Actual source code: ex6.c

  1: static char help[] = "Vlasov-Poisson example of central orbits\n";

  3: /*
  4:   To visualize the orbit, we can used

  6:     -ts_monitor_sp_swarm -ts_monitor_sp_swarm_retain -1 -ts_monitor_sp_swarm_phase 0 -draw_size 500,500

  8:   and we probably want it to run fast and not check convergence

 10:     -convest_num_refine 0 -ts_dt 0.01 -ts_max_steps 100 -ts_max_time 100 -output_step 10
 11: */

 13: #include <petscts.h>
 14: #include <petscdmplex.h>
 15: #include <petscdmswarm.h>
 16: #include <petsc/private/dmpleximpl.h>
 17: #include <petscfe.h>
 18: #include <petscds.h>
 19: #include <petsc/private/petscfeimpl.h>
 20: #include <petscksp.h>
 21: #include <petscsnes.h>

 23: PETSC_EXTERN PetscErrorCode circleSingleX(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
 24: PETSC_EXTERN PetscErrorCode circleSingleV(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
 25: PETSC_EXTERN PetscErrorCode circleMultipleX(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
 26: PETSC_EXTERN PetscErrorCode circleMultipleV(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);

 28: const char *EMTypes[] = {"primal", "mixed", "coulomb", "none", "EMType", "EM_", NULL};
 29: typedef enum {
 30:   EM_PRIMAL,
 31:   EM_MIXED,
 32:   EM_COULOMB,
 33:   EM_NONE
 34: } EMType;

 36: typedef struct {
 37:   PetscBool error;     /* Flag for printing the error */
 38:   PetscInt  ostep;     /* print the energy at each ostep time steps */
 39:   PetscReal timeScale; /* Nondimensionalizing time scale */
 40:   PetscReal sigma;     /* Linear charge per box length */
 41:   EMType    em;        /* Type of electrostatic model */
 42:   SNES      snes;
 43: } AppCtx;

 45: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
 46: {
 47:   PetscFunctionBeginUser;
 48:   options->error     = PETSC_FALSE;
 49:   options->ostep     = 100;
 50:   options->timeScale = 1.0e-6;
 51:   options->sigma     = 1.;
 52:   options->em        = EM_COULOMB;

 54:   PetscOptionsBegin(comm, "", "Central Orbit Options", "DMSWARM");
 55:   PetscCall(PetscOptionsBool("-error", "Flag to print the error", "ex6.c", options->error, &options->error, NULL));
 56:   PetscCall(PetscOptionsInt("-output_step", "Number of time steps between output", "ex6.c", options->ostep, &options->ostep, NULL));
 57:   PetscCall(PetscOptionsReal("-sigma", "Linear charge per box length", "ex6.c", options->sigma, &options->sigma, NULL));
 58:   PetscCall(PetscOptionsReal("-timeScale", "Nondimensionalizing time scale", "ex6.c", options->timeScale, &options->timeScale, NULL));
 59:   PetscCall(PetscOptionsEnum("-em_type", "Type of electrostatic solver", "ex6.c", EMTypes, (PetscEnum)options->em, (PetscEnum *)&options->em, NULL));
 60:   PetscOptionsEnd();
 61:   PetscFunctionReturn(PETSC_SUCCESS);
 62: }

 64: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
 65: {
 66:   PetscFunctionBeginUser;
 67:   PetscCall(DMCreate(comm, dm));
 68:   PetscCall(DMSetType(*dm, DMPLEX));
 69:   PetscCall(DMSetFromOptions(*dm));
 70:   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
 71:   PetscFunctionReturn(PETSC_SUCCESS);
 72: }

 74: static void laplacian_f1(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[])
 75: {
 76:   PetscInt d;
 77:   for (d = 0; d < dim; ++d) f1[d] = u_x[d];
 78: }

 80: static void laplacian_g3(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[])
 81: {
 82:   PetscInt d;
 83:   for (d = 0; d < dim; ++d) g3[d * dim + d] = 1.0;
 84: }

 86: /*
 87:    /  I   grad\ /q\ = /0\
 88:    \-div    0 / \u/   \f/
 89: */
 90: static void f0_q(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[])
 91: {
 92:   for (PetscInt c = 0; c < dim; ++c) f0[c] += u[uOff[0] + c];
 93: }

 95: static void f1_q(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[])
 96: {
 97:   for (PetscInt d = 0; d < dim; ++d) f1[d * dim + d] += u[uOff[1]];
 98: }

100: /* <t, q> */
101: static void g0_qq(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[])
102: {
103:   PetscInt c;
104:   for (c = 0; c < dim; ++c) g0[c * dim + c] += 1.0;
105: }

107: static void g2_qu(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 g2[])
108: {
109:   for (PetscInt d = 0; d < dim; ++d) g2[d * dim + d] += 1.0;
110: }

112: static void g1_uq(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[])
113: {
114:   for (PetscInt d = 0; d < dim; ++d) g1[d * dim + d] += 1.0;
115: }

117: static PetscErrorCode CreateFEM(DM dm, AppCtx *user)
118: {
119:   PetscFE   feu, feq;
120:   PetscDS   ds;
121:   PetscBool simplex;
122:   PetscInt  dim;

124:   PetscFunctionBeginUser;
125:   PetscCall(DMGetDimension(dm, &dim));
126:   PetscCall(DMPlexIsSimplex(dm, &simplex));
127:   if (user->em == EM_MIXED) {
128:     DMLabel label;

