Actual source code: ex48.c

  1: static char help[] = "Magnetohydrodynamics (MHD) with Poisson brackets and "
  2:                      "stream functions, solver testbed for M3D-C1. Used in https://arxiv.org/abs/2302.10242";

  4: /*F
  5: The strong form of a two field model for vorticity $\Omega$ and magnetic flux
  6: $\psi$, using auxiliary variables potential $\phi$ and (negative) current
  7: density $j_z$ \cite{Jardin04,Strauss98}.See http://arxiv.org/abs/  for more details
  8: F*/

 10: #include <assert.h>
 11: #include <petscdmplex.h>
 12: #include <petscds.h>
 13: #include <petscts.h>

 15: typedef enum _testidx {
 16:   TEST_TILT,
 17:   NUM_TEST_TYPES
 18: } TestType;
 19: const char *testTypes[NUM_TEST_TYPES + 1] = {"tilt", "unknown"};
 20: typedef enum _modelidx {
 21:   TWO_FILD,
 22:   ONE_FILD,
 23:   NUM_MODELS
 24: } ModelType;
 25: const char *modelTypes[NUM_MODELS + 1] = {"two-field", "one-field", "unknown"};
 26: typedef enum _fieldidx {
 27:   JZ,
 28:   PSI,
 29:   PHI,
 30:   OMEGA,
 31:   NUM_COMP
 32: } FieldIdx; // add more
 33: typedef enum _const_idx {
 34:   MU_CONST,
 35:   ETA_CONST,
 36:   TEST_CONST,
 37:   NUM_CONSTS
 38: } ConstIdx;

 40: typedef struct {
 41:   PetscInt  debug; /* The debugging level */
 42:   PetscReal plotDt;
 43:   PetscReal plotStartTime;
 44:   PetscInt  plotIdx;
 45:   PetscInt  plotStep;
 46:   PetscBool plotting;
 47:   PetscInt  dim;                          /* The topological mesh dimension */
 48:   char      filename[PETSC_MAX_PATH_LEN]; /* The optional ExodusII file */
 49:   PetscErrorCode (**initialFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
 50:   PetscReal mu, eta;
 51:   PetscReal perturb;
 52:   TestType  testType;
 53:   ModelType modelType;
 54:   PetscInt  Nf;
 55: } AppCtx;

 57: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
 58: {
 59:   PetscInt ii;

 61:   PetscFunctionBeginUser;
 62:   options->debug         = 1;
 63:   options->filename[0]   = '\0';
 64:   options->testType      = TEST_TILT;
 65:   options->modelType     = TWO_FILD;
 66:   options->mu            = 0.005;
 67:   options->eta           = 0.001;
 68:   options->perturb       = 0;
 69:   options->plotDt        = 0.1;
 70:   options->plotStartTime = 0.0;
 71:   options->plotIdx       = 0;
 72:   options->plotStep      = PETSC_MAX_INT;
 73:   options->plotting      = PETSC_FALSE;

 75:   PetscOptionsBegin(comm, "", "MHD Problem Options", "DMPLEX");
 76:   PetscCall(PetscOptionsInt("-debug", "The debugging level", "mhd.c", options->debug, &options->debug, NULL));
 77:   ii                = (PetscInt)options->testType;
 78:   options->testType = TEST_TILT;
 79:   ii                = options->testType;
 80:   PetscCall(PetscOptionsEList("-test_type", "The test type: 'tilt' Tilt instability", "mhd.c", testTypes, NUM_TEST_TYPES, testTypes[options->testType], &ii, NULL));
 81:   options->testType  = (TestType)ii;
 82:   ii                 = (PetscInt)options->modelType;
 83:   options->modelType = TWO_FILD;
 84:   ii                 = options->modelType;
 85:   PetscCall(PetscOptionsEList("-model_type", "The model type: 'two', 'one' field", "mhd.c", modelTypes, NUM_MODELS, modelTypes[options->modelType], &ii, NULL));
 86:   options->modelType = (ModelType)ii;
 87:   options->Nf        = options->modelType == TWO_FILD ? 4 : 2;

