157 = t47 * 0.3141592654e1;
2500:   t158 = t156 * t157;
2501:   t159 = t155 * t158;
2502:   t162 = t56 * ZA * t19 * t12;
2503:   t165 = t77 * t49;
2504:   t167 = t1 * t3;
2505:   t168 = t167 * t89;
2506:   t169 = t127 * t49;
2507:   t172 = t37 * t67;
2508:   t173 = t75 * t172;
2509:   t174 = t38 * t110;
2510:   t175 = t27 * t174;
2511:   t179 = t47 * t25;
2512:   t181 = t10 * t97;
2513:   t184 = t27 * t31;
2514:   t187 = t67 * t47;
2515:   t188 = t44 * t3;
2516:   t189 = t187 * t188;
2517:   t192 = t25 * t35;
2518:   t193 = t37 * t17;
2519:   t194 = t193 * t12;
2520:   t196 = nx * ZA;
2521:   t197 = t196 * t172;
2522:   t198 = ZB * t38;
2523:   t199 = t198 * t19;
2524:   t204 = t1 * t12 * t110;
2525:   t207 = nx * ZB;
2526:   t209 = t1 * ZA;
2527:   t215 = t67 * t3;
2528:   t216 = t47 * t8;
2529:   t217 = t215 * t216;
2530:   t218 = t9 * xc;
2531:   t222 = nx * t67;
2532:   t223 = t222 * t27;
2533:   t224 = t3 * t87;
2534:   t228 = t167 * t107;
2535:   t232 = t26 * t96;
2536:   t235 = t207 * t94;
2537:   t236 = t47 * ZA;
2538:   t243 = xc * t13;
2539:   t244 = t243 * t29;
2540:   t248 = t25 * nz;
2541:   t249 = t248 * 0.3141592654e1;
2542:   t253 = ZB * ZA;
2543:   t254 = t253 * t8;
2544:   t255 = t9 * nz;
2545:   t256 = t30 * t16;
2546:   t260 = 0.2e1 * t207 * t37 * t209 * t128 + 0.2e1 * t5 * t134 - 0.16e2 * t217 * t218 * t97 - 0.2e1 * t223 * t224 * t31 - 0.2e1 * t228 * t109 * t174 - 0.2e1 * t232 * t169 - 0.16e2 * t235 * t236 * t44 * t30 * t18 - 0.4e1 * t196 * t101 * t137 * t244 + t249 * t169 + 0.8e1 * t168 * t129 + 0.4e1 * t254 * t255 * t256;
2547:   t263 = t43 * t179;
2548:   t267 = t3 * nz;
2549:   t268 = t267 * t54;
2550:   t269 = t118 * t57;
2551:   t272 = t39 * t1;
2552:   t274 = t67 * t25;
2553:   t275 = t274 * t158;
2554:   t278 = t75 * t87;
2555:   t279 = t77 * t103;
2556:   t282 = t25 * t38;
2557:   t285 = ZA * t38;
2558:   t290 = t267 * 0.3141592654e1;
2559:   t296 = t77 * t111;
2560:   t298 = t196 * t37;
2561:   t299 = t1 * ZB;
2562:   t303 = t37 * t42;
2563:   t304 = t196 * t303;
2564:   t308 = t77 * t57;
2565:   t310 = t26 * t89;
2566:   t313 = t77 * t128;
2567:   t316 = t101 * t27;
2568:   t319 = t93 * t87;
2569:   t320 = t77 * t97;
2570:   t323 = t127 * t57;
2571:   t326 = t10 * nz;
2572:   t329 = t118 * t174;
2573:   t332 = -0.8e1 * t263 * t109 * t57 - 0.4e1 * t268 * t269 + t93 * t272 + 0.8e1 * t275 * t129 - 0.4e1 * t278 * t279 + t282 * nz * t84 - 0.2e1 * t285 * nz * t54 * t56 - t290 * t169 - 0.2e1 * t196 * t38 * t172 * t137 + t76 * t296 - 0.2e1 * t298 * t299 * t79 + 0.8e1 * t304 * t96 * t120 + t76 * t308 - 0.2e1 * t310 * t169 - t76 * t313 + 0.2e1 * t75 * t18 * t316 + 0.4e1 * t319 * t320 + t249 * t323 - 0.2e1 * t25 * t18 * t326 + 0.2e1 * t228 * t329;
2574:   t335 = t75 * t101;
2575:   t336 = t27 * t21;
2576:   t342 = t77 * t133;
2577:   t347 = t209 * t137;
2578:   t350 = t9 * t1;
2579:   t351 = t149 * t350;
2580:   t355 = t37 * t78 * t12;
2581:   t359 = t93 * t303;
2582:   t367 = t172 * 0.3141592654e1;
2583:   t369 = t96 * t103;
2584:   t376 = t209 * t107;
2585:   t379 = t10 * t103;
2586:   t383 = t207 * t101;
2587:   t389 = 0.3141592654e1 * ZA;
2588:   t390 = t222 * t389;
2589:   t391 = t87 * ZB;
2590:   t398 = -0.2e1 * t102 * t336 + t93 * t38 * t367 + 0.16e2 * t95 * t369 - t82 * t127 - 0.8e1 * t197 * t27 * t120 + 0.8e1 * t376 * t121 - 0.8e1 * t189 * t379 - t249 * t129 - 0.4e1 * t383 * t27 * ZA * t16 * t13 - 0.8e1 * t390 * t391 * t21 - 0.2e1 * t197 * t137 * t57;
2591:   t402 = t39 * t110;
2592:   t404 = t193 * t38;
2593:   t406 = t127 * t174;
2594:   t408 = t167 * 0.3141592654e1;
2595:   t411 = t44 * t157;
2596:   t412 = t155 * t411;
2597:   t413 = t285 * t19;
2598:   t414 = t56 * t413;
2599:   t417 = ZA * t30;
2600:   t424 = t93 * t37;
2601:   t426 = t248 * t54;
2602:   t427 = t17 * t12;
2603:   t428 = t118 * t427;
2604:   t431 = t77 * t21;
2605:   t438 = ZA * t13;
2606:   t443 = t93 * t172;
2607:   t444 = t27 * t427;
2608:   t448 = t1 * t78 * t12;
2609:   t455 = t274 * t89;
2610:   t461 = t118 * t111;
2611:   t464 = -t36 * t402 + t36 * t404 - t249 * t406 - 0.4e1 * t408 * t134 + 0.16e2 * t412 * t414 - 0.4e1 * t383 * t27 * t417 * t18 + 0.2e1 * t28 * t22 - t424 * t80 - 0.2e1 * t426 * t428 + 0.4e1 * t278 * t431 + 0.4e1 * t254 * t255 * t103 + t290 * t323 + 0.4e1 * t383 * t27 * t438 * t20 + 0.2e1 * t443 * t444 + t424 * t448 - t36 * t194 - 0.32e2 * t235 * t236 * t243 * t18 + 0.8e1 * t455 * t181 - 0.4e1 * t359 * t96 * t128 - 0.2e1 * t426 * t461;
2612:   t469 = nz * t16 * t13;
2613:   t474 = t1 * t38;
2614:   t475 = t474 * t19;
2615:   t480 = t89 * t103;
2616:   t483 = t67 * ZA;
2617:   t484 = t483 * t411;
2618:   t485 = t127 * t120;
2619:   t488 = t127 * t111;
2620:   t497 = t77 * t427;
2621:   t502 = t27 * t97;
2622:   t508 = t1 * t19 * t12;
2623:   t511 = t155 * t25 * t156;
2624:   t512 = t157 * t37;
2625:   t513 = t512 * t128;
2626:   t527 = t1 * t17;
2627:   t528 = t527 * t38;
2628:   t530 = -t76 * t497 - 0.4e1 * t254 * t255 * t97 - 0.2e1 * t102 * t502 - 0.4e1 * t108 * t269 - t76 * t508 + 0.8e1 * t511 * t513 + 0.4e1 * t150 * t63 * t18 + 0.4e1 * t383 * t27 * t438 * t18 + 0.4e1 * t132 * t379 + 0.2e1 * t168 * t488 - t76 * t528;
2629:   t535 = t44 * t13;
2630:   t542 = t527 * t12;
2631:   t544 = nz * t13;
2632:   t545 = t544 * t20;
2633:   t548 = t75 * t303;
2634:   t549 = t96 * t111;
2635:   t552 = ZA * t35;
2636:   t553 = t552 * t37;
2637:   t562 = t43 * t96;
2638:   t563 = t3 * t37;
2639:   t564 = t563 * t128;
2640:   t579 = t474 * t110;
2641:   t590 = t9 * t30;
2642:   t591 = t590 * t18;
2643:   t595 = t127 * t427;
2644:   t598 = t77 * t174;
2645:   t600 = 0.4e1 * t5 * t146 + 0.16e2 * t235 * t236 * t535 * t18 + 0.8e1 * t455 * t146 + t76 * t542 - 0.2e1 * t150 * t545 + 0.2e1 * t548 * t549 - 0.2e1 * t553 * t120 + t290 * t488 - 0.8e1 * t274 * t47 * t44 * t29 * t10 - 0.4e1 * t562 * t564 - 0.2e1 * t132 * xc * t20 * t10 - 0.32e2 * t562 * ZA * t87 * ZB * t13 * t29 - 0.8e1 * t347 * t379 + t76 * t579 - 0.4e1 * t359 * t96 * t57 + 0.4e1 * t408 * t181 - 0.4e1 * t223 * t564 - 0.12e2 * t209 * t27 * ZB * t8 * t591 + 0.2e1 * t310 * t595 + t76 * t598;
2646:   t601 = t27 * t49;
2647:   t604 = t127 * t79;
2648:   t606 = ZB * t29;
2649:   t616 = t139 * t140 * t18;
2650:   t638 = t10 * t256;
2651:   t643 = t118 * t199;
2652:   t653 = t544 * t29;
2653:   t658 = t3 * t29;
2654:   t660 = t350 * t27;
2655:   t663 = -0.4e1 * t254 * t255 * t145 + 0.2e1 * t267 * t20 * t8 * t9 - 0.4e1 * t138 * t139 * t9 * t16 * t13 - 0.2e1 * t5 * t638 + 0.2e1 * t126 * t169 + 0.8e1 * t376 * t643 + 0.4e1 * t335 * t27 * t145 + 0.16e2 * t235 * t236 * t535 * t29 + 0.6e1 * t150 * t653 - 0.4e1 * t426 * t269 + 0.4e1 * t658 * t8 * t660;
2656:   t670 = t274 * t411;
2657:   t673 = t118 * t49;
2658:   t694 = t155 * t45;
2659:   t713 = nz * t29 * t30;
2660:   t717 = t20 * t87;
2661:   t723 = t512 * t57;
2662:   t728 = -0.2e1 * t443 * t175 - 0.8e1 * t670 * t129 + 0.2e1 * t426 * t673 - 0.16e2 * t207 * t88 * t42 * t47 * ZA * t44 + 0.4e1 * t254 * t255 * t21 + t249 * t595 + 0.8e1 * t25 * t29 * t8 * t660 + 0.2e1 * t268 * t461 + 0.8e1 * t189 * t181 - 0.8e1 * t694 * t513 + 0.2e1 * t198 * t553 - 0.12e2 * t606 * t139 * t660 - 0.2e1 * t359 * t549 + 0.4e1 * t138 * t139 * t590 * t16 + 0.8e1 * t93 * t29 * t94 * t89 - 0.2e1 * t150 * t713 + 0.2e1 * t222 * t3 * t717 * t27 + 0.8e1 * t670 * t323 + 0.8e1 * t694 * t723 - 0.2e1 * t62 * t653;
2663:   t734 = t43 * t89;
2664:   t735 = t563 * t427;
2665:   t740 = t75 * t94;
2666:   t744 = ZB * xc;
2667:   t750 = t563 * t57;
2668:   t754 = t218 * t103;
2669:   t771 = t127 * t199;
2670:   t776 = t89 * t174;
2671:   t791 = -0.4e1 * t207 * t717 * t77 * xc * ZA + 0.4e1 * t443 * t27 * t57 + t192 * t40 - 0.8e1 * t55 * t643 - 0.16e2 * t209 * t89 * t771 - 0.8e1 * t275 * t323 + 0.2e1 * t359 * t776 + 0.16e2 * t304 * t89 * t199 + 0.4e1 * t278 * t320 + 0.2e1 * t207 * t172 * t389 * t79 - 0.8e1 * t390 * t391 * t97;
2672:   t794 = t483 * t158;
2673:   t801 = t2 * 0.3141592654e1;
2674:   t818 = t215 * t411;
2675:   t827 = t96 * t174;
2676:   t837 = t37 * t12 * t110;
2677:   t845 = 0.16e2 * t794 * t485 + 0.8e1 * t159 * t564 - 0.8e1 * t455 * t379 - 0.2e1 * t801 * t3 * t20 * t10 - 0.4e1 * t132 * t22 - 0.8e1 * t734 * t564 - 0.8e1 * t187 * t44 * t658 * t10 - 0.8e1 * t412 * t564 + 0.4e1 * t132 * t181 - 0.8e1 * t818 * t129 + 0.2e1 * t46 * t48 * t427 - 0.4e1 * t75 * t29 * t316 - 0.2e1 * t359 * t827 - t290 * t595 + 0.16e2 * t217 * t754 - t424 * t542 - 0.8e1 * t734 * t750 - t192 * t837 - 0.4e1 * t254 * t255 * t133 + 0.8e1 * t304 * t96 * t199;
2678:   t864 = t544 * t18;
2679:   t867 = t3 * t18;
2680:   t884 = t27 * t256;
2681:   t891 = t187 * t744;
2682:   t894 = t563 * t49;
2683:   t900 = -0.2e1 * t263 * t428 + 0.2e1 * t228 * t428 - 0.6e1 * t223 * t224 * t103 - t192 * t404 + 0.2e1 * t268 * t428 - 0.2e1 * t335 * t884 - t424 * t296 + 0.2e1 * t93 * t20 * t316 - 0.32e2 * t891 * t616 + 0.2e1 * t562 * t894 - 0.2e1 * t801 * t867 * t10;
2684:   t904 = t27 * t111;
2685:   t907 = t118 * t128;
2686:   t915 = t89 * t145;
2687:   t947 = t139 * t140 * t29;
2688:   t952 = -0.2e1 * t173 * t904 + 0.4e1 * t426 * t907 + 0.12e2 * t253 * t10 * t1 * 0.3141592654e1 * t244 + 0.8e1 * t95 * t915 - t36 * t355 - 0.16e2 * t794 * t771 - 0.8e1 * t511 * t723 + 0.16e2 * t734 * t162 + t36 * t837 + 0.2e1 * t298 * t299 * t57 - 0.2e1 * t28 * t638 - 0.2e1 * t62 * t545 + 0.2e1 * t310 * t406 + 0.12e2 * t138 * t616 + 0.4e1 * t223 * t750 + t424 * t497 + 0.2e1 * t734 * t894 + 0.2e1 * t132 * xc * t18 * t10 - 0.16e2 * t70 * t947 + 0.32e2 * t891 * t947;
2689:   t969 = t67 * t157 * t156 * t3;
2690:   t974 = t27 * t133;
2691:   t1001 = -0.8e1 * t159 * t750 - 0.16e2 * t412 * t162 - t290 * t129 + 0.8e1 * t310 * t323 - 0.4e1 * t319 * t342 + t75 * t272 + t192 * t402 - 0.8e1 * t359 * t89 * t128 - 0.10e2 * t61 * t350 * t502 + 0.8e1 * t818 * t323 - 0.4e1 * t108 * t907;
2692:   t1042 = t89 * t97;
2693:   t1055 = -0.2e1 * t168 * t595 + 0.16e2 * t484 * t771 + 0.4e1 * t11 * t125 * t129 - 0.2e1 * t173 * t444 + 0.2e1 * ZB * nz * t54 * t37 * ZA * t79 - t424 * t475 + 0.2e1 * t562 * t735 - 0.2e1 * t548 * t776 + t424 * t204 + 0.2e1 * t25 * t20 * t326 + 0.8e1 * t383 * t389 * t133 + t75 * t38 * t367 + 0.2e1 * t62 * t469 + 0.2e1 * t197 * t137 * t128 - 0.2e1 * t102 * t884 - 0.2e1 * t5 * t379 - 0.8e1 * t740 * t1042 - 0.16e2 * t159 * t414 - 0.2e1 * ZB * t35 * t37 * t413 + 0.2e1 * t553 * ZB * t78 * t12;
2694:   t1096 = 0.2e1 * t443 * t904 - 0.2e1 * t268 * t329 - 0.2e1 * t443 * t601 + 0.2e1 * t102 * t974 - 0.2e1 * t263 * t673 + t424 * t165 + 0.2e1 * t62 * t713 + t424 * t308 - t424 * t313 + 0.8e1 * t347 * t22 - t424 * t598;
2695:   t1103 = t42 * t1 * t157;
2696:   t1104 = t1103 * t25;
2697:   t1108 = t3 * t19;
2698:   t1112 = nz * t47;
2699:   t1113 = t9 * t9;
2700:   t1118 = t42 * t157;
2701:   t1119 = t1118 * t9;
2702:   t1120 = t25 * xc;
2703:   t1121 = t13 * t110;
2704:   t1122 = t1120 * t1121;
2705:   t1125 = t47 * t47;
2706:   t1126 = t67 * t1125;
2707:   t1127 = t1113 * ZA;
2708:   t1128 = t1126 * t1127;
2709:   t1129 = t19 * t13;
2710:   t1130 = t744 * t1129;
2711:   t1133 = t154 * t1125;
2712:   t1134 = t1133 * t9;
2713:   t1135 = t45 * t1129;
2714:   t1138 = t154 * t47;
2715:   t1139 = t25 * t30;
2716:   t1142 = t1126 * t1113;
2717:   t1145 = t125 * t1129;
2718:   t1148 = t1103 * xc;
2719:   t1149 = t3 * t13;
2720:   t1150 = t1149 * t17;
2721:   t1153 = t25 * t78;
2722:   t1156 = -0.8e1 * t1104 * t243 * t17 + 0.4e1 * t187 * t1108 * t9 - 0.2e1 * t1112 * t3 * t1113 * t30 + 0.16e2 * t1119 * t1122 + 0.64e2 * t1128 * t1130 + 0.64e2 * t1134 * t1135 - 0.2e1 * t1138 * t1139 + 0.32e2 * t1142 * t1135 - 0.32e2 * t1142 * t1145 + 0.8e1 * t1148 * t1150 - 0.2e1 * t1138 * t1153;
2723:   t1157 = t25 * t13;
2724:   t1158 = t1157 * t17;
2725:   t1161 = t13 * t17;
2726:   t1162 = t1120 * t1161;
2727:   t1165 = t3 * t78;
2728:   t1170 = t42 * t67 * t1125;
2729:   t1172 = t1108 * t13;
2730:   t1175 = t1 * t157;
2731:   t1176 = t1175 * t1113;
2732:   t1182 = t1120 * t1129;
2733:   t1189 = t110 * t9 * xc;
2734:   t1192 = t1149 * t110;
2735:   t1201 = 0.8e1 * t1103 * t1158 - 0.16e2 * t1119 * t1162 - 0.2e1 * t1112 * t1165 * t1113 + 0.32e2 * t1170 * t44 * t1172 - 0.8e1 * t1176 * t1162 + 0.8e1 * t1104 * t243 * t110 - 0.64e2 * t1134 * t1182 - 0.64e2 * t1134 * t1145 + 0.16e2 * t1118 * t3 * t1189 + 0.16e2 * t1119 * t1192 - 0.4e1 * t187 * t1165 * t9 - 0.4e1 * t187 * t1139 * t9;
2736:   t1209 = t17 * t30;
2737:   t1210 = t125 * t1209;
2738:   t1213 = t1138 * ZA;
2739:   t1214 = ZB * t30;
2740:   t1218 = t1157 * t110;
2741:   t1226 = t3 * t30;
2742:   t1237 = t1170 * t25;
2743:   t1242 = 0.4e1 * t1112 * ZA * t119 * t1113 - 0.16e2 * t1119 * t1150 - 0.8e1 * t1176 * t1210 + 0.4e1 * t1213 * t1214 * t19 - 0.16e2 * t1119 * t1218 - 0.32e2 * t1142 * t1182 - 0.8e1 * t1103 * t1120 * t110 - 0.4e1 * t187 * t1226 * t9 + 0.8e1 * t1103 * t1192 + 0.4e1 * t1112 * ZB * t1113 * t30 * ZA - 0.32e2 * t1237 * xc * t19 * t13;
2744:   t1251 = t125 * t1121;
2745:   t1260 = t1120 * t1209;
2746:   t1263 = t1139 * t19;
2747:   t1282 = 0.8e1 * t1103 * t110 * t3 * xc + 0.8e1 * t1104 * xc * t17 * t30 - 0.8e1 * t1176 * t1251 + 0.16e2 * t1119 * t1158 + 0.4e1 * t1112 * t78 * t1127 * ZB + 0.16e2 * t1119 * t1260 + 0.2e1 * t1138 * t1263 - 0.32e2 * t1170 * xc * t1172 - 0.16e2 * t1213 * t119 * t13 + 0.4e1 * t1138 * t1214 * ZA + 0.32e2 * t1237 * t44 * t19 * t13 - 0.16e2 * t1118 * t25 * t1189;
2748:   t1287 = t188 * t1129;
2749:   t1292 = t25 * t19;
2750:   t1296 = t187 * t9;
2751:   t1297 = t1226 * t19;
2752:   t1311 = t1112 * t1113;
2753:   t1317 = -0.8e1 * t1176 * t1150 + 0.32e2 * t1142 * t1287 - 0.8e1 * t1103 * t1150 + 0.2e1 * t1112 * t1292 * t1113 + 0.4e1 * t1296 * t1297 + 0.8e1 * t1176 * t1192 + 0.4e1 * t1296 * t1263 + 0.8e1 * t1176 * t1158 - 0.8e1 * t1175 * t25 * t1113 * xc * t110 + 0.2e1 * t1311 * t1297 + 0.2e1 * t1112 * t1108 * t1113;
2754:   t1320 = t253 * t1129;
2755:   t1328 = t253 * t30 * t19;
2756:   t1333 = t125 * t1161;
2757:   t1343 = ZB * t44 * t1129;
2758:   t1350 = -0.8e1 * t1176 * t1218 - 0.16e2 * t1311 * t1320 + 0.8e1 * t1176 * t1260 - 0.16e2 * t1119 * t1210 + 0.4e1 * t1311 * t1328 + 0.2e1 * t1311 * t1263 + 0.8e1 * t1176 * t1333 + 0.8e1 * t187 * ZB * t417 * t9 - 0.2e1 * t1138 * t1165 - 0.64e2 * t1128 * t1343 + 0.64e2 * t1134 * t1287 + 0.2e1 * t1138 * t1108;
2759:   t1369 = t1133 * t9 * ZA;
2760:   t1378 = t187 * ZA;
2761:   t1383 = t1170 * ZA;
2762:   t1388 = 0.2e1 * t1138 * t1297 - 0.8e1 * t1148 * t1192 + 0.2e1 * t1138 * t1292 - 0.16e2 * t1119 * t1251 + 0.8e1 * t1175 * xc * t110 * t1113 * t3 - 0.2e1 * t1112 * t1153 * t1113 + 0.128e3 * t1369 * t1130 + 0.16e2 * t1119 * t1333 + 0.4e1 * t1138 * t78 * ZA * ZB + 0.8e1 * t1378 * t78 * t9 * ZB - 0.64e2 * t1383 * t1343 + 0.64e2 * t1383 * t1130;
2763:   t1420 = 0.4e1 * t1138 * t119 * ZA - 0.128e3 * t1369 * t1343 - 0.4e1 * t187 * t1153 * t9 - 0.2e1 * t1138 * t1226 + 0.8e1 * t1296 * t1328 - 0.2e1 * t1112 * t1139 * t1113 - 0.8e1 * t1148 * t3 * t17 * t30 - 0.32e2 * t1296 * t1320 + 0.8e1 * t1176 * t1122 + 0.4e1 * t187 * t1292 * t9 + 0.8e1 * t1378 * t119 * t9 - 0.8e1 * t1103 * t1218;