130:     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "field_", PETSC_DETERMINE, &feq));
131:     PetscCall(PetscObjectSetName((PetscObject)feq, "field"));
132:     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "potential_", PETSC_DETERMINE, &feu));
133:     PetscCall(PetscObjectSetName((PetscObject)feu, "potential"));
134:     PetscCall(PetscFECopyQuadrature(feq, feu));
135:     PetscCall(DMSetField(dm, 0, NULL, (PetscObject)feq));
136:     PetscCall(DMSetField(dm, 1, NULL, (PetscObject)feu));
137:     PetscCall(DMCreateDS(dm));
138:     PetscCall(PetscFEDestroy(&feu));
139:     PetscCall(PetscFEDestroy(&feq));

141:     PetscCall(DMGetLabel(dm, "marker", &label));
142:     PetscCall(DMGetDS(dm, &ds));
143:     PetscCall(PetscDSSetResidual(ds, 0, f0_q, f1_q));
144:     PetscCall(PetscDSSetJacobian(ds, 0, 0, g0_qq, NULL, NULL, NULL));
145:     PetscCall(PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_qu, NULL));
146:     PetscCall(PetscDSSetJacobian(ds, 1, 0, NULL, g1_uq, NULL, NULL));
147:   } else if (user->em == EM_PRIMAL) {
148:     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, PETSC_DETERMINE, &feu));
149:     PetscCall(PetscObjectSetName((PetscObject)feu, "potential"));
150:     PetscCall(DMSetField(dm, 0, NULL, (PetscObject)feu));
151:     PetscCall(DMCreateDS(dm));
152:     PetscCall(PetscFEDestroy(&feu));
153:     PetscCall(DMGetDS(dm, &ds));
154:     PetscCall(PetscDSSetResidual(ds, 0, NULL, laplacian_f1));
155:     PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, laplacian_g3));
156:   }
157:   PetscFunctionReturn(PETSC_SUCCESS);
158: }

160: static PetscErrorCode CreatePoisson(DM dm, AppCtx *user)
161: {
162:   SNES         snes;
163:   Mat          J;
164:   MatNullSpace nullSpace;

166:   PetscFunctionBeginUser;
167:   PetscCall(CreateFEM(dm, user));
168:   PetscCall(SNESCreate(PetscObjectComm((PetscObject)dm), &snes));
169:   PetscCall(SNESSetOptionsPrefix(snes, "em_"));
170:   PetscCall(SNESSetDM(snes, dm));
171:   PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, user));
172:   PetscCall(SNESSetFromOptions(snes));

174:   PetscCall(DMCreateMatrix(dm, &J));
175:   PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_TRUE, 0, NULL, &nullSpace));
176:   PetscCall(MatSetNullSpace(J, nullSpace));
177:   PetscCall(MatNullSpaceDestroy(&nullSpace));
178:   PetscCall(SNESSetJacobian(snes, J, J, NULL, NULL));
179:   PetscCall(MatDestroy(&J));
180:   user->snes = snes;
181:   PetscFunctionReturn(PETSC_SUCCESS);
182: }

184: static PetscErrorCode CreateSwarm(DM dm, AppCtx *user, DM *sw)
185: {
186:   PetscReal v0[1] = {1.};
187:   PetscInt  dim;

189:   PetscFunctionBeginUser;
190:   PetscCall(DMGetDimension(dm, &dim));
191:   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), sw));
192:   PetscCall(DMSetType(*sw, DMSWARM));
193:   PetscCall(DMSetDimension(*sw, dim));
194:   PetscCall(DMSwarmSetType(*sw, DMSWARM_PIC));
195:   PetscCall(DMSwarmSetCellDM(*sw, dm));
196:   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "w_q", 1, PETSC_SCALAR));
197:   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "velocity", dim, PETSC_REAL));
198:   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "species", 1, PETSC_INT));
199:   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "initCoordinates", dim, PETSC_REAL));
200:   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "initVelocity", dim, PETSC_REAL));
201:   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "E_field", dim, PETSC_REAL));
202:   PetscCall(DMSwarmFinalizeFieldRegister(*sw));
203:   PetscCall(DMSwarmComputeLocalSizeFromOptions(*sw));
204:   PetscCall(DMSwarmInitializeCoordinates(*sw));
205:   PetscCall(DMSwarmInitializeVelocitiesFromOptions(*sw, v0));
206:   PetscCall(DMSetFromOptions(*sw));
207:   PetscCall(DMSetApplicationContext(*sw, user));
208:   PetscCall(PetscObjectSetName((PetscObject)*sw, "Particles"));
209:   PetscCall(DMViewFromOptions(*sw, NULL, "-sw_view"));
210:   {
211:     Vec gc, gc0, gv, gv0;

213:     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, DMSwarmPICField_coor, &gc));
214:     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, "initCoordinates", &gc0));
215:     PetscCall(VecCopy(gc, gc0));
216:     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, DMSwarmPICField_coor, &gc));
217:     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, "initCoordinates", &gc0));
218:     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, "velocity", &gv));
219:     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, "initVelocity", &gv0));
220:     PetscCall(VecCopy(gv, gv0));
221:     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, "velocity", &gv));
222:     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, "initVelocity", &gv0));
223:   }
224:   {
225:     const char *fieldnames[2] = {DMSwarmPICField_coor, "velocity"};