 89:   PetscCall(PetscOptionsReal("-mu", "Magnetic resistivity", "mhd.c", options->mu, &options->mu, NULL));
 90:   PetscCall(PetscOptionsReal("-eta", "Viscosity", "mhd.c", options->eta, &options->eta, NULL));
 91:   PetscCall(PetscOptionsReal("-plot_dt", "Plot frequency in time", "mhd.c", options->plotDt, &options->plotDt, NULL));
 92:   PetscCall(PetscOptionsReal("-plot_start_time", "Time to delay start of plotting", "mhd.c", options->plotStartTime, &options->plotStartTime, NULL));
 93:   PetscCall(PetscOptionsReal("-perturbation", "Random perturbation of initial psi scale", "mhd.c", options->perturb, &options->perturb, NULL));
 94:   PetscCall(PetscPrintf(comm, "Test Type = %s\n", testTypes[options->testType]));
 95:   PetscCall(PetscPrintf(comm, "Model Type = %s\n", modelTypes[options->modelType]));
 96:   PetscCall(PetscPrintf(comm, "eta = %g\n", (double)options->eta));
 97:   PetscCall(PetscPrintf(comm, "mu = %g\n", (double)options->mu));
 98:   PetscOptionsEnd();

100:   PetscFunctionReturn(PETSC_SUCCESS);
101: }

103: // | 0 1 | matrix to apply bracket
104: // |-1 0 |
105: static PetscReal s_K[2][2] = {
106:   {0,  1},
107:   {-1, 0}
108: };

110: /*
111:  dt - "g0" are mass terms
112: */
113: static void g0_dt(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
114: {
115:   g0[0] = u_tShift;
116: }

118: /*
119:  Identity, Mass
120: */
121: static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
122: {
123:   g0[0] = 1;
124: }
125: /* 'right' Poisson bracket -<.,phi>, linearized variable is left (column), data
126:  * variable right */
127: static void g1_phi_right(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
128: {
129:   PetscInt           i, j;
130:   const PetscScalar *pphiDer = &u_x[uOff_x[PHI]]; // get derivative of the 'right' ("dg") and apply to
131:                                                   // live var "df"
132:   for (i = 0; i < dim; ++i)
133:     for (j = 0; j < dim; ++j)
134:       //  indexing with inner, j, index generates the left live variable [dy,-]
135:       //  by convention, put j index on right, with i destination: [ d/dy,
136:       //  -d/dx]'
137:       g1[i] += s_K[i][j] * pphiDer[j];
138: }
139: /* 'left' bracket -{jz,.}, "n" for negative, linearized variable right (column),
140:  * data variable left */
141: static void g1_njz_left(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
142: {
143:   PetscInt           i, j;
144:   const PetscScalar *jzDer = &u_x[uOff_x[JZ]]; // get derivative of the 'left' ("df") and apply to live
145:                                                // var "dg"
146:   for (i = 0; i < dim; ++i)
147:     for (j = 0; j < dim; ++j)
148:       // live right: Der[i] * K: Der[j] --> j: [d/dy, -d/dx]'
149:       g1[j] += -jzDer[i] * s_K[i][j];
150: }
151: /* 'left' Poisson bracket -< . , psi> */
152: static void g1_npsi_right(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
153: {
154:   PetscInt           i, j;
155:   const PetscScalar *psiDer = &u_x[uOff_x[PSI]];
156:   for (i = 0; i < dim; ++i)
157:     for (j = 0; j < dim; ++j) g1[i] += -s_K[i][j] * psiDer[j];
158: }

160: /* < Omega , . > */
161: static void g1_omega_left(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
162: {
163:   PetscInt           i, j;
164:   const PetscScalar *pOmegaDer = &u_x[uOff_x[OMEGA]];
165:   for (i = 0; i < dim; ++i)
166:     for (j = 0; j < dim; ++j) g1[j] += pOmegaDer[i] * s_K[i][j];
167: }

169: /* < psi , . > */
170: static void g1_psi_left(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
171: {
172:   PetscInt           i, j;
173:   const PetscScalar *pPsiDer = &u_x[uOff_x[PSI]];
174:   for (i = 0; i < dim; ++i)
175:     for (j = 0; j < dim; ++j) g1[j] += pPsiDer[i] * s_K[i][j];
176: }