2765:   _PC4B = (-t424 * t508 + 0.8e1 * t412 * t750 - 0.2e1 * t232 * t595 - 0.4e1 * t126 * t323 + t1096 - t76 * t204 + t728 + 0.2e1 * t548 * t827 + 0.2e1 * t150 * t469 + t398 + 0.8e1 * t189 * t146 + t260 - 0.2e1 * t351 * t184 - 0.2e1 * t268 * t673 - 0.4e1 * t319 * t279 + t464 - 0.2e1 * t108 * t461 + 0.16e2 * t740 * t369 + 0.16e2 * t274 * t216 * t754 - 0.16e2 * t70 * t139 * t591 + 0.2e1 * t55 * t56 * t128 - 0.2e1 * t359 * t89 * t111 + 0.2e1 * t734 * t563 * t111 + 0.6e1 * t223 * t224 * t97 + 0.8e1 * t383 * t389 * t103 + 0.4e1 * t606 * ZA * t326 - 0.2e1 * t93 * t18 * t316 - 0.4e1 * t443 * t27 * t128 + 0.8e1 * t197 * t27 * t199 + 0.8e1 * t108 * t109 * t128 - t249 * t604 + 0.16e2 * t70 * t616 - 0.8e1 * t969 * t323 + t845 - t424 * t579 + 0.16e2 * t159 * t162 + t290 * t406 - 0.6e1 * t150 * t864 + t192 * t116 + 0.2e1 * t867 * t326 - 0.4e1 * t658 * t326 - 0.2e1 * t351 * t502 - t76 * t165 + t900 + 0.8e1 * t168 * t323 + t791 + 0.8e1 * t740 * t915 - 0.4e1 * t562 * t750 - 0.4e1 * t278 * t342 + 0.4e1 * t319 * t431 + 0.2e1 * t173 * t175 + t424 * t528 + 0.8e1 * t969 * t129 - 0.8e1 * t347 * t181 + t332 + t530 - 0.2e1 * t108 * t329 - 0.2e1 * t207 * t38 * t37 * t1 * ZA + t1001 + 0.4e1 * t408 * t379 + t76 * t448 + 0.2e1 * t102 * t184 + 0.2e1 * t426 * t329 + 0.16e2 * t740 * t98 - t282 * t127 - 0.16e2 * t1 * t44 * t69 * t552 * t116 + 0.2e1 * t168 * t169 + 0.2e1 * t28 * t134 - t290 * t604 - 0.16e2 * t484 * t485 - 0.8e1 * t740 * t480 + 0.2e1 * t173 * t601 - 0.2e1 * t335 * t336 + t600 + 0.2e1 * t62 * t864 + t952 + 0.8e1 * t347 * t134 - t192 * t355 + t192 * t194 + 0.2e1 * t228 * t461 + t663 + 0.4e1 * t383 * t27 * t417 * t16 + 0.4e1 * t138 * t20 * ZA * t10 - 0.4e1 * t20 * ZB * ZA * t326 + 0.4e1 * t196 * t88 * t77 * t744 - 0.16e2 * t67 * xc * t179 * t181 - 0.8e1 * t95 * t480 - t249 * t488 - t76 * t475 + t1055 - 0.4e1 * t408 * t22 - 0.10e2 * t28 * t379 + 0.2e1 * t335 * t974 + t153 - 0.8e1 * t95 * t1042 - 0.2e1 * t734 * t735) / (t1156 + t1201 + t1242 + t1282 + t1317 + t1350 + t1388 + t1420);
2766:   /****************************************************************************************/
2767:   /****************************************************************************************/

