Actual source code: ex5.c
petsc-3.8.4 2018-03-24
2: static char help[] = "Bratu nonlinear PDE in 2d.\n\
3: We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
4: domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\
5: The command line options include:\n\
6: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
7: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n\
8: -m_par/n_par <parameter>, where <parameter> indicates an integer\n \
9: that MMS3 will be evaluated with 2^m_par, 2^n_par";
11: /*T
12: Concepts: SNES^parallel Bratu example
13: Concepts: DMDA^using distributed arrays;
14: Concepts: IS coloirng types;
15: Processors: n
16: T*/
18: /* ------------------------------------------------------------------------
20: Solid Fuel Ignition (SFI) problem. This problem is modeled by
21: the partial differential equation
23: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
25: with boundary conditions
27: u = 0 for x = 0, x = 1, y = 0, y = 1.
29: A finite difference approximation with the usual 5-point stencil
30: is used to discretize the boundary value problem to obtain a nonlinear
31: system of equations.
34: This example shows how geometric multigrid can be run transparently with a nonlinear solver so long
35: as SNESSetDM() is provided. Example usage
37: ./ex5 -pc_type mg -ksp_monitor -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17
38: -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full
40: or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
41: multigrid levels, it will be determined automatically based on the number of refinements done)
43: ./ex5 -pc_type mg -ksp_monitor -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
44: -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full
46: ------------------------------------------------------------------------- */
48: /*
49: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
50: Include "petscsnes.h" so that we can use SNES solvers. Note that this
51: */
52: #include <petscdm.h>
53: #include <petscdmda.h>
54: #include <petscsnes.h>
55: #include <petscmatlab.h>
57: /*
58: User-defined application context - contains data needed by the
59: application-provided call-back routines, FormJacobianLocal() and
60: FormFunctionLocal().
61: */
62: typedef struct AppCtx AppCtx;
63: struct AppCtx {
64: PetscReal param; /* test problem parameter */
65: PetscInt m,n; /* MMS3 parameters */
66: PetscErrorCode (*mms_solution)(AppCtx*,const DMDACoor2d*,PetscScalar*);
67: PetscErrorCode (*mms_forcing)(AppCtx*,const DMDACoor2d*,PetscScalar*);
68: };
70: /*
71: User-defined routines
72: */
73: extern PetscErrorCode FormInitialGuess(DM,AppCtx*,Vec);
74: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
75: extern PetscErrorCode FormExactSolution(DM,AppCtx*,Vec);
76: extern PetscErrorCode ZeroBCSolution(AppCtx*,const DMDACoor2d*,PetscScalar*);
77: extern PetscErrorCode MMSSolution1(AppCtx*,const DMDACoor2d*,PetscScalar*);
78: extern PetscErrorCode MMSForcing1(AppCtx*,const DMDACoor2d*,PetscScalar*);
79: extern PetscErrorCode MMSSolution2(AppCtx*,const DMDACoor2d*,PetscScalar*);
80: extern PetscErrorCode MMSForcing2(AppCtx*,const DMDACoor2d*,PetscScalar*);
81: extern PetscErrorCode MMSSolution3(AppCtx*,const DMDACoor2d*,PetscScalar*);
82: extern PetscErrorCode MMSForcing3(AppCtx*,const DMDACoor2d*,PetscScalar*);
83: extern PetscErrorCode MMSSolution4(AppCtx*,const DMDACoor2d*,PetscScalar*);
84: extern PetscErrorCode MMSForcing4(AppCtx*,const DMDACoor2d*,PetscScalar*);
85: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,Mat,AppCtx*);
86: extern PetscErrorCode FormObjectiveLocal(DMDALocalInfo*,PetscScalar**,PetscReal*,AppCtx*);
87: #if defined(PETSC_HAVE_MATLAB_ENGINE)
88: extern PetscErrorCode FormFunctionMatlab(SNES,Vec,Vec,void*);
89: #endif
90: extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*);
92: int main(int argc,char **argv)
93: {
94: SNES snes; /* nonlinear solver */
95: Vec x; /* solution vector */
96: AppCtx user; /* user-defined work context */
97: PetscInt its; /* iterations for convergence */
99: PetscReal bratu_lambda_max = 6.81;
100: PetscReal bratu_lambda_min = 0.;
101: PetscInt MMS = 0;
102: PetscBool flg = PETSC_FALSE;
103: DM da;
104: #if defined(PETSC_HAVE_MATLAB_ENGINE)
105: Vec r = NULL;
106: PetscBool matlab_function = PETSC_FALSE;
107: #endif
108: KSP ksp;
109: PetscInt lits,slits;
111: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
112: Initialize program
113: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