178: // -Lapacians (resistivity), negative sign goes away from IBP
179: static void g3_nmu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
180: {
181:   PetscReal mu = PetscRealPart(constants[MU_CONST]);
182:   for (PetscInt d = 0; d < dim; ++d) g3[d * dim + d] = mu;
183: }

185: // Auxiliary variable = -del^2 x, negative sign goes away from IBP
186: static void g3_n1(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
187: {
188:   PetscInt d;
189:   for (d = 0; d < dim; ++d) g3[d * dim + d] = 1;
190: }

192: /* residual point methods */
193: static PetscScalar poissonBracket(PetscInt dim, const PetscScalar df[], const PetscScalar dg[])
194: {
195:   PetscScalar ret = df[0] * dg[1] - df[1] * dg[0];
196:   if (dim == 3) {
197:     ret += df[1] * dg[2] - df[2] * dg[1];
198:     ret += df[2] * dg[0] - df[0] * dg[2];
199:   }
200:   return ret;
201: }
202: //
203: static void f0_Omega(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
204: {
205:   const PetscScalar *omegaDer = &u_x[uOff_x[OMEGA]];
206:   const PetscScalar *psiDer   = &u_x[uOff_x[PSI]];
207:   const PetscScalar *phiDer   = &u_x[uOff_x[PHI]];
208:   const PetscScalar *jzDer    = &u_x[uOff_x[JZ]];

210:   f0[0] += poissonBracket(dim, omegaDer, phiDer) - poissonBracket(dim, jzDer, psiDer);

212:   if (u_t) f0[0] += u_t[OMEGA];
213: }

215: static void f1_Omega(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
216: {
217:   const PetscScalar *omegaDer = &u_x[uOff_x[OMEGA]];
218:   PetscReal          mu       = PetscRealPart(constants[MU_CONST]);

220:   for (PetscInt d = 0; d < dim; ++d) f1[d] += mu * omegaDer[d];
221: }

223: // d/dt + {psi,phi} - eta j_z
224: static void f0_psi_4f(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
225: {
226:   const PetscScalar *psiDer = &u_x[uOff_x[PSI]];
227:   const PetscScalar *phiDer = &u_x[uOff_x[PHI]];
228:   PetscReal          eta    = PetscRealPart(constants[ETA_CONST]);

230:   f0[0] = -eta * u[uOff[JZ]];
231:   f0[0] += poissonBracket(dim, psiDer, phiDer);

233:   if (u_t) f0[0] += u_t[PSI];
234:   // printf("psiDer = %20.15e %20.15e psi = %20.15e
235: }

237: // d/dt - eta j_z
238: static void f0_psi_2f(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
239: {
240:   PetscReal eta = PetscRealPart(constants[ETA_CONST]);

242:   f0[0] = -eta * u[uOff[JZ]];

244:   if (u_t) f0[0] += u_t[PSI];
245:   // printf("psiDer = %20.15e %20.15e psi = %20.15e
246: }

248: static void f0_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
249: {
250:   f0[0] += u[uOff[OMEGA]];
251: }

253: static void f1_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
254: {
255:   const PetscScalar *phiDer = &u_x[uOff_x[PHI]];

257:   for (PetscInt d = 0; d < dim; ++d) f1[d] = phiDer[d];
258: }

260: /* - eta M */
261: static void g0_neta(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
262: {
263:   PetscReal eta = PetscRealPart(constants[ETA_CONST]);

265:   g0[0] = -eta;
266: }

268: static void f0_jz(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
269: {
270:   f0[0] = u[uOff[JZ]];
271: }

273: /* -del^2 psi = (grad v, grad psi) */
274: static void f1_jz(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
275: {
276:   const PetscScalar *psiDer = &u_x[uOff_x[PSI]];

278:   for (PetscInt d = 0; d < dim; ++d) f1[d] = psiDer[d];
279: }

281: static void f0_mhd_B_energy2(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
282: {
283:   const PetscScalar *psiDer = &u_x[uOff_x[PSI]];
284:   PetscScalar        b2     = 0;
285:   for (int i = 0; i < dim; ++i) b2 += psiDer[i] * psiDer[i];
286:   f0[0] = b2;
287: }