2769:   if (x>xc) {
2770:     _PC1=_PC1B; _PC2=_PC2B; _PC3=_PC3B; _PC4=_PC4B; Z=ZB;
2771:   }
2772:   else {
2773:     _PC1=_PC1A; _PC2=_PC2A; _PC3=_PC3A; _PC4=_PC4A; Z=ZA;
2774:   }
2775:   /****************************************************************************************/
2776:   /****************************************************************************************/
2777:   t1 = nz * nz;
2778:   t2 = t1 * t1;
2779:   t3 = t2 * nz;
2780:   t4 = x * t3;
2781:   t5 = 0.3141592654e1 * 0.3141592654e1;
2782:   t6 = t5 * 0.3141592654e1;
2783:   t11 = _PC3 * t6;
2784:   t12 = x * nz;
2785:   t13 = nx * nx;
2786:   t14 = t13 * t13;
2787:   t15 = t12 * t14;
2788:   t19 = PetscExpReal(t12 * 0.3141592654e1);
2789:   t20 = t19 * t19;
2790:   t21 = t4 * t20;
2791:   t24 = _PC1 * t5;
2792:   t25 = Z * t20;
2793:   t29 = _PC1 * t6;
2794:   t30 = t29 * Z;
2795:   t31 = t1 * nz;
2796:   t32 = x * t31;
2797:   t33 = t32 * t13;
2798:   t36 = t11 * x;
2799:   t41 = nz * t20;
2800:   t45 = t6 * _PC4;
2801:   t49 = t20 * t1;
2802:   t51 = _PC2 * Z;
2803:   t55 = -0.2e1 * t4 * t6 * _PC2 * Z - 0.2e1 * t11 * t15 - 0.2e1 * t11 * t21 + 0.2e1 * t24 * t25 * t14 - t13 + 0.4e1 * t30 * t33 - 0.4e1 * t36 * t31 * t20 * t13 - 0.2e1 * t36 * t41 * t14 - 0.2e1 * t4 * t45 * t20 - t49 - 0.2e1 * t4 * t6 * t51 * t20;
2804:   t58 = t32 * t6;
2805:   t59 = _PC4 * t20;
2806:   t63 = t20 * t13;
2807:   t67 = t12 * t6;
2808:   t68 = t20 * t14;
2809:   t87 = t49 * t13;
2810:   t90 = -0.4e1 * t11 * t33 - 0.4e1 * t58 * t59 * t13 - 0.4e1 * t58 * t51 * t63 - 0.2e1 * t67 * t51 * t68 + 0.4e1 * t32 * t45 * t13 - 0.2e1 * t67 * t59 * t14 - 0.2e1 * t30 * t21 + t1 + 0.2e1 * t24 * t25 * t2 + 0.2e1 * t12 * t45 * t14 + 0.4e1 * t24 * Z * t87;
2811:   t106 = _PC3 * t5;
2812:   t120 = -0.4e1 * t30 * t32 * t63 + t63 + 0.4e1 * t24 * Z * t1 * t13 + 0.2e1 * t29 * Z * x * t3 - 0.4e1 * t58 * t51 * t13 - 0.2e1 * t106 * t2 + t32 * 0.3141592654e1 - 0.2e1 * t106 * t14 - 0.2e1 * t30 * t12 * t68 - 0.2e1 * t67 * t51 * t14 + 0.4e1 * t106 * t87;
2813:   t129 = PetscSinReal(nx * 0.3141592654e1 * x);
2814:   t155 = 0.2e1 * t30 * t15 + x * 0.3141592654e1 * t41 * t13 - 0.4e1 * t19 * nx * t129 * nz + t32 * 0.3141592654e1 * t20 + 0.2e1 * t106 * t68 + 0.2e1 * t106 * t20 * t2 - 0.4e1 * t106 * t1 * t13 - 0.2e1 * t11 * t4 + 0.2e1 * t4 * t45 + 0.2e1 * t24 * Z * t2 + 0.2e1 * t24 * Z * t14 + t12 * 0.3141592654e1 * t13;
2815:   t158 = t5 * Z;