227:     PetscCall(DMSwarmVectorDefineFields(*sw, 2, fieldnames));
228:   }
229:   PetscFunctionReturn(PETSC_SUCCESS);
230: }

232: static PetscErrorCode ComputeFieldAtParticles_Coulomb(SNES snes, DM sw, PetscReal E[])
233: {
234:   PetscReal  *coords;
235:   PetscInt    dim, d, Np, p, q;
236:   PetscMPIInt size;

238:   PetscFunctionBegin;
239:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)snes), &size));
240:   PetscCheck(size == 1, PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "Coulomb code only works in serial");
241:   PetscCall(DMGetDimension(sw, &dim));
242:   PetscCall(DMSwarmGetLocalSize(sw, &Np));

244:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
245:   for (p = 0; p < Np; ++p) {
246:     PetscReal *pcoord = &coords[p * dim];
247:     PetscReal *pE     = &E[p * dim];
248:     /* Calculate field at particle p due to particle q */
249:     for (q = 0; q < Np; ++q) {
250:       PetscReal *qcoord = &coords[q * dim];
251:       PetscReal  rpq[3], r;

253:       if (p == q) continue;
254:       for (d = 0; d < dim; ++d) rpq[d] = pcoord[d] - qcoord[d];
255:       r = DMPlex_NormD_Internal(dim, rpq);
256:       for (d = 0; d < dim; ++d) pE[d] += rpq[d] / PetscPowRealInt(r, 3);
257:     }
258:   }
259:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
260:   PetscFunctionReturn(PETSC_SUCCESS);
261: }

263: static PetscErrorCode ComputeFieldAtParticles_Primal(SNES snes, DM sw, PetscReal E[])
264: {
265:   DM           dm;
266:   PetscDS      ds;
267:   PetscFE      fe;
268:   Mat          M_p;
269:   Vec          phi, locPhi, rho, f;
270:   PetscReal   *coords, chargeTol = 1e-13;
271:   PetscInt     dim, d, cStart, cEnd, c, Np;
272:   const char **oldFields;
273:   PetscInt     Nf;
274:   const char **tmp;

276:   PetscFunctionBegin;
277:   PetscCall(DMGetDimension(sw, &dim));
278:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
279:   PetscCall(SNESGetDM(snes, &dm));

281:   PetscCall(DMSwarmVectorGetField(sw, &Nf, &tmp));
282:   PetscCall(PetscMalloc1(Nf, &oldFields));
283:   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscStrallocpy(tmp[f], (char **)&oldFields[f]));
284:   PetscCall(DMSwarmVectorDefineField(sw, "w_q"));
285:   PetscCall(DMCreateMassMatrix(sw, dm, &M_p));
286:   PetscCall(DMSwarmVectorDefineFields(sw, Nf, oldFields));
287:   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscFree(oldFields[f]));
288:   PetscCall(PetscFree(oldFields));

290:   /* Create the charges rho */
291:   PetscCall(DMGetGlobalVector(dm, &rho));
292:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
293:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
294:   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
295:   PetscCall(MatMultTranspose(M_p, f, rho));
296:   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
297:   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
298:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
299:   PetscCall(MatDestroy(&M_p));
300:   {
301:     PetscScalar sum;
302:     PetscInt    n;
303:     PetscReal   phi_0 = 1.; /* (sigma*sigma*sigma)*(timeScale*timeScale)/(m_e*q_e*epsi_0)*/

305:     /* Remove constant from rho */
306:     PetscCall(VecGetSize(rho, &n));
307:     PetscCall(VecSum(rho, &sum));
308:     PetscCall(VecShift(rho, -sum / n));
309:     PetscCall(VecSum(rho, &sum));
310:     PetscCheck(PetscAbsScalar(sum) < chargeTol, PetscObjectComm((PetscObject)sw), PETSC_ERR_PLIB, "Charge should have no DC component: %g", (double)PetscRealPart(sum));
311:     /* Nondimensionalize rho */
312:     PetscCall(VecScale(rho, phi_0));
313:   }
314:   PetscCall(VecViewFromOptions(rho, NULL, "-poisson_rho_view"));

316:   PetscCall(DMGetGlobalVector(dm, &phi));
317:   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
318:   PetscCall(VecSet(phi, 0.0));
319:   PetscCall(SNESSolve(snes, rho, phi));
320:   PetscCall(DMRestoreGlobalVector(dm, &rho));
321:   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));

323:   PetscCall(DMGetLocalVector(dm, &locPhi));
324:   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
325:   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
326:   PetscCall(DMRestoreGlobalVector(dm, &phi));

328:   PetscCall(DMGetDS(dm, &ds));
329:   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
330:   PetscCall(DMSwarmSortGetAccess(sw));
331:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
332:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
333:   for (c = cStart; c < cEnd; ++c) {
334:     PetscTabulation tab;
335:     PetscScalar    *clPhi = NULL;
336:     PetscReal      *pcoord, *refcoord;
337:     PetscReal       v[3], J[9], invJ[9], detJ;
338:     PetscInt       *points;
339:     PetscInt        Ncp, cp;