289: static void f0_mhd_v_energy2(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
290: {
291:   const PetscScalar *phiDer = &u_x[uOff_x[PHI]];
292:   PetscScalar        v2     = 0;
293:   for (int i = 0; i < dim; ++i) v2 += phiDer[i] * phiDer[i];
294:   f0[0] = v2;
295: }

297: static PetscErrorCode Monitor(TS ts, PetscInt stepi, PetscReal time, Vec X, void *actx)
298: {
299:   AppCtx             *ctx = (AppCtx *)actx; /* user-defined application context */
300:   SNES                snes;
301:   SNESConvergedReason reason;
302:   TSConvergedReason   tsreason;

304:   PetscFunctionBegin;
305:   // PetscCall(TSGetApplicationContext(ts, &ctx));
306:   if (ctx->debug < 1) PetscFunctionReturn(PETSC_SUCCESS);
307:   PetscCall(TSGetSNES(ts, &snes));
308:   PetscCall(SNESGetConvergedReason(snes, &reason));
309:   if (reason < 0) {
310:     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)ts), "\t\t ***************** Monitor: SNES diverged with reason %d.\n", (int)reason));
311:     PetscFunctionReturn(PETSC_SUCCESS);
312:   }
313:   if (stepi > ctx->plotStep && ctx->plotting) {
314:     ctx->plotting = PETSC_FALSE; /* was doing diagnostics, now done */
315:     ctx->plotIdx++;
316:   }
317:   PetscCall(TSGetTime(ts, &time));
318:   PetscCall(TSGetConvergedReason(ts, &tsreason));
319:   if (((time - ctx->plotStartTime) / ctx->plotDt >= (PetscReal)ctx->plotIdx && time >= ctx->plotStartTime) || (tsreason == TS_CONVERGED_TIME || tsreason == TS_CONVERGED_ITS) || ctx->plotIdx == 0) {
320:     DM          dm, plex;
321:     Vec         X;
322:     PetscReal   val;
323:     PetscScalar tt[12]; // FE integral seems to need a large array
324:     PetscDS     prob;
325:     if (!ctx->plotting) { /* first step of possible backtracks */
326:       ctx->plotting = PETSC_TRUE;
327:     } else {
328:       PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\t\t ?????? ------\n"));
329:       ctx->plotting = PETSC_TRUE;
330:     }
331:     ctx->plotStep = stepi;
332:     PetscCall(TSGetSolution(ts, &X));
333:     PetscCall(VecGetDM(X, &dm));
334:     PetscCall(DMGetOutputSequenceNumber(dm, NULL, &val));
335:     PetscCall(DMSetOutputSequenceNumber(dm, ctx->plotIdx, val));
336:     PetscCall(VecViewFromOptions(X, NULL, "-vec_view_mhd"));
337:     if (ctx->debug > 2) {
338:       Vec R;
339:       PetscCall(SNESGetFunction(snes, &R, NULL, NULL));
340:       PetscCall(VecViewFromOptions(R, NULL, "-vec_view_res"));
341:     }
342:     // compute energy
343:     PetscCall(DMGetDS(dm, &prob));
344:     PetscCall(DMConvert(dm, DMPLEX, &plex));
345:     PetscCall(PetscDSSetObjective(prob, 0, &f0_mhd_v_energy2));
346:     PetscCall(DMPlexComputeIntegralFEM(plex, X, &tt[0], ctx));
347:     val = PetscRealPart(tt[0]);
348:     PetscCall(PetscDSSetObjective(prob, 0, &f0_mhd_B_energy2));
349:     PetscCall(DMPlexComputeIntegralFEM(plex, X, &tt[0], ctx));
350:     val = PetscSqrtReal(val) * 0.5 + PetscSqrtReal(PetscRealPart(tt[0])) * 0.5;
351:     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)ts), "MHD %4d) time = %9.5g, Eergy= %20.13e (plot ID %d)\n", (int)ctx->plotIdx, (double)time, (double)val, (int)ctx->plotIdx));
352:     /* clean up */
353:     PetscCall(DMDestroy(&plex));
354:   }
355:   PetscFunctionReturn(PETSC_SUCCESS);
356: }