2817:   u1 = (t55 + t90 + t120 + t155) / (0.4e1 * t158 * t19 * t2 + 0.8e1 * t158 * t19 * t1 * t13 + 0.4e1 * t158 * t19 * t14);
2818:   /****************************************************************************************/
2819:   /****************************************************************************************/
2820:   t1 = nz * nz;
2821:   t2 = t1 * nz;
2822:   t3 = x * t2;
2823:   t4 = 0.3141592654e1 * 0.3141592654e1;
2824:   t5 = t4 * 0.3141592654e1;
2825:   t6 = t3 * t5;
2826:   t7 = _PC2 * Z;
2827:   t8 = nx * nx;
2828:   t12 = t1 * t1;
2829:   t13 = t12 * nz;
2830:   t14 = x * t13;
2831:   t15 = t5 * _PC4;
2832:   t16 = x * nz;
2833:   t18 = PetscExpReal(t16 * 0.3141592654e1);
2834:   t19 = t18 * t18;
2835:   t23 = t16 * t5;
2836:   t24 = t8 * t8;
2837:   t28 = _PC3 * t5;
2838:   t29 = t14 * t19;
2839:   t32 = _PC1 * t5;
2840:   t33 = t32 * Z;
2841:   t34 = t16 * t24;
2842:   t37 = _PC4 * t19;
2843:   t45 = _PC2 * t4;
2844:   t53 = t19 * t8;
2845:   t58 = _PC4 * t4;
2846:   t60 = t1 * t19 * t8;
2847:   t63 = t19 * t24;
2848:   t67 = t3 * t8;
2849:   t73 = nz * t19;
2850:   t86 = t28 * x;
2851:   t91 = 0.4e1 * t58 * t60 + 0.2e1 * t33 * t16 * t63 + 0.4e1 * t33 * t67 + 0.2e1 * t33 * t29 - x * 0.3141592654e1 * t73 * t8 - 0.2e1 * t53 + 0.2e1 * t32 * Z * x * t13 - 0.2e1 * t58 * t12 - 0.2e1 * t58 * t24 + t3 * 0.3141592654e1 + 0.4e1 * t86 * t2 * t19 * t8;
2852:   t94 = Z * t12;
2853:   t121 = -0.2e1 * t8 + 0.2e1 * t45 * t94 * t19 + 0.2e1 * t14 * t5 * t7 * t19 + 0.4e1 * t6 * t7 * t53 + 0.2e1 * t23 * t7 * t63 - 0.4e1 * t28 * t67 + 0.2e1 * t45 * t94 + 0.2e1 * t58 * t12 * t19 + t16 * 0.3141592654e1 * t8 + 0.2e1 * t14 * t15 - 0.2e1 * t28 * t14;
2854:   t146 = PetscCosReal(nx * 0.3141592654e1 * x);
2855:   t156 = -t3 * 0.3141592654e1 * t19 + 0.2e1 * t58 * t63 - 0.4e1 * t58 * t1 * t8 + 0.4e1 * t45 * Z * t1 * t8 - 0.2e1 * t28 * t34 + 0.2e1 * t86 * t73 * t24 + 0.4e1 * t3 * t15 * t8 + 0.4e1 * t45 * Z * t60 + 0.4e1 * t18 * t146 * t8 + 0.2e1 * t45 * Z * t24 + 0.2e1 * t16 * t15 * t24;
2856:   t159 = t4 * Z;