117: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118: Initialize problem parameters
119: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
120: user.param = 6.0;
121: PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);
122: if (user.param > bratu_lambda_max || user.param < bratu_lambda_min) SETERRQ3(PETSC_COMM_SELF,1,"Lambda, %g, is out of range, [%g, %g]", user.param, bratu_lambda_min, bratu_lambda_max);
123: PetscOptionsGetInt(NULL,NULL,"-mms",&MMS,NULL);
124: if (MMS == 3) {
125: PetscInt mPar = 2, nPar = 1;
126: PetscOptionsGetInt(NULL,NULL,"-m_par",&mPar,NULL);
127: PetscOptionsGetInt(NULL,NULL,"-n_par",&nPar,NULL);
128: user.m = PetscPowInt(2,mPar);
129: user.n = PetscPowInt(2,nPar);
130: }
132: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Create nonlinear solver context
134: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: SNESCreate(PETSC_COMM_WORLD,&snes);
136: SNESSetCountersReset(snes,PETSC_FALSE);
137: SNESSetNGS(snes, NonlinearGS, NULL);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Create distributed array (DMDA) to manage parallel grid and vectors
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
143: DMSetFromOptions(da);
144: DMSetUp(da);
145: DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
146: DMSetApplicationContext(da,&user);
147: SNESSetDM(snes,da);
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Extract global vectors from DMDA; then duplicate for remaining
150: vectors that are the same types
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: DMCreateGlobalVector(da,&x);
154: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: Set local function evaluation routine
156: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157: user.mms_solution = ZeroBCSolution;
158: switch (MMS) {
159: case 0: user.mms_solution = NULL; user.mms_forcing = NULL;
160: case 1: user.mms_solution = MMSSolution1; user.mms_forcing = MMSForcing1; break;
161: case 2: user.mms_solution = MMSSolution2; user.mms_forcing = MMSForcing2; break;
162: case 3: user.mms_solution = MMSSolution3; user.mms_forcing = MMSForcing3; break;
163: case 4: user.mms_solution = MMSSolution4; user.mms_forcing = MMSForcing4; break;
164: default: SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_USER,"Unknown MMS type %d",MMS);
165: }
166: DMDASNESSetFunctionLocal(da,INSERT_VALUES,(DMDASNESFunction)FormFunctionLocal,&user);
167: PetscOptionsGetBool(NULL,NULL,"-fd",&flg,NULL);
168: if (!flg) {
169: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);
170: }
172: PetscOptionsGetBool(NULL,NULL,"-obj",&flg,NULL);
173: if (flg) {
174: DMDASNESSetObjectiveLocal(da,(DMDASNESObjective)FormObjectiveLocal,&user);
175: }
177: #if defined(PETSC_HAVE_MATLAB_ENGINE)
178: PetscOptionsGetBool(NULL,NULL,"-matlab_function",&matlab_function,0);
179: if (matlab_function) {
180: VecDuplicate(x,&r);
181: SNESSetFunction(snes,r,FormFunctionMatlab,&user);
182: }
183: #endif
185: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186: Customize nonlinear solver; set runtime options
187: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: SNESSetFromOptions(snes);
190: FormInitialGuess(da,&user,x);
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Solve nonlinear system
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: SNESSolve(snes,NULL,x);
196: SNESGetIterationNumber(snes,&its);
198: SNESGetLinearSolveIterations(snes,&slits);
199: SNESGetKSP(snes,&ksp);
200: KSPGetTotalIterations(ksp,&lits);
201: if (lits != slits) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Number of total linear iterations reported by SNES %D does not match reported by KSP %D",slits,lits);
202: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
206: If using MMS, check the l_2 error
207: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
208: if (MMS) {
209: Vec e;
210: PetscReal errorl2, errorinf;
211: PetscInt N;
213: VecDuplicate(x, &e);
214: PetscObjectViewFromOptions((PetscObject) x, NULL, "-sol_view");
215: FormExactSolution(da, &user, e);
216: PetscObjectViewFromOptions((PetscObject) e, NULL, "-exact_view");
217: VecAXPY(e, -1.0, x);
218: PetscObjectViewFromOptions((PetscObject) e, NULL, "-error_view");
219: VecNorm(e, NORM_2, &errorl2);
220: VecNorm(e, NORM_INFINITY, &errorinf);
221: VecGetSize(e, &N);
222: PetscPrintf(PETSC_COMM_WORLD, "N: %D error L2 %g inf %g\n", N, (double) errorl2/PetscSqrtReal(N), (double) errorinf);
223: VecDestroy(&e);
224: }
226: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
227: Free work space. All PETSc objects should be destroyed when they
228: are no longer needed.