358: static PetscErrorCode CreateBCLabel(DM dm, const char name[])
359: {
360:   DMLabel label;
361:   PetscFunctionBeginUser;
362:   PetscCall(DMCreateLabel(dm, name));
363:   PetscCall(DMGetLabel(dm, name, &label));
364:   PetscCall(DMPlexMarkBoundaryFaces(dm, PETSC_DETERMINE, label));
365:   PetscCall(DMPlexLabelComplete(dm, label));
366:   PetscFunctionReturn(PETSC_SUCCESS);
367: }
368: // Create mesh, dim is set here
369: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *ctx, DM *dm)
370: {
371:   const char *filename = ctx->filename;
372:   size_t      len;
373:   char        buff[256];
374:   PetscMPIInt size;
375:   PetscInt    nface = 1;
376:   PetscFunctionBeginUser;
377:   PetscCall(PetscStrlen(filename, &len));
378:   if (len) {
379:     PetscCall(DMPlexCreateFromFile(comm, filename, "", PETSC_TRUE, dm));
380:   } else {
381:     PetscCall(DMCreate(comm, dm));
382:     PetscCall(DMSetType(*dm, DMPLEX));
383:   }
384:   PetscCallMPI(MPI_Comm_size(comm, &size));
385:   while (nface * nface < size) nface *= 2; // 2D
386:   if (nface < 2) nface = 2;
387:   PetscCall(PetscSNPrintf(buff, sizeof(buff), "-dm_plex_box_faces %d,%d -petscpartitioner_type simple", (int)nface, (int)nface));
388:   PetscCall(PetscOptionsInsertString(NULL, buff));
389:   PetscCall(PetscOptionsInsertString(NULL, "-dm_plex_box_lower -2,-2 -dm_plex_box_upper 2,2"));
390:   PetscCall(DMSetFromOptions(*dm));
391:   PetscCall(DMPlexDistributeSetDefault(*dm, PETSC_FALSE));
392:   PetscCall(DMGetDimension(*dm, &ctx->dim));
393:   {
394:     char      convType[256];
395:     PetscBool flg;
396:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
397:     PetscCall(PetscOptionsFList("-dm_plex_convert_type", "Convert DMPlex to another format", "mhd", DMList, DMPLEX, convType, 256, &flg));
398:     PetscOptionsEnd();
399:     if (flg) {
400:       DM dmConv;
401:       PetscCall(DMConvert(*dm, convType, &dmConv));
402:       if (dmConv) {
403:         PetscCall(DMDestroy(dm));
404:         *dm = dmConv;
405:       }
406:     }
407:   }
408:   PetscCall(DMLocalizeCoordinates(*dm)); /* needed for periodic */
409:   {
410:     PetscBool hasLabel;
411:     PetscCall(DMHasLabel(*dm, "marker", &hasLabel));
412:     if (!hasLabel) PetscCall(CreateBCLabel(*dm, "marker"));
413:   }
414:   PetscCall(PetscObjectSetName((PetscObject)*dm, "Mesh"));
415:   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view_mhd"));
416:   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view_res"));

418:   PetscFunctionReturn(PETSC_SUCCESS);
419: }

421: static PetscErrorCode initialSolution_Omega(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
422: {
423:   u[0] = 0.0;
424:   return PETSC_SUCCESS;
425: }

427: static PetscErrorCode initialSolution_Psi(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *a_ctx)
428: {
429:   AppCtx   *ctx = (AppCtx *)a_ctx;
430:   PetscReal r   = 0, theta, cos_theta;
431:   // k = sp.jn_zeros(1, 1)[0]
432:   const PetscReal k = 3.8317059702075125;
433:   for (PetscInt i = 0; i < dim; i++) r += x[i] * x[i];
434:   r = PetscSqrtReal(r);
435:   // r = sqrt(dot(x,x))
436:   theta     = PetscAtan2Real(x[1], x[0]);
437:   cos_theta = PetscCosReal(theta);
438:   // f = conditional(gt(r, 1.0), outer_f, inner_f)
439:   if (r < 1.0) {
440:     // inner_f =
441:     // (2/(Constant(k)*bessel_J(0,Constant(k))))*bessel_J(1,Constant(k)*r)*cos_theta
442:     u[0] = 2.0 / (k * j0(k)) * j1(k * r) * cos_theta;
443:   } else {
444:     // outer_f =  (1/r - r)*cos_theta
445:     u[0] = (r - 1.0 / r) * cos_theta;
446:   }
447:   u[0] += ctx->perturb * ((double)rand() / (double)RAND_MAX - 0.5);
448:   return PETSC_SUCCESS;
449: }