2858:   u2 = (-0.4e1 * t6 * t7 * t8 + 0.2e1 * t14 * t15 * t19 - 0.2e1 * t23 * t7 * t24 + 0.2e1 * t28 * t29 + 0.2e1 * t33 * t34 + 0.4e1 * t6 * t37 * t8 - 0.2e1 * t14 * t5 * _PC2 * Z + 0.2e1 * t45 * Z * t19 * t24 + 0.2e1 * t23 * t37 * t24 + 0.4e1 * t33 * t3 * t53 + t91 + t121 + t156) / (0.4e1 * t159 * t18 * t12 + 0.8e1 * t159 * t18 * t1 * t8 + 0.4e1 * t159 * t18 * t24);
2859:   /****************************************************************************************/
2860:   /****************************************************************************************/
2861:   t1 = 0.3141592654e1 * 0.3141592654e1;
2862:   t2 = t1 * 0.3141592654e1;
2863:   t3 = _PC1 * t2;
2864:   t4 = t3 * Z;
2865:   t5 = nz * nz;
2866:   t6 = t5 * t5;
2867:   t7 = t6 * nz;
2868:   t8 = x * t7;
2869:   t9 = x * nz;
2870:   t11 = PetscExpReal(t9 * 0.3141592654e1);
2871:   t12 = t11 * t11;
2872:   t13 = t8 * t12;
2873:   t16 = t5 * nz;
2874:   t17 = x * t16;
2875:   t18 = t17 * t2;
2876:   t19 = _PC4 * t12;
2877:   t20 = nx * nx;
2878:   t24 = t2 * _PC4;
2879:   t28 = _PC3 * t2;
2880:   t29 = t28 * x;
2881:   t30 = t12 * nz;
2882:   t31 = t20 * t20;
2883:   t40 = _PC2 * Z;
2884:   t44 = t9 * t2;
2885:   t48 = t12 * t20;
2886:   t52 = t17 * t20;
2887:   t57 = -0.2e1 * t4 * t13 - 0.4e1 * t18 * t19 * t20 - 0.2e1 * t8 * t24 * t12 - 0.2e1 * t29 * t30 * t31 + 0.2e1 * t8 * t2 * _PC2 * Z - 0.2e1 * t8 * t2 * t40 * t12 - 0.2e1 * t44 * t19 * t31 - 0.4e1 * t18 * t40 * t48 + t20 + 0.4e1 * t28 * t52 + t17 * 0.3141592654e1 * t12;
2888:   t58 = t9 * t31;
2889:   t61 = _PC3 * t1;
2890:   t62 = t12 * t31;
2891:   t73 = t5 * t20;
2892:   t78 = _PC1 * t1;
2893:   t90 = Z * t12;
2894:   t94 = 0.2e1 * t28 * t58 + 0.2e1 * t61 * t62 + 0.2e1 * t61 * t12 * t6 - 0.4e1 * t4 * t17 * t48 + 0.2e1 * t28 * t8 + 0.4e1 * t61 * t73 - 0.2e1 * t8 * t24 - 0.2e1 * t78 * Z * t6 - 0.2e1 * t44 * t40 * t62 - 0.2e1 * t78 * Z * t31 - t9 * 0.3141592654e1 * t20 + 0.2e1 * t78 * t90 * t6;
2895:   t101 = PetscCosReal(nx * 0.3141592654e1 * x);
2896:   t102 = t11 * t101;
2897:   t109 = t12 * t5;
2898:   t110 = t109 * t20;
2899:   t128 = 0.2e1 * t61 * t6 - t17 * 0.3141592654e1 + 0.2e1 * t102 * t5 - 0.4e1 * t17 * t24 * t20 + 0.4e1 * t78 * Z * t110 - 0.2e1 * t9 * t24 * t31 - 0.4e1 * t4 * t52 - 0.2e1 * t4 * t9 * t62 + x * 0.3141592654e1 * t30 * t20 - t5 - 0.4e1 * t78 * Z * t5 * t20;
2900:   t156 = 0.2e1 * t78 * t90 * t31 - 0.2e1 * t3 * Z * x * t7 + t48 + 0.4e1 * t61 * t110 + 0.4e1 * t18 * t40 * t20 - 0.2e1 * t102 * t20 + 0.2e1 * t61 * t31 + 0.2e1 * t44 * t40 * t31 - t109 - 0.2e1 * t4 * t58 - 0.2e1 * t28 * t13 - 0.4e1 * t29 * t16 * t12 * t20;
2901:   t159 = t1 * t11;

2903:   u3 = (t57 + t94 + t128 + t156) / (0.4e1 * t159 * t6 + 0.8e1 * t159 * t73 + 0.4e1 * t159 * t31);
2904:   /****************************************************************************************/
2905:   /****************************************************************************************/
2906:   t1 = _PC2 * Z;
2907:   t2 = 0.3141592654e1 * 0.3141592654e1;
2908:   t3 = t2 * 0.3141592654e1;
2909:   t4 = nz * nz;
2910:   t5 = t4 * t4;
2911:   t6 = t5 * t4;
2912:   t8 = t3 * t6 * x;
2913:   t11 = x * t4;
2914:   t12 = t11 * t3;
2915:   t15 = PetscExpReal(x * nz * 0.3141592654e1);
2916:   t16 = t15 * t15;
2917:   t17 = _PC3 * t16;
2918:   t18 = nx * nx;
2919:   t19 = t18 * t18;
2920:   t23 = t5 * nz;
2921:   t24 = t2 * t23;
2922:   t28 = t1 * t3;
2923:   t29 = t6 * x;
2924:   t30 = t29 * t16;
2925:   t33 = _PC4 * t3;
2926:   t34 = t5 * x;
2927:   t35 = t34 * t18;
2928:   t41 = PetscSinReal(nx * 0.3141592654e1 * x);
2929:   t47 = t11 * t19;
2930:   t54 = t3 * _PC3;
2931:   t57 = 0.2e1 * t1 * t8 + 0.2e1 * t12 * t17 * t19 + 0.2e1 * t1 * t24 * t16 + 0.2e1 * t28 * t30 - 0.4e1 * t33 * t35 + 0.2e1 * t15 * nx * t41 * t4 + 0.4e1 * t28 * t35 - 0.2e1 * t33 * t47 - 0.2e1 * t1 * t24 - 0.2e1 * t33 * t29 + 0.2e1 * t29 * t54;
2932:   t58 = 0.3141592654e1 * t16;
2933:   t60 = t2 * _PC4;
2934:   t69 = t4 * nz;
2935:   t73 = t1 * t2;
2936:   t75 = t69 * t16 * t18;
2937:   t79 = x * t16;
2938:   t83 = nz * t16;
2939:   t84 = t83 * t19;
2940:   t95 = -t34 * t58 + 0.2e1 * t60 * t23 * t16 + 0.2e1 * t60 * nz * t19 - t11 * 0.3141592654e1 * t18 + 0.4e1 * t60 * t69 * t18 + 0.4e1 * t73 * t75 + 0.4e1 * t33 * t5 * t79 * t18 + 0.2e1 * t73 * t84 + 0.2e1 * t60 * t84 + 0.2e1 * t33 * t4 * t79 * t19 + 0.4e1 * t60 * t75;
2941:   t97 = t34 * t3;
2942:   t101 = Z * _PC1;
2943:   t102 = t16 * t19;
2944:   t106 = t16 * t18;
2945:   t127 = t2 * t69;
2946:   t131 = t2 * nz;
2947:   t135 = 0.4e1 * t97 * t17 * t18 + 0.2e1 * t12 * t101 * t102 + 0.4e1 * t28 * t34 * t106 + 0.2e1 * t28 * t11 * t102 - 0.2e1 * t29 * t3 * Z * _PC1 - 0.4e1 * t97 * t101 * t18 - 0.2e1 * t12 * t101 * t19 + 0.2e1 * t60 * t23 - 0.2e1 * t83 * t18 - 0.4e1 * t1 * t127 * t18 - 0.2e1 * t1 * t131 * t19;
2948:   t164 = 0.2e1 * t28 * t47 + 0.2e1 * t11 * t54 * t19 + 0.2e1 * t8 * t101 * t16 + 0.2e1 * t33 * t30 - t11 * t58 * t18 + 0.2e1 * t29 * t54 * t16 + 0.4e1 * t34 * t54 * t18 + 0.4e1 * t97 * t101 * t106 - 0.2e1 * t15 * t18 * nx * t41 - t34 * 0.3141592654e1 + 0.2e1 * nz * t18;

2950:   u4 = (t57 + t95 + t135 + t164) / (0.4e1 * t24 * t15 + 0.8e1 * t127 * t15 * t18 + 0.4e1 * t131 * t15 * t19);

2952:   /****************************************************************************************/
2953:   /****************************************************************************************/

2955:   u5 = (PetscReal)(-2*Z*nz*PETSC_PI*u2-u3*2*nz*PETSC_PI)*PetscCosReal(nz*PETSC_PI*z); /* pressure */

2957:   u6 = (PetscReal)(u3*2*nz*PETSC_PI + 4*Z*nz*PETSC_PI*u2)*PetscCosReal(nz*PETSC_PI*z); /* zz stress */
2958:   sum5 +=u5;
2959:   sum6 +=u6;