341:     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
342:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
343:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
344:     for (cp = 0; cp < Ncp; ++cp)
345:       for (d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
346:     PetscCall(DMPlexCoordinatesToReference(dm, c, Ncp, pcoord, refcoord));
347:     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
348:     PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v, J, invJ, &detJ));
349:     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
350:     for (cp = 0; cp < Ncp; ++cp) {
351:       const PetscReal *basisDer = tab->T[1];
352:       const PetscInt   p        = points[cp];

354:       for (d = 0; d < dim; ++d) E[p * dim + d] = 0.;
355:       PetscCall(PetscFEFreeInterpolateGradient_Static(fe, basisDer, clPhi, dim, invJ, NULL, cp, &E[p * dim]));
356:       for (d = 0; d < dim; ++d) E[p * dim + d] *= -1.0;
357:     }
358:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
359:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
360:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
361:     PetscCall(PetscTabulationDestroy(&tab));
362:     PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Ncp, &points));
363:   }
364:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
365:   PetscCall(DMSwarmSortRestoreAccess(sw));
366:   PetscCall(DMRestoreLocalVector(dm, &locPhi));
367:   PetscFunctionReturn(PETSC_SUCCESS);
368: }

370: static PetscErrorCode ComputeFieldAtParticles_Mixed(SNES snes, DM sw, PetscReal E[])
371: {
372:   DM              dm, potential_dm;
373:   IS              potential_IS;
374:   PetscDS         ds;
375:   PetscFE         fe;
376:   PetscFEGeom     feGeometry;
377:   Mat             M_p;
378:   Vec             phi, locPhi, rho, f, temp_rho;
379:   PetscQuadrature q;
380:   PetscReal      *coords, chargeTol = 1e-13;
381:   PetscInt        dim, d, cStart, cEnd, c, Np, pot_field = 1;
382:   const char    **oldFields;
383:   PetscInt        Nf;
384:   const char    **tmp;

386:   PetscFunctionBegin;
387:   PetscCall(DMGetDimension(sw, &dim));
388:   PetscCall(DMSwarmGetLocalSize(sw, &Np));

390:   /* Create the charges rho */
391:   PetscCall(SNESGetDM(snes, &dm));
392:   PetscCall(DMGetGlobalVector(dm, &rho));
393:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
394:   PetscCall(DMCreateSubDM(dm, 1, &pot_field, &potential_IS, &potential_dm));

396:   PetscCall(DMSwarmVectorGetField(sw, &Nf, &tmp));
397:   PetscCall(PetscMalloc1(Nf, &oldFields));
398:   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscStrallocpy(tmp[f], (char **)&oldFields[f]));
399:   PetscCall(DMSwarmVectorDefineField(sw, "w_q"));
400:   PetscCall(DMCreateMassMatrix(sw, potential_dm, &M_p));
401:   PetscCall(DMSwarmVectorDefineFields(sw, Nf, oldFields));
402:   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscFree(oldFields[f]));
403:   PetscCall(PetscFree(oldFields));

405:   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
406:   PetscCall(DMGetGlobalVector(potential_dm, &temp_rho));
407:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
408:   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
409:   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
410:   PetscCall(MatMultTranspose(M_p, f, temp_rho));
411:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
412:   PetscCall(MatDestroy(&M_p));
413:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
414:   PetscCall(VecViewFromOptions(rho, NULL, "-poisson_rho_view"));
415:   PetscCall(VecISCopy(rho, potential_IS, SCATTER_FORWARD, temp_rho));
416:   PetscCall(DMRestoreGlobalVector(potential_dm, &temp_rho));
417:   PetscCall(DMDestroy(&potential_dm));
418:   PetscCall(ISDestroy(&potential_IS));
419:   {
420:     PetscScalar sum;
421:     PetscInt    n;
422:     PetscReal   phi_0 = 1.; /*(sigma*sigma*sigma)*(timeScale*timeScale)/(m_e*q_e*epsi_0);*/

424:     /*Remove constant from rho*/
425:     PetscCall(VecGetSize(rho, &n));
426:     PetscCall(VecSum(rho, &sum));
427:     PetscCall(VecShift(rho, -sum / n));
428:     PetscCall(VecSum(rho, &sum));
429:     PetscCheck(PetscAbsScalar(sum) < chargeTol, PetscObjectComm((PetscObject)sw), PETSC_ERR_PLIB, "Charge should have no DC component: %g", (double)PetscRealPart(sum));
430:     /* Nondimensionalize rho */
431:     PetscCall(VecScale(rho, phi_0));
432:   }
433:   PetscCall(DMGetGlobalVector(dm, &phi));
434:   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
435:   PetscCall(VecSet(phi, 0.0));
436:   PetscCall(SNESSolve(snes, NULL, phi));
437:   PetscCall(DMRestoreGlobalVector(dm, &rho));
438:   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));

440:   PetscCall(DMGetLocalVector(dm, &locPhi));
441:   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
442:   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
443:   PetscCall(DMRestoreGlobalVector(dm, &phi));

445:   PetscCall(DMGetDS(dm, &ds));
446:   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
447:   PetscCall(DMSwarmSortGetAccess(sw));
448:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
449:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
450:   for (c = cStart; c < cEnd; ++c) {
451:     PetscTabulation tab;
452:     PetscScalar    *clPhi = NULL;
453:     PetscReal      *pcoord, *refcoord;
454:     PetscReal       v[3], J[9], invJ[9], detJ;
455:     PetscInt       *points;
456:     PetscInt        Ncp, cp;