451: static PetscErrorCode initialSolution_Phi(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
452: {
453:   u[0] = 0.0;
454:   return PETSC_SUCCESS;
455: }

457: static PetscErrorCode initialSolution_Jz(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
458: {
459:   u[0] = 0.0;
460:   return PETSC_SUCCESS;
461: }

463: static PetscErrorCode SetupProblem(PetscDS prob, DM dm, AppCtx *ctx)
464: {
465:   PetscInt f;

467:   PetscFunctionBeginUser;
468:   // for both 2 & 4 field (j_z is same)
469:   PetscCall(PetscDSSetJacobian(prob, JZ, JZ, g0_1, NULL, NULL, NULL));
470:   PetscCall(PetscDSSetJacobian(prob, JZ, PSI, NULL, NULL, NULL, g3_n1));
471:   PetscCall(PetscDSSetResidual(prob, JZ, f0_jz, f1_jz));

473:   PetscCall(PetscDSSetJacobian(prob, PSI, JZ, g0_neta, NULL, NULL, NULL));
474:   if (ctx->modelType == ONE_FILD) {
475:     PetscCall(PetscDSSetJacobian(prob, PSI, PSI, g0_dt, NULL, NULL,
476:                                  NULL)); // remove phi term

478:     PetscCall(PetscDSSetResidual(prob, PSI, f0_psi_2f, NULL));
479:   } else {
480:     PetscCall(PetscDSSetJacobian(prob, PSI, PSI, g0_dt, g1_phi_right, NULL, NULL));
481:     PetscCall(PetscDSSetJacobian(prob, PSI, PHI, NULL, g1_psi_left, NULL, NULL));
482:     PetscCall(PetscDSSetResidual(prob, PSI, f0_psi_4f, NULL));

484:     PetscCall(PetscDSSetJacobian(prob, PHI, PHI, NULL, NULL, NULL, g3_n1));
485:     PetscCall(PetscDSSetJacobian(prob, PHI, OMEGA, g0_1, NULL, NULL, NULL));
486:     PetscCall(PetscDSSetResidual(prob, PHI, f0_phi, f1_phi));

488:     PetscCall(PetscDSSetJacobian(prob, OMEGA, OMEGA, g0_dt, g1_phi_right, NULL, g3_nmu));
489:     PetscCall(PetscDSSetJacobian(prob, OMEGA, PSI, NULL, g1_njz_left, NULL, NULL));
490:     PetscCall(PetscDSSetJacobian(prob, OMEGA, PHI, NULL, g1_omega_left, NULL, NULL));
491:     PetscCall(PetscDSSetJacobian(prob, OMEGA, JZ, NULL, g1_npsi_right, NULL, NULL));
492:     PetscCall(PetscDSSetResidual(prob, OMEGA, f0_Omega, f1_Omega));
493:   }
494:   /* Setup constants - is this persistent? */
495:   {
496:     PetscScalar scales[NUM_CONSTS]; // +1 adding in testType for use in the f
497:                                     // and g functions
498:     /* These could be set from the command line */
499:     scales[MU_CONST]  = ctx->mu;
500:     scales[ETA_CONST] = ctx->eta;
501:     // scales[TEST_CONST] = (PetscReal)ctx->testType; -- how to make work with complex
502:     PetscCall(PetscDSSetConstants(prob, NUM_CONSTS, scales));
503:   }
504:   for (f = 0; f < ctx->Nf; ++f) {
505:     ctx->initialFuncs[f] = NULL;
506:     PetscCall(PetscDSSetImplicit(prob, f, PETSC_TRUE));
507:   }
508:   if (ctx->testType == TEST_TILT) {
509:     const PetscInt id = 1;
510:     DMLabel        label;
511:     PetscCall(DMGetLabel(dm, "marker", &label));