2961:   u1 *= PetscCosReal(nz*PETSC_PI*z); /* x velocity */
2962:   sum1 += u1;
2963:   u2 *= PetscSinReal(nz*PETSC_PI*z); /* z velocity */
2964:   sum2 += u2;
2965:   u3 *= 2*nz*PETSC_PI*PetscCosReal(nz*PETSC_PI*z); /* xx stress */
2966:   sum3 += u3;
2967:   u4 *= 2*nz*PETSC_PI*PetscSinReal(nz*PETSC_PI*z); /* zx stress */
2968:   sum4 += u4;

2970:   /* Output */
2971:   if (mu) {
2972:     *mu = Z;
2973:   }
2974:   if (vel) {
2975:     vel[0] = sum1;
2976:     vel[1] = sum2;
2977:   }
2978:   if (p) {
2979:     (*p) = sum5;
2980:   }
2981:   if (s) {
2982:     s[0] = sum3;
2983:     s[1] = sum4;
2984:     s[2] = sum6;
2985:   }
2986:   if (gamma) {
2987:     /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
2988:     gamma[0] = (sum3+sum5)/(2.0*Z);
2989:     gamma[1] = (sum4)/(2.0*Z);
2990:     gamma[2] = (sum6+sum5)/(2.0*Z);
2991:   }
2992:   return(0);
2993: }

2995: static PetscErrorCode SolCxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
2996: {
2997:   Parameter     *s = (Parameter *) ctx;

3001:   SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, v, NULL, NULL, NULL, NULL);
3002:   return(0);
3003: }

3005: static PetscErrorCode SolCxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
3006: {
3007:   Parameter     *s = (Parameter *) ctx;

3011:   SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, NULL, p, NULL, NULL, NULL);
3012:   return(0);
3013: }

3015: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
3016: {
3017:   PetscInt       sol;

3021:   options->solType = SOLKX;

3023:   PetscOptionsBegin(comm, "", "Variable-Viscosity Stokes Problem Options", "DMPLEX");
3024:   sol  = options->solType;
3025:   PetscOptionsEList("-sol_type", "Type of exact solution", "ex69.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL);
3026:   options->solType = (SolutionType) sol;
3027:   PetscOptionsEnd();
3028:   return(0);
3029: }

3031: static PetscErrorCode SetUpParameters(AppCtx *user)
3032: {
3033:   PetscBag       bag;
3034:   Parameter     *p;

3038:   /* setup PETSc parameter bag */
3039:   PetscBagGetData(user->bag, (void **) &p);
3040:   PetscBagSetName(user->bag, "par", "Problem parameters");
3041:   bag  = user->bag;
3042:   switch (user->solType) {
3043:   case SOLKX:
3044:     PetscBagRegisterInt(bag,  &p->n, 1,   "n", "x-wavelength for forcing variation");
3045:     PetscBagRegisterInt(bag,  &p->m, 1,   "m", "z-wavelength for forcing variation");
3046:     PetscBagRegisterReal(bag, &p->B, 1.0, "B", "Exponential scale for viscosity variation");
3047:     break;
3048:   case SOLCX:
3049:     PetscBagRegisterInt(bag,  &p->n,    1,   "n",    "x-wavelength for forcing variation");
3050:     PetscBagRegisterInt(bag,  &p->m,    1,   "m",    "z-wavelength for forcing variation");
3051:     PetscBagRegisterReal(bag, &p->etaA, 1.0, "etaA", "Viscosity for x < xc");
3052:     PetscBagRegisterReal(bag, &p->etaB, 1.0, "etaB", "Viscosity for x > xc");
3053:     PetscBagRegisterReal(bag, &p->xc,   0.5, "xc",   "x-coordinate of the viscosity jump");
3054:     break;
3055:   default:
3056:     SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3057:   }
3058:   PetscBagSetFromOptions(bag);
3059:   PetscBagViewFromOptions(bag, NULL, "-param_view");
3060:   return(0);
3061: }

3063: /* Make split labels so that we can have corners in multiple labels */
3064: static PetscErrorCode CreateSplitLabels(DM dm)
3065: {
3066:   const char    *names[4] = {"markerBottom", "markerRight", "markerTop", "markerLeft"};
3067:   PetscInt       ids[4]   = {1, 2, 3, 4};
3068:   DMLabel        label;
3069:   IS             is;
3070:   PetscInt       f;

3074:   for (f = 0; f < 4; ++f) {
3075:     DMCreateLabel(dm, names[f]);
3076:     DMGetStratumIS(dm, "marker", ids[f],  &is);
3077:     if (!is) continue;
3078:     DMGetLabel(dm, names[f], &label);
3079:     DMLabelInsertIS(label, is, 1);
3080:     ISDestroy(&is);
3081:   }
3082:   return(0);
3083: }

3085: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
3086: {
3087:   DM             cdm;

3091:   DMCreate(comm, dm);
3092:   DMSetType(*dm, DMPLEX);
3093:   DMSetFromOptions(*dm);
3094:   cdm  = *dm;
3095:   while (cdm) {
3096:     CreateSplitLabels(cdm);
3097:     DMGetCoarseDM(cdm, &cdm);
3098:   }
3099:   DMViewFromOptions(*dm, NULL, "-dm_view");
3100:   return(0);
3101: }

3103: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
3104: {
3105:   PetscErrorCode (*exactFunc)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3106:   PetscDS        prob;
3107:   DMLabel        label;
3108:   const PetscInt id  = 1;
3109:   PetscInt       dim, comp;
3110:   Parameter     *ctx;
3111:   void          *data;

3115:   DMGetDimension(dm, &dim);
3116:   DMGetDS(dm, &prob);
3117:   switch (user->solType) {
3118:   case SOLKX:
3119:     PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_kx);
3120:     PetscDSSetResidual(prob, 1, stokes_mass, f1_zero);
3121:     PetscDSSetJacobian(prob, 0, 0, NULL, NULL,  NULL,  stokes_momentum_vel_J_kx);
3122:     PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  stokes_momentum_pres_J, NULL);
3123:     PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL,  NULL);
3124:     PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);
3125:     PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_kx, NULL, NULL, NULL);
3126:     break;
3127:   case SOLCX:
3128:     PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_cx);
3129:     PetscDSSetResidual(prob, 1, stokes_mass, f1_zero);
3130:     PetscDSSetJacobian(prob, 0, 0, NULL, NULL,  NULL,  stokes_momentum_vel_J_cx);
3131:     PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  stokes_momentum_pres_J, NULL);
3132:     PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL,  NULL);
3133:     PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);
3134:     PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL);
3135:     break;
3136:   default:
3137:     SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3138:   }
3139:   PetscBagGetData(user->bag, &data);
3140:   switch (dim) {
3141:   case 2:
3142:     switch (user->solType) {
3143:     case SOLKX:
3144:       PetscDSSetExactSolution(prob, 0, SolKxSolutionVelocity, data);
3145:       PetscDSSetExactSolution(prob, 1, SolKxSolutionPressure, data);
3146:       break;
3147:     case SOLCX:
3148:       PetscDSSetExactSolution(prob, 0, SolCxSolutionVelocity, data);
3149:       PetscDSSetExactSolution(prob, 1, SolCxSolutionPressure, data);
3150:       break;
3151:     default:
3152:       SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3153:     }
3154:     break;
3155:   default:
3156:     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %D", dim);
3157:   }
3158:   /* Setup constants */
3159:   {
3160:     Parameter *param;

3162:     PetscBagGetData(user->bag, (void **) &param);
3163:     switch (user->solType) {
3164:     case SOLKX:
3165:     {
3166:       PetscScalar constants[3];

3168:       constants[0] = param->m;
3169:       constants[1] = param->n;
3170:       constants[2] = param->B;
3171:       PetscDSSetConstants(prob, 3, constants);
3172:     }
3173:     break;
3174:     case SOLCX:
3175:     {
3176:       PetscScalar constants[5];

3178:       constants[0] = param->m;
3179:       constants[1] = param->n;
3180:       constants[2] = param->etaA;
3181:       constants[3] = param->etaB;
3182:       constants[4] = param->xc;
3183:       PetscDSSetConstants(prob, 5, constants);
3184:     }
3185:     break;
3186:     default: SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP, "No parameter information for solution type %d", user->solType);
3187:     }
3188:   }
3189:   /* Setup Boundary Conditions */
3190:   PetscDSGetExactSolution(prob, 0, &exactFunc, (void **) &ctx);
3191:   comp = 1;
3192:   DMGetLabel(dm, "markerBottom", &label);
3193:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3194:   comp = 0;
3195:   DMGetLabel(dm, "markerRight", &label);
3196:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallR", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3197:   comp = 1;
3198:   DMGetLabel(dm, "markerTop", &label);
3199:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3200:   comp = 0;
3201:   DMGetLabel(dm, "markerLeft", &label);
3202:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallL", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3203:   return(0);
3204: }

3206: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
3207: {
3208:   Vec              vec;
3209:   PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero, one};
3210:   PetscErrorCode   ierr;