229: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
230: #if defined(PETSC_HAVE_MATLAB_ENGINE)
231: VecDestroy(&r);
232: #endif
233: VecDestroy(&x);
234: SNESDestroy(&snes);
235: DMDestroy(&da);
236: PetscFinalize();
237: return ierr;
238: }
239: /* ------------------------------------------------------------------- */
240: /*
241: FormInitialGuess - Forms initial approximation.
243: Input Parameters:
244: da - The DM
245: user - user-defined application context
247: Output Parameter:
248: X - vector
249: */
250: PetscErrorCode FormInitialGuess(DM da,AppCtx *user,Vec X)
251: {
252: PetscInt i,j,Mx,My,xs,ys,xm,ym;
254: PetscReal lambda,temp1,temp,hx,hy;
255: PetscScalar **x;
258: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
260: lambda = user->param;
261: hx = 1.0/(PetscReal)(Mx-1);
262: hy = 1.0/(PetscReal)(My-1);
263: temp1 = lambda/(lambda + 1.0);
265: /*
266: Get a pointer to vector data.
267: - For default PETSc vectors, VecGetArray() returns a pointer to
268: the data array. Otherwise, the routine is implementation dependent.
269: - You MUST call VecRestoreArray() when you no longer need access to
270: the array.
271: */
272: DMDAVecGetArray(da,X,&x);
274: /*
275: Get local grid boundaries (for 2-dimensional DMDA):
276: xs, ys - starting grid indices (no ghost points)
277: xm, ym - widths of local grid (no ghost points)
279: */
280: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
282: /*
283: Compute initial guess over the locally owned part of the grid
284: */
285: for (j=ys; j<ys+ym; j++) {
286: temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
287: for (i=xs; i<xs+xm; i++) {
288: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
289: /* boundary conditions are all zero Dirichlet */
290: x[j][i] = 0.0;
291: } else {
292: x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
293: }
294: }
295: }
297: /*
298: Restore vector
299: */
300: DMDAVecRestoreArray(da,X,&x);
301: return(0);
302: }
304: /*
305: FormExactSolution - Forms MMS solution
307: Input Parameters:
308: da - The DM
309: user - user-defined application context
311: Output Parameter:
312: X - vector
313: */
314: PetscErrorCode FormExactSolution(DM da, AppCtx *user, Vec U)
315: {
316: DM coordDA;
317: Vec coordinates;
318: DMDACoor2d **coords;
319: PetscScalar **u;
320: PetscInt xs, ys, xm, ym, i, j;
324: DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
325: DMGetCoordinateDM(da, &coordDA);
326: DMGetCoordinates(da, &coordinates);
327: DMDAVecGetArray(coordDA, coordinates, &coords);
328: DMDAVecGetArray(da, U, &u);
329: for (j = ys; j < ys+ym; ++j) {
330: for (i = xs; i < xs+xm; ++i) {
331: user->mms_solution(user,&coords[j][i],&u[j][i]);
332: }
333: }
334: DMDAVecRestoreArray(da, U, &u);
335: DMDAVecRestoreArray(coordDA, coordinates, &coords);
336: return(0);
337: }
339: PetscErrorCode ZeroBCSolution(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
340: {
341: u[0] = 0.;
342: return 0;
343: }
345: /* The functions below evaluate the MMS solution u(x,y) and associated forcing
347: f(x,y) = -u_xx - u_yy - lambda exp(u)
349: such that u(x,y) is an exact solution with f(x,y) as the right hand side forcing term.