513:     ctx->initialFuncs[JZ]  = initialSolution_Jz;
514:     ctx->initialFuncs[PSI] = initialSolution_Psi;

516:     PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "Jz for tilt test", label, 1, &id, JZ, 0, NULL, (void (*)(void))initialSolution_Jz, NULL, ctx, NULL));
517:     PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "Psi for tilt test", label, 1, &id, PSI, 0, NULL, (void (*)(void))initialSolution_Psi, NULL, ctx, NULL));
518:     if (ctx->modelType == TWO_FILD) {
519:       ctx->initialFuncs[OMEGA] = initialSolution_Omega;
520:       ctx->initialFuncs[PHI]   = initialSolution_Phi;
521:       PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "Omega for tilt test", label, 1, &id, OMEGA, 0, NULL, (void (*)(void))initialSolution_Omega, NULL, ctx, NULL));
522:       PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "Phi for tilt test", label, 1, &id, PHI, 0, NULL, (void (*)(void))initialSolution_Phi, NULL, ctx, NULL));
523:     }
524:   } else {
525:     PetscCheck(0, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unsupported test type: %s (%d)", testTypes[PetscMin(ctx->testType, NUM_TEST_TYPES)], (int)ctx->testType);
526:   }
527:   PetscCall(PetscDSSetContext(prob, 0, ctx));
528:   PetscCall(PetscDSSetFromOptions(prob));
529:   PetscFunctionReturn(PETSC_SUCCESS);
530: }

532: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *ctx)
533: {
534:   DM             cdm;
535:   const PetscInt dim = ctx->dim;
536:   PetscFE        fe[NUM_COMP];
537:   PetscDS        prob;
538:   PetscInt       Nf           = ctx->Nf, f;
539:   PetscBool      cell_simplex = PETSC_TRUE;
540:   MPI_Comm       comm         = PetscObjectComm((PetscObject)dm);

542:   PetscFunctionBeginUser;
543:   /* Create finite element */
544:   PetscCall(PetscFECreateDefault(comm, dim, 1, cell_simplex, NULL, -1, &fe[JZ]));
545:   PetscCall(PetscObjectSetName((PetscObject)fe[JZ], "j_z"));
546:   PetscCall(DMSetField(dm, JZ, NULL, (PetscObject)fe[JZ]));
547:   PetscCall(PetscFECreateDefault(comm, dim, 1, cell_simplex, NULL, -1, &fe[PSI]));
548:   PetscCall(PetscObjectSetName((PetscObject)fe[PSI], "psi"));
549:   PetscCall(DMSetField(dm, PSI, NULL, (PetscObject)fe[PSI]));
550:   if (ctx->modelType == TWO_FILD) {
551:     PetscCall(PetscFECreateDefault(comm, dim, 1, cell_simplex, NULL, -1, &fe[OMEGA]));
552:     PetscCall(PetscObjectSetName((PetscObject)fe[OMEGA], "Omega"));
553:     PetscCall(DMSetField(dm, OMEGA, NULL, (PetscObject)fe[OMEGA]));

555:     PetscCall(PetscFECreateDefault(comm, dim, 1, cell_simplex, NULL, -1, &fe[PHI]));
556:     PetscCall(PetscObjectSetName((PetscObject)fe[PHI], "phi"));
557:     PetscCall(DMSetField(dm, PHI, NULL, (PetscObject)fe[PHI]));
558:   }
559:   /* Set discretization and boundary conditions for each mesh */
560:   PetscCall(DMCreateDS(dm));
561:   PetscCall(DMGetDS(dm, &prob));
562:   for (f = 0; f < Nf; ++f) PetscCall(PetscDSSetDiscretization(prob, f, (PetscObject)fe[f]));
563:   PetscCall(SetupProblem(prob, dm, ctx));
564:   cdm = dm;
565:   while (cdm) {
566:     PetscCall(DMCopyDisc(dm, cdm));
567:     if (dm != cdm) PetscCall(PetscObjectSetName((PetscObject)cdm, "Coarse"));
568:     PetscCall(DMGetCoarseDM(cdm, &cdm));
569:   }
570:   for (f = 0; f < Nf; ++f) PetscCall(PetscFEDestroy(&fe[f]));
571:   PetscFunctionReturn(PETSC_SUCCESS);
572: }