458:     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
459:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
460:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
461:     for (cp = 0; cp < Ncp; ++cp)
462:       for (d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
463:     PetscCall(DMPlexCoordinatesToReference(dm, c, Ncp, pcoord, refcoord));
464:     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
465:     PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v, J, invJ, &detJ));
466:     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
467:     for (cp = 0; cp < Ncp; ++cp) {
468:       const PetscInt p = points[cp];

470:       for (d = 0; d < dim; ++d) E[p * dim + d] = 0.;
471:       PetscCall(PetscFEGetQuadrature(fe, &q));
472:       PetscCall(PetscFECreateCellGeometry(fe, q, &feGeometry));
473:       PetscCall(PetscFEInterpolateAtPoints_Static(fe, tab, clPhi, &feGeometry, cp, &E[p * dim]));
474:       PetscCall(PetscFEDestroyCellGeometry(fe, &feGeometry));
475:     }
476:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
477:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
478:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
479:     PetscCall(PetscTabulationDestroy(&tab));
480:     PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Ncp, &points));
481:   }
482:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
483:   PetscCall(DMSwarmSortRestoreAccess(sw));
484:   PetscCall(DMRestoreLocalVector(dm, &locPhi));
485:   PetscFunctionReturn(PETSC_SUCCESS);
486: }

488: static PetscErrorCode ComputeFieldAtParticles(SNES snes, DM sw, PetscReal E[])
489: {
490:   AppCtx  *ctx;
491:   PetscInt dim, Np;

493:   PetscFunctionBegin;
496:   PetscAssertPointer(E, 3);
497:   PetscCall(DMGetDimension(sw, &dim));
498:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
499:   PetscCall(DMGetApplicationContext(sw, &ctx));
500:   PetscCall(PetscArrayzero(E, Np * dim));

502:   switch (ctx->em) {
503:   case EM_PRIMAL:
504:     PetscCall(ComputeFieldAtParticles_Primal(snes, sw, E));
505:     break;
506:   case EM_COULOMB:
507:     PetscCall(ComputeFieldAtParticles_Coulomb(snes, sw, E));
508:     break;
509:   case EM_MIXED:
510:     PetscCall(ComputeFieldAtParticles_Mixed(snes, sw, E));
511:     break;
512:   case EM_NONE:
513:     break;
514:   default:
515:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No solver for electrostatic model %s", EMTypes[ctx->em]);
516:   }
517:   PetscFunctionReturn(PETSC_SUCCESS);
518: }

520: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec G, void *ctx)
521: {
522:   DM                 sw;
523:   SNES               snes = ((AppCtx *)ctx)->snes;
524:   const PetscReal   *coords, *vel;
525:   const PetscScalar *u;
526:   PetscScalar       *g;
527:   PetscReal         *E;
528:   PetscInt           dim, d, Np, p;

530:   PetscFunctionBeginUser;
531:   PetscCall(TSGetDM(ts, &sw));
532:   PetscCall(DMGetDimension(sw, &dim));
533:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
534:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
535:   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
536:   PetscCall(VecGetLocalSize(U, &Np));
537:   PetscCall(VecGetArrayRead(U, &u));
538:   PetscCall(VecGetArray(G, &g));

540:   PetscCall(ComputeFieldAtParticles(snes, sw, E));

542:   Np /= 2 * dim;
543:   for (p = 0; p < Np; ++p) {
544:     const PetscReal x0    = coords[p * dim + 0];
545:     const PetscReal vy0   = vel[p * dim + 1];
546:     const PetscReal omega = vy0 / x0;

548:     for (d = 0; d < dim; ++d) {
549:       g[(p * 2 + 0) * dim + d] = u[(p * 2 + 1) * dim + d];
550:       g[(p * 2 + 1) * dim + d] = E[p * dim + d] - PetscSqr(omega) * u[(p * 2 + 0) * dim + d];
551:     }
552:   }
553:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
554:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
555:   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
556:   PetscCall(VecRestoreArrayRead(U, &u));
557:   PetscCall(VecRestoreArray(G, &g));
558:   PetscFunctionReturn(PETSC_SUCCESS);
559: }

561: /* J_{ij} = dF_i/dx_j
562:    J_p = (  0   1)
563:          (-w^2  0)
564:    TODO Now there is another term with w^2 from the electric field. I think we will need to invert the operator.
565:         Perhaps we can approximate the Jacobian using only the cellwise P-P gradient from Coulomb
566: */
567: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat J, Mat P, void *ctx)
568: {
569:   DM               sw;
570:   const PetscReal *coords, *vel;
571:   PetscInt         dim, d, Np, p, rStart;

573:   PetscFunctionBeginUser;
574:   PetscCall(TSGetDM(ts, &sw));
575:   PetscCall(DMGetDimension(sw, &dim));
576:   PetscCall(VecGetLocalSize(U, &Np));
577:   PetscCall(MatGetOwnershipRange(J, &rStart, NULL));
578:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
579:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
580:   Np /= 2 * dim;
581:   for (p = 0; p < Np; ++p) {
582:     const PetscReal x0      = coords[p * dim + 0];
583:     const PetscReal vy0     = vel[p * dim + 1];
584:     const PetscReal omega   = vy0 / x0;
585:     PetscScalar     vals[4] = {0., 1., -PetscSqr(omega), 0.};