3213:   if (origField != 1) SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Field %D should be 1 for pressure", origField);
3214:   funcs[field] = one;
3215:   {
3216:     PetscDS ds;
3217:     DMGetDS(dm, &ds);
3218:     PetscObjectViewFromOptions((PetscObject) ds, NULL, "-ds_view");
3219:   }
3220:   DMCreateGlobalVector(dm, &vec);
3221:   DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);
3222:   VecNormalize(vec, NULL);
3223:   MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace);
3224:   VecDestroy(&vec);
3225:   /* New style for field null spaces */
3226:   {
3227:     PetscObject  pressure;
3228:     MatNullSpace nullspacePres;

3230:     DMGetField(dm, field, NULL, &pressure);
3231:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres);
3232:     PetscObjectCompose(pressure, "nullspace", (PetscObject) nullspacePres);
3233:     MatNullSpaceDestroy(&nullspacePres);
3234:   }
3235:   return(0);
3236: }

3238: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
3239: {
3240:   DM             cdm = dm;
3241:   PetscFE        fe[2];
3242:   DMPolytopeType ct;
3243:   PetscInt       dim, cStart;
3244:   PetscBool      simplex;

3248:   DMGetDimension(dm, &dim);
3249:   DMPlexGetHeightStratum(dm, 0, &cStart, NULL);
3250:   DMPlexGetCellType(dm, cStart, &ct);
3251:   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE;
3252:   /* Create discretization of solution fields */
3253:   PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]);
3254:   PetscObjectSetName((PetscObject) fe[0], "velocity");
3255:   PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]);
3256:   PetscFECopyQuadrature(fe[0], fe[1]);
3257:   PetscObjectSetName((PetscObject) fe[1], "pressure");
3258:   /* Set discretization and boundary conditions for each mesh */
3259:   DMSetField(dm, 0, NULL, (PetscObject) fe[0]);
3260:   DMSetField(dm, 1, NULL, (PetscObject) fe[1]);
3261:   DMCreateDS(dm);
3262:   SetupProblem(dm, user);
3263:   while (cdm) {
3264:     DMCopyDisc(dm, cdm);
3265:     DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace);
3266:     DMGetCoarseDM(cdm, &cdm);
3267:   }
3268:   PetscFEDestroy(&fe[0]);
3269:   PetscFEDestroy(&fe[1]);
3270:   {
3271:     PetscObject  pressure;
3272:     MatNullSpace nullSpacePres;

3274:     DMGetField(dm, 1, NULL, &pressure);
3275:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres);
3276:     PetscObjectCompose(pressure, "nullspace", (PetscObject) nullSpacePres);
3277:     MatNullSpaceDestroy(&nullSpacePres);
3278:   }
3279:   return(0);
3280: }

3282: /* Add a vector in the nullspace to make the continuum integral 0.

3284:    If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0
3285: */
3286: static void pressure(PetscInt dim, PetscInt Nf, PetscInt NfAux,
3287:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
3288:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
3289:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar p[])
3290: {
3291:   p[0] = u[uOff[1]];
3292: }
3293: static PetscErrorCode CorrectDiscretePressure(DM dm, MatNullSpace nullspace, Vec u, AppCtx *user)
3294: {
3295:   PetscDS        ds;
3296:   const Vec     *nullvecs;
3297:   PetscScalar    pintd, intc[2], intn[2];
3298:   MPI_Comm       comm;

3302:   PetscObjectGetComm((PetscObject) dm, &comm);
3303:   DMGetDS(dm, &ds);
3304:   PetscDSSetObjective(ds, 1, pressure);
3305:   MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs);
3306:   VecDot(nullvecs[0], u, &pintd);
3307:   if (PetscAbsScalar(pintd) > PETSC_SMALL) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g\n", (double) PetscRealPart(pintd));
3308:   DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, user);
3309:   DMPlexComputeIntegralFEM(dm, u, intc, user);
3310:   VecAXPY(u, -intc[1]/intn[1], nullvecs[0]);
3311:   DMPlexComputeIntegralFEM(dm, u, intc, user);
3312:   if (PetscAbsScalar(intc[1]) > PETSC_SMALL) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g\n", (double) PetscRealPart(intc[1]));
3313:   return(0);
3314: }

3316: static PetscErrorCode SNESConvergenceCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *user)
3317: {

3321:   SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, user);
3322:   if (*reason > 0) {
3323:     DM           dm;
3324:     Mat          J;
3325:     Vec          u;
3326:     MatNullSpace nullspace;

3328:     SNESGetDM(snes, &dm);
3329:     SNESGetSolution(snes, &u);
3330:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
3331:     MatGetNullSpace(J, &nullspace);
3332:     if (!nullspace) SETERRQ(PetscObjectComm((PetscObject) snes), PETSC_ERR_ARG_WRONG, "SNES Jacobian has no attached null space");
3333:     CorrectDiscretePressure(dm, nullspace, u, (AppCtx *) user);
3334:   }
3335:   return(0);
3336: }

3338: int main(int argc, char **argv)
3339: {
3340:   SNES            snes;      /* nonlinear solver */
3341:   DM              dm;        /* problem definition */
3342:   Vec             u,r;       /* solution, residual vectors */
3343:   Mat             J, M;      /* Jacobian and preconditiong matrix */
3344:   MatNullSpace    nullSpace; /* May be necessary for pressure */
3345:   AppCtx          user;      /* user-defined work context */
3346:   PetscErrorCode  (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero, zero};
3347:   PetscErrorCode  ierr;

3349:   PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
3350:   ProcessOptions(PETSC_COMM_WORLD, &user);
3351:   SNESCreate(PETSC_COMM_WORLD, &snes);
3352:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
3353:   SNESSetDM(snes, dm);
3354:   DMSetApplicationContext(dm, &user);
3355:   /* Setup problem parameters */
3356:   PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);
3357:   SetUpParameters(&user);
3358:   /* Setup problem */
3359:   SetupDiscretization(dm, &user);
3360:   DMPlexCreateClosureIndex(dm, NULL);

3362:   DMCreateGlobalVector(dm, &u);
3363:   VecDuplicate(u, &r);

3365:   DMPlexSetSNESLocalFEM(dm,&user,&user,&user);
3366:   CreatePressureNullSpace(dm, 1, 1, &nullSpace);

3368:   { /* set tolerances */
3369:     KSP ksp;

3371:     SNESGetKSP(snes, &ksp);
3372:     KSPSetTolerances(ksp,1.e-2*PETSC_SMALL,PETSC_SMALL,PETSC_DEFAULT,PETSC_DEFAULT);
3373:   }

3375:   /* There should be a way to express this using the DM */
3376:   SNESSetFromOptions(snes);
3377:   SNESSetUp(snes);
3378:   SNESGetJacobian(snes, &J, &M, NULL, NULL);
3379:   MatSetNullSpace(J, nullSpace);
3380:   PetscObjectSetOptionsPrefix((PetscObject) M, "prec_");
3381:   MatSetFromOptions(M);
3382:   SNESSetConvergenceTest(snes, SNESConvergenceCorrectPressure, &user, NULL);

3384:   DMSNESCheckFromOptions(snes, u);
3385:   DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);
3386:   PetscObjectSetName((PetscObject) u, "Solution");
3387:   SNESSolve(snes, NULL, u);
3388:   {
3389:     PetscErrorCode (*exacts[2])(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3390:     void            *ectxs[2];
3391:     PetscDS          ds;
3392:     Vec              e;

3394:     DMGetDS(dm, &ds);
3395:     PetscDSGetExactSolution(ds, 0, &exacts[0], &ectxs[0]);
3396:     PetscDSGetExactSolution(ds, 1, &exacts[1], &ectxs[1]);

3398:     DMGetGlobalVector(dm, &e);
3399:     PetscObjectCompose((PetscObject) e, "__Vec_bc_zero__", (PetscObject) dm);
3400:     DMPlexComputeL2DiffVec(dm, 0.0, exacts, ectxs, u, e);
3401:     PetscObjectSetName((PetscObject) e, "Solution Error");
3402:     VecViewFromOptions(e, NULL, "-error_vec_view");
3403:     PetscObjectCompose((PetscObject) e, "__Vec_bc_zero__", NULL);
3404:     DMRestoreGlobalVector(dm, &e);
3405:   }
3406:   VecViewFromOptions(u, NULL, "-sol_vec_view");

3408:   MatNullSpaceDestroy(&nullSpace);
3409:   VecDestroy(&u);
3410:   VecDestroy(&r);
3411:   SNESDestroy(&snes);
3412:   DMDestroy(&dm);
3413:   PetscBagDestroy(&user.bag);
3414:   PetscFinalize();
3415:   return ierr;
3416: }