574: int main(int argc, char **argv)
575: {
576:   DM          dm;
577:   TS          ts;
578:   Vec         u, r;
579:   AppCtx      ctx;
580:   PetscReal   t        = 0.0;
581:   AppCtx     *ctxarr[] = {&ctx, &ctx, &ctx, &ctx}; // each variable could have a different context
582:   PetscMPIInt rank;

584:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
585:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
586:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &ctx)); // dim is not set
587:   /* create mesh and problem */
588:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &ctx, &dm));
589:   PetscCall(DMView(dm, PETSC_VIEWER_STDOUT_WORLD));
590:   PetscCall(DMSetApplicationContext(dm, &ctx));
591:   PetscCall(PetscMalloc1(ctx.Nf, &ctx.initialFuncs));
592:   PetscCall(SetupDiscretization(dm, &ctx));
593:   PetscCall(DMCreateGlobalVector(dm, &u));
594:   PetscCall(PetscObjectSetName((PetscObject)u, "u"));
595:   PetscCall(VecDuplicate(u, &r));
596:   PetscCall(PetscObjectSetName((PetscObject)r, "r"));
597:   /* create TS */
598:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
599:   PetscCall(TSSetDM(ts, dm));
600:   PetscCall(TSSetApplicationContext(ts, &ctx));
601:   PetscCall(DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &ctx));
602:   PetscCall(DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &ctx));
603:   PetscCall(DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &ctx));
604:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
605:   PetscCall(TSSetMaxTime(ts, 15.0));
606:   PetscCall(TSSetFromOptions(ts));
607:   PetscCall(TSMonitorSet(ts, Monitor, &ctx, NULL));
608:   /* make solution */
609:   PetscCall(DMProjectFunction(dm, t, ctx.initialFuncs, (void **)ctxarr, INSERT_ALL_VALUES, u));
610:   ctx.perturb = 0.0;
611:   PetscCall(TSSetSolution(ts, u));
612:   // solve
613:   PetscCall(TSSolve(ts, u));
614:   // cleanup
615:   PetscCall(VecDestroy(&u));
616:   PetscCall(VecDestroy(&r));
617:   PetscCall(TSDestroy(&ts));
618:   PetscCall(DMDestroy(&dm));
619:   PetscCall(PetscFree(ctx.initialFuncs));
620:   PetscCall(PetscFinalize());
621:   return 0;
622: }

624: /*TEST

626:   test:
627:     suffix: 0
628:     requires: triangle !complex
629:     nsize: 4
630:     args: -dm_plex_box_lower -2,-2 -dm_plex_box_upper 2,2 -dm_plex_simplex 1 -dm_refine_hierarchy 2 \
631:       -eta 0.0001 -ksp_converged_reason -ksp_max_it 50 -ksp_rtol 1e-3 -ksp_type fgmres -mg_coarse_ksp_rtol 1e-1 \
632:       -mg_coarse_ksp_type fgmres -mg_coarse_mg_levels_ksp_type gmres -mg_coarse_pc_type gamg -mg_levels_ksp_max_it 4 \
633:       -mg_levels_ksp_type gmres -mg_levels_pc_type jacobi -mu 0.005 -pc_mg_type full -pc_type mg \
634:       -petscpartitioner_type simple -petscspace_degree 2 -snes_converged_reason -snes_max_it 10 -snes_monitor \
635:       -snes_rtol 1.e-9 -snes_stol 1.e-9 -ts_adapt_dt_max 0.01 -ts_adapt_monitor -ts_arkimex_type 1bee \
636:       -ts_dt 0.001 -ts_max_reject 10 -ts_max_snes_failures -1 -ts_max_steps 1 -ts_max_time -ts_monitor -ts_type arkimex
637:     filter: grep -v DM_

639: TEST*/