350: */
351: PetscErrorCode MMSSolution1(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
352: {
353: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
354: u[0] = x*(1 - x)*y*(1 - y);
355: PetscLogFlops(5);
356: return 0;
357: }
358: PetscErrorCode MMSForcing1(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
359: {
360: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
361: f[0] = 2*x*(1 - x) + 2*y*(1 - y) - user->param*PetscExpReal(x*(1 - x)*y*(1 - y));
362: return 0;
363: }
365: PetscErrorCode MMSSolution2(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
366: {
367: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
368: u[0] = PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y);
369: PetscLogFlops(5);
370: return 0;
371: }
372: PetscErrorCode MMSForcing2(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
373: {
374: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
375: f[0] = 2*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y) - user->param*PetscExpReal(PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y));
376: return 0;
377: }
379: PetscErrorCode MMSSolution3(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
380: {
381: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
382: u[0] = PetscSinReal(user->m*PETSC_PI*x*(1-y))*PetscSinReal(user->n*PETSC_PI*y*(1-x));
383: PetscLogFlops(5);
384: return 0;
385: }
386: PetscErrorCode MMSForcing3(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
387: {
388: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
389: PetscReal m = user->m, n = user->n, lambda = user->param;
390: f[0] = (-(PetscExpReal(PetscSinReal(m*PETSC_PI*x*(1 - y))*PetscSinReal(n*PETSC_PI*(1 - x)*y))*lambda)
391: + PetscSqr(PETSC_PI)*(-2*m*n*((-1 + x)*x + (-1 + y)*y)*PetscCosReal(m*PETSC_PI*x*(-1 + y))*PetscCosReal(n*PETSC_PI*(-1 + x)*y)
392: + (PetscSqr(m)*(PetscSqr(x) + PetscSqr(-1 + y)) + PetscSqr(n)*(PetscSqr(-1 + x) + PetscSqr(y)))
393: *PetscSinReal(m*PETSC_PI*x*(-1 + y))*PetscSinReal(n*PETSC_PI*(-1 + x)*y)));
394: return 0;
395: }
397: PetscErrorCode MMSSolution4(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
398: {
399: const PetscReal Lx = 1.,Ly = 1.;
400: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
401: u[0] = (PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y));
402: PetscLogFlops(9);
403: return 0;
404: }
405: PetscErrorCode MMSForcing4(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
406: {
407: const PetscReal Lx = 1.,Ly = 1.;
408: PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
409: f[0] = (2*PetscSqr(x)*(PetscSqr(x)-PetscSqr(Lx))*(PetscSqr(Ly)-6*PetscSqr(y))
410: + 2*PetscSqr(y)*(PetscSqr(Lx)-6*PetscSqr(x))*(PetscSqr(y)-PetscSqr(Ly))
411: - user->param*PetscExpReal((PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y))));
412: return 0;
413: }
415: /* ------------------------------------------------------------------- */
416: /*
417: FormFunctionLocal - Evaluates nonlinear function, F(x) on local process patch
420: */
421: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
422: {
424: PetscInt i,j;
425: PetscReal lambda,hx,hy,hxdhy,hydhx;
426: PetscScalar u,ue,uw,un,us,uxx,uyy,mms_solution,mms_forcing;
427: DMDACoor2d c;
430: lambda = user->param;
431: hx = 1.0/(PetscReal)(info->mx-1);
432: hy = 1.0/(PetscReal)(info->my-1);
433: hxdhy = hx/hy;
434: hydhx = hy/hx;
435: /*
436: Compute function over the locally owned part of the grid
437: */
438: for (j=info->ys; j<info->ys+info->ym; j++) {
439: for (i=info->xs; i<info->xs+info->xm; i++) {
440: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