587:     for (d = 0; d < dim; ++d) {
588:       const PetscInt rows[2] = {(p * 2 + 0) * dim + d + rStart, (p * 2 + 1) * dim + d + rStart};
589:       PetscCall(MatSetValues(J, 2, rows, 2, rows, vals, INSERT_VALUES));
590:     }
591:   }
592:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
593:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
594:   PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
595:   PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
596:   PetscFunctionReturn(PETSC_SUCCESS);
597: }

599: static PetscErrorCode RHSFunctionX(TS ts, PetscReal t, Vec V, Vec Xres, void *ctx)
600: {
601:   DM                 sw;
602:   const PetscScalar *v;
603:   PetscScalar       *xres;
604:   PetscInt           Np, p, dim, d;

606:   PetscFunctionBeginUser;
607:   PetscCall(TSGetDM(ts, &sw));
608:   PetscCall(DMGetDimension(sw, &dim));
609:   PetscCall(VecGetLocalSize(Xres, &Np));
610:   Np /= dim;
611:   PetscCall(VecGetArrayRead(V, &v));
612:   PetscCall(VecGetArray(Xres, &xres));
613:   for (p = 0; p < Np; ++p) {
614:     for (d = 0; d < dim; ++d) xres[p * dim + d] = v[p * dim + d];
615:   }
616:   PetscCall(VecRestoreArrayRead(V, &v));
617:   PetscCall(VecRestoreArray(Xres, &xres));
618:   PetscFunctionReturn(PETSC_SUCCESS);
619: }

621: static PetscErrorCode RHSFunctionV(TS ts, PetscReal t, Vec X, Vec Vres, void *ctx)
622: {
623:   DM                 sw;
624:   SNES               snes = ((AppCtx *)ctx)->snes;
625:   const PetscScalar *x;
626:   const PetscReal   *coords, *vel;
627:   PetscScalar       *vres;
628:   PetscReal         *E;
629:   PetscInt           Np, p, dim, d;

631:   PetscFunctionBeginUser;
632:   PetscCall(TSGetDM(ts, &sw));
633:   PetscCall(DMGetDimension(sw, &dim));
634:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
635:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
636:   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
637:   PetscCall(VecGetLocalSize(Vres, &Np));
638:   PetscCall(VecGetArrayRead(X, &x));
639:   PetscCall(VecGetArray(Vres, &vres));
640:   PetscCheck(dim == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension must be 2");

642:   PetscCall(ComputeFieldAtParticles(snes, sw, E));

644:   Np /= dim;
645:   for (p = 0; p < Np; ++p) {
646:     const PetscReal x0    = coords[p * dim + 0];
647:     const PetscReal vy0   = vel[p * dim + 1];
648:     const PetscReal omega = vy0 / x0;

650:     for (d = 0; d < dim; ++d) vres[p * dim + d] = E[p * dim + d] - PetscSqr(omega) * x[p * dim + d];
651:   }
652:   PetscCall(VecRestoreArrayRead(X, &x));
653:   PetscCall(VecRestoreArray(Vres, &vres));
654:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
655:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
656:   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
657:   PetscFunctionReturn(PETSC_SUCCESS);
658: }

660: static PetscErrorCode CreateSolution(TS ts)
661: {
662:   DM       sw;
663:   Vec      u;
664:   PetscInt dim, Np;

666:   PetscFunctionBegin;
667:   PetscCall(TSGetDM(ts, &sw));
668:   PetscCall(DMGetDimension(sw, &dim));
669:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
670:   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
671:   PetscCall(VecSetBlockSize(u, dim));
672:   PetscCall(VecSetSizes(u, 2 * Np * dim, PETSC_DECIDE));
673:   PetscCall(VecSetUp(u));
674:   PetscCall(TSSetSolution(ts, u));
675:   PetscCall(VecDestroy(&u));
676:   PetscFunctionReturn(PETSC_SUCCESS);
677: }

679: static PetscErrorCode SetProblem(TS ts)
680: {
681:   AppCtx *user;
682:   DM      sw;

684:   PetscFunctionBegin;
685:   PetscCall(TSGetDM(ts, &sw));
686:   PetscCall(DMGetApplicationContext(sw, (void **)&user));
687:   // Define unified system for (X, V)
688:   {
689:     Mat      J;
690:     PetscInt dim, Np;

692:     PetscCall(DMGetDimension(sw, &dim));
693:     PetscCall(DMSwarmGetLocalSize(sw, &Np));
694:     PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
695:     PetscCall(MatSetSizes(J, 2 * Np * dim, 2 * Np * dim, PETSC_DECIDE, PETSC_DECIDE));
696:     PetscCall(MatSetBlockSize(J, 2 * dim));
697:     PetscCall(MatSetFromOptions(J));
698:     PetscCall(MatSetUp(J));
699:     PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, user));
700:     PetscCall(TSSetRHSJacobian(ts, J, J, RHSJacobian, user));
701:     PetscCall(MatDestroy(&J));
702:   }
703:   /* Define split system for X and V */
704:   {
705:     Vec             u;
706:     IS              isx, isv, istmp;
707:     const PetscInt *idx;
708:     PetscInt        dim, Np, rstart;