3418: /*TEST

3420:   # 2D serial discretization tests
3421:   test:
3422:     suffix: p2p1
3423:     requires: triangle
3424:     args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3425:       -snes_error_if_not_converged -dmsnes_check .001 \
3426:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3427:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3428:         -fieldsplit_velocity_pc_type lu \
3429:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3430:   test:
3431:     suffix: p2p1_gmg
3432:     requires: triangle
3433:     args: -dm_plex_separate_marker -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3434:       -snes_error_if_not_converged -dmsnes_check .001 \
3435:       -ksp_type fgmres -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3436:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3437:         -fieldsplit_velocity_pc_type mg \
3438:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3439:   test:
3440:     suffix: p2p1_conv
3441:     requires: triangle
3442:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.2]
3443:     args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3444:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3445:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3446:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3447:         -fieldsplit_velocity_pc_type lu \
3448:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3449:   test:
3450:     suffix: q2q1_conv
3451:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.1]
3452:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3453:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3454:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3455:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3456:         -fieldsplit_velocity_pc_type lu \
3457:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3458:   test:
3459:     suffix: q1p0_conv
3460:     # -dm_refine 2 gives L_2 convergence rate: [2.0, 1.0]
3461:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
3462:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3463:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3464:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3465:         -fieldsplit_velocity_pc_type lu \
3466:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3467:   test:
3468:     suffix: q2p1_conv
3469:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.0]
3470:     args: -dm_plex_simplex 0 -dm_plex_separate_marker \
3471:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 \
3472:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3473:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3474:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3475:         -fieldsplit_velocity_pc_type lu \
3476:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu

3478:   # FETI-DP tests
3479:   testset:
3480:     output_file: output/ex69_q2p1fetidp.out
3481:     suffix: q2p1fetidp
3482:     requires: !single
3483:     nsize: 5
3484:     args: -dm_distribute -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3485:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3486:       -snes_error_if_not_converged \
3487:       -ksp_error_if_not_converged \
3488:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3489:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd
3490:     test:
3491:       suffix: aij
3492:       args: -matis_localmat_type aij
3493:     test:
3494:       requires: viennacl !CUDA_VERSION_11PLUS
3495:       suffix: aijviennacl
3496:       args: -matis_localmat_type aijviennacl
3497:     test:
3498:       requires: cuda
3499:       suffix: aijcusparse
3500:       args: -matis_localmat_type aijcusparse

3502:   testset:
3503:     suffix: q2p1fetidp_deluxe
3504:     output_file: output/ex69_q2p1fetidp_deluxe.out
3505:     requires: mumps double
3506:     nsize: 5
3507:     args: -dm_distribute -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3508:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3509:       -snes_error_if_not_converged \
3510:       -ksp_error_if_not_converged \
3511:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3512:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_pc_bddc_deluxe_zerorows \
3513:       -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd
3514:     test:
3515:       suffix: aij
3516:       args: -matis_localmat_type aij
3517:     test:
3518:       suffix: aij_seqdense
3519:       args: -matis_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3520:     test:
3521:       requires: viennacl !CUDA_VERSION_11PLUS
3522:       suffix: aijviennacl
3523:       args: -matis_localmat_type aijviennacl
3524:     test:
3525:       requires: cuda
3526:       suffix: aijcusparse
3527:       args: -matis_localmat_type aijcusparse

3529:   testset:
3530:     suffix: q2p1fetidp_deluxe_adaptive
3531:     output_file: output/ex69_q2p1fetidp_deluxe_adaptive.out
3532:     requires: mumps double
3533:     nsize: 5
3534:     args: -dm_distribute -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3535:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3536:       -snes_error_if_not_converged \
3537:       -ksp_error_if_not_converged \
3538:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3539:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_pc_bddc_adaptive_userdefined -fetidp_bddc_pc_bddc_adaptive_threshold 1.3 \
3540:       -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd
3541:     test:
3542:       suffix: aij
3543:       args: -matis_localmat_type aij
3544:     test:
3545:       suffix: aij_seqdense
3546:       args: -matis_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3547:     test:
3548:       requires: viennacl !CUDA_VERSION_11PLUS
3549:       suffix: aijviennacl
3550:       args: -matis_localmat_type aijviennacl
3551:     test:
3552:       requires: cuda
3553:       suffix: aijcusparse
3554:       args: -matis_localmat_type aijcusparse

3556:   test:
3557:     suffix: p2p1fetidp
3558:     requires: triangle
3559:     nsize: 4
3560:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3561:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3562:       -snes_error_if_not_converged \
3563:       -ksp_error_if_not_converged \
3564:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3565:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3566:       -fetidp_fieldsplit_lag_ksp_type preonly \
3567:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd

3569:   test:
3570:     suffix: p2p1fetidp_allp
3571:     requires: triangle
3572:     nsize: 4
3573:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3574:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3575:       -snes_error_if_not_converged \
3576:       -ksp_error_if_not_converged \
3577:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag -ksp_fetidp_pressure_all \
3578:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3579:       -fetidp_fieldsplit_lag_ksp_type preonly \
3580:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd

3582:   test:
3583:     suffix: p2p1fetidp_discharm
3584:     requires: triangle
3585:     nsize: 4
3586:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3587:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3588:       -snes_error_if_not_converged \
3589:       -ksp_error_if_not_converged \
3590:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_type cholesky \
3591:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3592:       -fetidp_fieldsplit_lag_ksp_type preonly \
3593:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd

3595:   test:
3596:     suffix: p2p1fetidp_lumped
3597:     requires: triangle
3598:     nsize: 4
3599:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3600:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3601:       -snes_error_if_not_converged \
3602:       -ksp_error_if_not_converged \
3603:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_pc_lumped \
3604:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3605:       -fetidp_fieldsplit_lag_ksp_type preonly \
3606:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd

3608:   test:
3609:     suffix: p2p1fetidp_deluxe
3610:     requires: triangle mumps
3611:     nsize: 4
3612:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3613:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3614:       -snes_error_if_not_converged \
3615:       -ksp_error_if_not_converged \
3616:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3617:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3618:       -fetidp_fieldsplit_lag_ksp_type preonly \
3619:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat \
3620:       -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0

3622:   test:
3623:     suffix: p2p1fetidp_deluxe_discharm
3624:     requires: triangle mumps
3625:     nsize: 4
3626:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3627:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3628:       -snes_error_if_not_converged \
3629:       -ksp_error_if_not_converged \
3630:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3631:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3632:       -fetidp_fieldsplit_lag_ksp_type preonly \
3633:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat \
3634:       -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0  -fetidp_bddc_sub_schurs_discrete_harmonic

3636:   testset:
3637:     nsize: 4
3638:     requires: triangle
3639:     output_file: output/ex69_p2p1fetidp_olof.out
3640:     args: -dm_distribute -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3641:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3642:       -snes_error_if_not_converged \
3643:       -ksp_error_if_not_converged \
3644:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_discrete_harmonic 1 -fetidp_harmonic_pc_type cholesky -ksp_fetidp_pressure_schur \
3645:       -fetidp_fieldsplit_p_pc_type bddc -fetidp_fieldsplit_p_pc_bddc_dirichlet_pc_type none -fetidp_fieldsplit_p_ksp_type preonly \
3646:       -fetidp_fieldsplit_lag_ksp_error_if_not_converged 0 -fetidp_fieldsplit_lag_ksp_type chebyshev -fetidp_fieldsplit_lag_ksp_max_it 2 \
3647:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd
3648:     test:
3649:       suffix: p2p1fetidp_olof_full
3650:       args: -fetidp_pc_fieldsplit_schur_fact_type full
3651:     test:
3652:       suffix: p2p1fetidp_olof_diag
3653:       args: -fetidp_pc_fieldsplit_schur_fact_type diag
3654:     test:
3655:       suffix: p2p1fetidp_olof_additive
3656:       args: -fetidp_pc_fieldsplit_type additive

3658:   #BDDC with benign trick
3659:   testset:
3660:     suffix: q2p1bddc
3661:     output_file: output/ex69_q2p1fetidp_deluxe.out
3662:     nsize: 5
3663:     args: -dm_distribute -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 -petscds_jac_pre 0 -snes_error_if_not_converged -ksp_error_if_not_converged -ksp_type cg -ksp_norm_type natural -pc_type bddc -pc_bddc_benign_trick -pc_bddc_nonetflux -pc_bddc_detect_disconnected -pc_bddc_vertex_size 2 -pc_bddc_coarse_redundant_pc_type svd -pc_bddc_use_qr_single
3664:     test:
3665:       requires: double
3666:       suffix: benign_card
3667:       # no native support for saddle point factorizations from PETSc
3668:       args: -pc_bddc_dirichlet_pc_type svd -pc_bddc_neumann_pc_type svd
3669:     test:
3670:       requires: mumps double
3671:       suffix: benign_deluxe_mumps
3672:       args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3673:     test:
3674:       requires: mumps double
3675:       suffix: benign_deluxe_adaptive_mumps
3676:       args: -pc_bddc_adaptive_threshold 1.7 -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3677:     test:
3678:       TODO: broken (INDEFINITE PC)
3679:       requires: mkl_pardiso double
3680:       suffix: benign_deluxe_mkl
3681:       args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7
3682:     test:
3683:       TODO: broken (INDEFINITE PC)
3684:       requires: mkl_pardiso double
3685:       suffix: benign_deluxe_adaptive_mkl
3686:       args: -pc_bddc_adaptive_threshold 1.7 -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7

3688: TEST*/