441: c.x = i*hx; c.y = j*hy;
442: user->mms_solution(user,&c,&mms_solution);
443: f[j][i] = 2.0*(hydhx+hxdhy)*(x[j][i] - mms_solution);
444: } else {
445: u = x[j][i];
446: uw = x[j][i-1];
447: ue = x[j][i+1];
448: un = x[j-1][i];
449: us = x[j+1][i];
451: /* Enforce boundary conditions at neighboring points -- setting these values causes the Jacobian to be symmetric. */
452: if (i-1 == 0) {c.x = (i-1)*hx; c.y = j*hy; user->mms_solution(user,&c,&uw);}
453: if (i+1 == info->mx-1) {c.x = (i+1)*hx; c.y = j*hy; user->mms_solution(user,&c,&ue);}
454: if (j-1 == 0) {c.x = i*hx; c.y = (j-1)*hy; user->mms_solution(user,&c,&un);}
455: if (j+1 == info->my-1) {c.x = i*hx; c.y = (j+1)*hy; user->mms_solution(user,&c,&us);}
457: uxx = (2.0*u - uw - ue)*hydhx;
458: uyy = (2.0*u - un - us)*hxdhy;
459: mms_forcing = 0;
460: c.x = i*hx; c.y = j*hy;
461: if (user->mms_forcing) {user->mms_forcing(user,&c,&mms_forcing);}
462: f[j][i] = uxx + uyy - hx*hy*(lambda*PetscExpScalar(u) + mms_forcing);
463: }
464: }
465: }
466: PetscLogFlops(11.0*info->ym*info->xm);
467: return(0);
468: }
470: /* FormObjectiveLocal - Evaluates nonlinear function, F(x) on local process patch */
471: PetscErrorCode FormObjectiveLocal(DMDALocalInfo *info,PetscScalar **x,PetscReal *obj,AppCtx *user)
472: {
474: PetscInt i,j;
475: PetscReal lambda,hx,hy,hxdhy,hydhx,sc,lobj=0;
476: PetscScalar u,ue,uw,un,us,uxux,uyuy;
477: MPI_Comm comm;
480: *obj = 0;
481: PetscObjectGetComm((PetscObject)info->da,&comm);
482: lambda = user->param;
483: hx = 1.0/(PetscReal)(info->mx-1);
484: hy = 1.0/(PetscReal)(info->my-1);
485: sc = hx*hy*lambda;
486: hxdhy = hx/hy;
487: hydhx = hy/hx;
488: /*
489: Compute function over the locally owned part of the grid
490: */
491: for (j=info->ys; j<info->ys+info->ym; j++) {
492: for (i=info->xs; i<info->xs+info->xm; i++) {
493: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
494: lobj += PetscRealPart((hydhx + hxdhy)*x[j][i]*x[j][i]);
495: } else {
496: u = x[j][i];
497: uw = x[j][i-1];
498: ue = x[j][i+1];
499: un = x[j-1][i];
500: us = x[j+1][i];
502: if (i-1 == 0) uw = 0.;
503: if (i+1 == info->mx-1) ue = 0.;
504: if (j-1 == 0) un = 0.;
505: if (j+1 == info->my-1) us = 0.;
507: /* F[u] = 1/2\int_{\omega}\nabla^2u(x)*u(x)*dx */
509: uxux = u*(2.*u - ue - uw)*hydhx;
510: uyuy = u*(2.*u - un - us)*hxdhy;
512: lobj += PetscRealPart(0.5*(uxux + uyuy) - sc*PetscExpScalar(u));
513: }
514: }
515: }
516: PetscLogFlops(12.0*info->ym*info->xm);
517: MPI_Allreduce(&lobj,obj,1,MPIU_REAL,MPIU_SUM,comm);
518: return(0);
519: }
521: /*
522: FormJacobianLocal - Evaluates Jacobian matrix on local process patch
523: */
524: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,Mat jacpre,AppCtx *user)
525: {
527: PetscInt i,j,k;
528: MatStencil col[5],row;
529: PetscScalar lambda,v[5],hx,hy,hxdhy,hydhx,sc;
530: DM coordDA;
531: Vec coordinates;
532: DMDACoor2d **coords;
535: lambda = user->param;
536: /* Extract coordinates */
537: DMGetCoordinateDM(info->da, &coordDA);
538: DMGetCoordinates(info->da, &coordinates);
539: DMDAVecGetArray(coordDA, coordinates, &coords);
540: hx = info->xm > 1 ? PetscRealPart(coords[info->ys][info->xs+1].x) - PetscRealPart(coords[info->ys][info->xs].x) : 1.0;
541: hy = info->ym > 1 ? PetscRealPart(coords[info->ys+1][info->xs].y) - PetscRealPart(coords[info->ys][info->xs].y) : 1.0;
542: DMDAVecRestoreArray(coordDA, coordinates, &coords);
543: hxdhy = hx/hy;
544: hydhx = hy/hx;
545: sc = hx*hy*lambda;
548: /*
549: Compute entries for the locally owned part of the Jacobian.