710:     PetscCall(TSGetSolution(ts, &u));
711:     PetscCall(DMGetDimension(sw, &dim));
712:     PetscCall(DMSwarmGetLocalSize(sw, &Np));
713:     PetscCall(VecGetOwnershipRange(u, &rstart, NULL));
714:     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 0, 2, &istmp));
715:     PetscCall(ISGetIndices(istmp, &idx));
716:     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isx));
717:     PetscCall(ISRestoreIndices(istmp, &idx));
718:     PetscCall(ISDestroy(&istmp));
719:     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 1, 2, &istmp));
720:     PetscCall(ISGetIndices(istmp, &idx));
721:     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isv));
722:     PetscCall(ISRestoreIndices(istmp, &idx));
723:     PetscCall(ISDestroy(&istmp));
724:     PetscCall(TSRHSSplitSetIS(ts, "position", isx));
725:     PetscCall(TSRHSSplitSetIS(ts, "momentum", isv));
726:     PetscCall(ISDestroy(&isx));
727:     PetscCall(ISDestroy(&isv));
728:     PetscCall(TSRHSSplitSetRHSFunction(ts, "position", NULL, RHSFunctionX, user));
729:     PetscCall(TSRHSSplitSetRHSFunction(ts, "momentum", NULL, RHSFunctionV, user));
730:   }
731:   PetscFunctionReturn(PETSC_SUCCESS);
732: }

734: PetscErrorCode circleSingleX(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
735: {
736:   x[0] = p + 1.;
737:   x[1] = 0.;
738:   return PETSC_SUCCESS;
739: }

741: PetscErrorCode circleSingleV(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar v[], void *ctx)
742: {
743:   v[0] = 0.;
744:   v[1] = PetscSqrtReal(1000. / (p + 1.));
745:   return PETSC_SUCCESS;
746: }

748: /* Put 5 particles into each circle */
749: PetscErrorCode circleMultipleX(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
750: {
751:   const PetscInt  n   = 5;
752:   const PetscReal r0  = (p / n) + 1.;
753:   const PetscReal th0 = (2. * PETSC_PI * (p % n)) / n;

755:   x[0] = r0 * PetscCosReal(th0);
756:   x[1] = r0 * PetscSinReal(th0);
757:   return PETSC_SUCCESS;
758: }

760: /* Put 5 particles into each circle */
761: PetscErrorCode circleMultipleV(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar v[], void *ctx)
762: {
763:   const PetscInt  n     = 5;
764:   const PetscReal r0    = (p / n) + 1.;
765:   const PetscReal th0   = (2. * PETSC_PI * (p % n)) / n;
766:   const PetscReal omega = PetscSqrtReal(1000. / r0) / r0;

768:   v[0] = -r0 * omega * PetscSinReal(th0);
769:   v[1] = r0 * omega * PetscCosReal(th0);
770:   return PETSC_SUCCESS;
771: }

773: /*
774:   InitializeSolveAndSwarm - Set the solution values to the swarm coordinates and velocities, and also possibly set the initial values.

776:   Input Parameters:
777: + ts         - The TS
778: - useInitial - Flag to also set the initial conditions to the current coordinates and velocities and setup the problem

780:   Output Parameter:
781: . u - The initialized solution vector

783:   Level: advanced

785: .seealso: InitializeSolve()
786: */
787: static PetscErrorCode InitializeSolveAndSwarm(TS ts, PetscBool useInitial)
788: {
789:   DM      sw;
790:   Vec     u, gc, gv, gc0, gv0;
791:   IS      isx, isv;
792:   AppCtx *user;

794:   PetscFunctionBeginUser;
795:   PetscCall(TSGetDM(ts, &sw));
796:   PetscCall(DMGetApplicationContext(sw, &user));
797:   if (useInitial) {
798:     PetscReal v0[1] = {1.};

800:     PetscCall(DMSwarmInitializeCoordinates(sw));
801:     PetscCall(DMSwarmInitializeVelocitiesFromOptions(sw, v0));
802:     PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
803:     PetscCall(TSReset(ts));
804:     PetscCall(CreateSolution(ts));
805:     PetscCall(SetProblem(ts));
806:   }
807:   PetscCall(TSGetSolution(ts, &u));
808:   PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
809:   PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
810:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
811:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initCoordinates", &gc0));
812:   if (useInitial) PetscCall(VecCopy(gc, gc0));
813:   PetscCall(VecISCopy(u, isx, SCATTER_FORWARD, gc));
814:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
815:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initCoordinates", &gc0));
816:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
817:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initVelocity", &gv0));
818:   if (useInitial) PetscCall(VecCopy(gv, gv0));
819:   PetscCall(VecISCopy(u, isv, SCATTER_FORWARD, gv));
820:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
821:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initVelocity", &gv0));
822:   PetscFunctionReturn(PETSC_SUCCESS);
823: }

825: static PetscErrorCode InitializeSolve(TS ts, Vec u)
826: {
827:   PetscFunctionBegin;
828:   PetscCall(TSSetSolution(ts, u));
829:   PetscCall(InitializeSolveAndSwarm(ts, PETSC_TRUE));
830:   PetscFunctionReturn(PETSC_SUCCESS);
831: }

833: static PetscErrorCode ComputeError(TS ts, Vec U, Vec E)
834: {
835:   MPI_Comm           comm;
836:   DM                 sw;
837:   AppCtx            *user;
838:   const PetscScalar *u;
839:   const PetscReal   *coords, *vel;
840:   PetscScalar       *e;
841:   PetscReal          t;
842:   PetscInt           dim, Np, p;