550: - Currently, all PETSc parallel matrix formats are partitioned by
551: contiguous chunks of rows across the processors.
552: - Each processor needs to insert only elements that it owns
553: locally (but any non-local elements will be sent to the
554: appropriate processor during matrix assembly).
555: - Here, we set all entries for a particular row at once.
556: - We can set matrix entries either using either
557: MatSetValuesLocal() or MatSetValues(), as discussed above.
558: */
559: for (j=info->ys; j<info->ys+info->ym; j++) {
560: for (i=info->xs; i<info->xs+info->xm; i++) {
561: row.j = j; row.i = i;
562: /* boundary points */
563: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
564: v[0] = 2.0*(hydhx + hxdhy);
565: MatSetValuesStencil(jacpre,1,&row,1,&row,v,INSERT_VALUES);
566: } else {
567: k = 0;
568: /* interior grid points */
569: if (j-1 != 0) {
570: v[k] = -hxdhy;
571: col[k].j = j - 1; col[k].i = i;
572: k++;
573: }
574: if (i-1 != 0) {
575: v[k] = -hydhx;
576: col[k].j = j; col[k].i = i-1;
577: k++;
578: }
580: v[k] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[k].j = row.j; col[k].i = row.i; k++;
582: if (i+1 != info->mx-1) {
583: v[k] = -hydhx;
584: col[k].j = j; col[k].i = i+1;
585: k++;
586: }
587: if (j+1 != info->mx-1) {
588: v[k] = -hxdhy;
589: col[k].j = j + 1; col[k].i = i;
590: k++;
591: }
592: MatSetValuesStencil(jacpre,1,&row,k,col,v,INSERT_VALUES);
593: }
594: }
595: }
597: /*
598: Assemble matrix, using the 2-step process:
599: MatAssemblyBegin(), MatAssemblyEnd().
600: */
601: MatAssemblyBegin(jacpre,MAT_FINAL_ASSEMBLY);
602: MatAssemblyEnd(jacpre,MAT_FINAL_ASSEMBLY);
603: /*
604: Tell the matrix we will never add a new nonzero location to the
605: matrix. If we do, it will generate an error.
606: */
607: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
608: return(0);
609: }
611: #if defined(PETSC_HAVE_MATLAB_ENGINE)
612: PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
613: {
614: AppCtx *user = (AppCtx*)ptr;
616: PetscInt Mx,My;
617: PetscReal lambda,hx,hy;
618: Vec localX,localF;
619: MPI_Comm comm;
620: DM da;
623: SNESGetDM(snes,&da);
624: DMGetLocalVector(da,&localX);
625: DMGetLocalVector(da,&localF);
626: PetscObjectSetName((PetscObject)localX,"localX");
627: PetscObjectSetName((PetscObject)localF,"localF");
628: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
630: lambda = user->param;
631: hx = 1.0/(PetscReal)(Mx-1);
632: hy = 1.0/(PetscReal)(My-1);
634: PetscObjectGetComm((PetscObject)snes,&comm);
635: /*
636: Scatter ghost points to local vector,using the 2-step process
637: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
638: By placing code between these two statements, computations can be
639: done while messages are in transition.
640: */
641: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
642: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
643: PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);
644: PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);
645: PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);
647: /*
648: Insert values into global vector
649: */
650: DMLocalToGlobalBegin(da,localF,INSERT_VALUES,F);
651: DMLocalToGlobalEnd(da,localF,INSERT_VALUES,F);
652: DMRestoreLocalVector(da,&localX);
653: DMRestoreLocalVector(da,&localF);
654: return(0);
655: }
656: #endif
658: /* ------------------------------------------------------------------- */
659: /*
660: Applies some sweeps on nonlinear Gauss-Seidel on each process
662: */
663: PetscErrorCode NonlinearGS(SNES snes,Vec X, Vec B, void *ctx)
664: {
665: PetscInt i,j,k,Mx,My,xs,ys,xm,ym,its,tot_its,sweeps,l;
667: PetscReal lambda,hx,hy,hxdhy,hydhx,sc;
668: PetscScalar **x,**b,bij,F,F0=0,J,u,un,us,ue,eu,uw,uxx,uyy,y;
669: PetscReal atol,rtol,stol;
670: DM da;
671: AppCtx *user;
672: Vec localX,localB;
675: tot_its = 0;
676: SNESNGSGetSweeps(snes,&sweeps);
677: SNESNGSGetTolerances(snes,&atol,&rtol,&stol,&its);
678: SNESGetDM(snes,&da);
679: DMGetApplicationContext(da,(void**)&user);
681: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
683: lambda = user->param;
684: hx = 1.0/(PetscReal)(Mx-1);
685: hy = 1.0/(PetscReal)(My-1);
686: sc = hx*hy*lambda;
687: hxdhy = hx/hy;
688: hydhx = hy/hx;
691: DMGetLocalVector(da,&localX);
692: if (B) {
693: DMGetLocalVector(da,&localB);
694: }
695: for (l=0; l<sweeps; l++) {
697: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
698: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
699: if (B) {
700: DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);
701: DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);
702: }
703: /*
704: Get a pointer to vector data.
705: - For default PETSc vectors, VecGetArray() returns a pointer to
706: the data array. Otherwise, the routine is implementation dependent.
707: - You MUST call VecRestoreArray() when you no longer need access to
708: the array.
709: */
710: DMDAVecGetArray(da,localX,&x);
711: if (B) DMDAVecGetArray(da,localB,&b);
712: /*
713: Get local grid boundaries (for 2-dimensional DMDA):
714: xs, ys - starting grid indices (no ghost points)
715: xm, ym - widths of local grid (no ghost points)
716: */
717: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
719: for (j=ys; j<ys+ym; j++) {
720: for (i=xs; i<xs+xm; i++) {
721: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
722: /* boundary conditions are all zero Dirichlet */
723: x[j][i] = 0.0;
724: } else {
725: if (B) bij = b[j][i];
726: else bij = 0.;
728: u = x[j][i];
729: un = x[j-1][i];
730: us = x[j+1][i];
731: ue = x[j][i-1];
732: uw = x[j][i+1];
734: for (k=0; k<its; k++) {
735: eu = PetscExpScalar(u);
736: uxx = (2.0*u - ue - uw)*hydhx;
737: uyy = (2.0*u - un - us)*hxdhy;
738: F = uxx + uyy - sc*eu - bij;
739: if (k == 0) F0 = F;
740: J = 2.0*(hydhx + hxdhy) - sc*eu;
741: y = F/J;
742: u -= y;
743: tot_its++;
745: if (atol > PetscAbsReal(PetscRealPart(F)) ||
746: rtol*PetscAbsReal(PetscRealPart(F0)) > PetscAbsReal(PetscRealPart(F)) ||
747: stol*PetscAbsReal(PetscRealPart(u)) > PetscAbsReal(PetscRealPart(y))) {
748: break;
749: }
750: }
751: x[j][i] = u;
752: }
753: }
754: }
755: /*
756: Restore vector
757: */
758: DMDAVecRestoreArray(da,localX,&x);
759: DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
760: DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
761: }
762: PetscLogFlops(tot_its*(21.0));
763: DMRestoreLocalVector(da,&localX);
764: if (B) {
765: DMDAVecRestoreArray(da,localB,&b);
766: DMRestoreLocalVector(da,&localB);
767: }
768: return(0);
769: }
771: /*TEST
772: # ASM vs MSM
773: test:
774: suffix: asm_0
775: requires: !single
776: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu
777: test:
778: suffix: msm_0
779: requires: !single
780: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu
781: test:
782: suffix: asm_1
783: requires: !single
784: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8
785: test:
786: suffix: msm_1
787: requires: !single
788: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8
789: test:
790: suffix: asm_2
791: requires: !single
792: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8
793: test:
794: suffix: msm_2
795: requires: !single
796: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8
797: test:
798: suffix: asm_3
799: requires: !single
800: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8
801: test:
802: suffix: msm_3
803: requires: !single
804: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8
805: test:
806: suffix: asm_4
807: requires: !single
808: nsize: 2
809: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8
810: test:
811: suffix: msm_4
812: requires: !single
813: nsize: 2
814: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8
815: test:
816: suffix: asm_5
817: requires: !single
818: nsize: 2
819: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8
820: test:
821: suffix: msm_5
822: requires: !single
823: nsize: 2
824: args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8
826: TEST*/