844:   PetscFunctionBeginUser;
845:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
846:   PetscCall(TSGetDM(ts, &sw));
847:   PetscCall(DMGetApplicationContext(sw, &user));
848:   PetscCall(DMGetDimension(sw, &dim));
849:   PetscCall(TSGetSolveTime(ts, &t));
850:   PetscCall(VecGetArray(E, &e));
851:   PetscCall(VecGetArrayRead(U, &u));
852:   PetscCall(VecGetLocalSize(U, &Np));
853:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
854:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
855:   Np /= 2 * dim;
856:   for (p = 0; p < Np; ++p) {
857:     /* TODO generalize initial conditions and project into plane instead of assuming x-y */
858:     const PetscReal    r0    = DMPlex_NormD_Internal(dim, &coords[p * dim]);
859:     const PetscReal    th0   = PetscAtan2Real(coords[p * dim + 1], coords[p * dim + 0]);
860:     const PetscReal    v0    = DMPlex_NormD_Internal(dim, &vel[p * dim]);
861:     const PetscReal    omega = v0 / r0;
862:     const PetscReal    ct    = PetscCosReal(omega * t + th0);
863:     const PetscReal    st    = PetscSinReal(omega * t + th0);
864:     const PetscScalar *x     = &u[(p * 2 + 0) * dim];
865:     const PetscScalar *v     = &u[(p * 2 + 1) * dim];
866:     const PetscReal    xe[3] = {r0 * ct, r0 * st, 0.0};
867:     const PetscReal    ve[3] = {-v0 * st, v0 * ct, 0.0};
868:     PetscInt           d;

870:     for (d = 0; d < dim; ++d) {
871:       e[(p * 2 + 0) * dim + d] = x[d] - xe[d];
872:       e[(p * 2 + 1) * dim + d] = v[d] - ve[d];
873:     }
874:     if (user->error) {
875:       const PetscReal en   = 0.5 * DMPlex_DotRealD_Internal(dim, v, v);
876:       const PetscReal exen = 0.5 * PetscSqr(v0);
877:       PetscCall(PetscPrintf(comm, "t %.4g: p%" PetscInt_FMT " error [%.2f %.2f] sol [(%.6lf %.6lf) (%.6lf %.6lf)] exact [(%.6lf %.6lf) (%.6lf %.6lf)] energy/exact energy %g / %g (%.10lf%%)\n", (double)t, p, (double)DMPlex_NormD_Internal(dim, &e[(p * 2 + 0) * dim]), (double)DMPlex_NormD_Internal(dim, &e[(p * 2 + 1) * dim]), (double)x[0], (double)x[1], (double)v[0], (double)v[1], (double)xe[0], (double)xe[1], (double)ve[0], (double)ve[1], (double)en, (double)exen, (double)(PetscAbsReal(exen - en) * 100. / exen)));
878:     }
879:   }
880:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
881:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
882:   PetscCall(VecRestoreArrayRead(U, &u));
883:   PetscCall(VecRestoreArray(E, &e));
884:   PetscFunctionReturn(PETSC_SUCCESS);
885: }

887: static PetscErrorCode EnergyMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
888: {
889:   const PetscInt     ostep = ((AppCtx *)ctx)->ostep;
890:   const EMType       em    = ((AppCtx *)ctx)->em;
891:   DM                 sw;
892:   const PetscScalar *u;
893:   PetscReal         *coords, *E;
894:   PetscReal          enKin = 0., enEM = 0.;
895:   PetscInt           dim, d, Np, p, q;

897:   PetscFunctionBeginUser;
898:   if (step % ostep == 0) {
899:     PetscCall(TSGetDM(ts, &sw));
900:     PetscCall(DMGetDimension(sw, &dim));
901:     PetscCall(VecGetArrayRead(U, &u));
902:     PetscCall(VecGetLocalSize(U, &Np));
903:     Np /= 2 * dim;
904:     PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
905:     PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
906:     if (!step) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)ts), "Time     Step Part     Energy\n"));
907:     for (p = 0; p < Np; ++p) {
908:       const PetscReal v2     = DMPlex_DotRealD_Internal(dim, &u[(p * 2 + 1) * dim], &u[(p * 2 + 1) * dim]);
909:       PetscReal      *pcoord = &coords[p * dim];

911:       PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " %5" PetscInt_FMT " %10.4lf\n", (double)t, step, p, (double)(0.5 * v2)));
912:       enKin += 0.5 * v2;
913:       if (em == EM_NONE) {
914:         continue;
915:       } else if (em == EM_COULOMB) {
916:         for (q = p + 1; q < Np; ++q) {
917:           PetscReal *qcoord = &coords[q * dim];
918:           PetscReal  rpq[3], r;
919:           for (d = 0; d < dim; ++d) rpq[d] = pcoord[d] - qcoord[d];
920:           r = DMPlex_NormD_Internal(dim, rpq);
921:           enEM += 1. / r;
922:         }
923:       } else if (em == EM_PRIMAL || em == EM_MIXED) {
924:         for (d = 0; d < dim; ++d) enEM += E[p * dim + d];
925:       }
926:     }
927:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " KE\t    %10.4lf\n", (double)t, step, (double)enKin));
928:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " PE\t    %1.10g\n", (double)t, step, (double)enEM));
929:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " E\t    %10.4lf\n", (double)t, step, (double)(enKin + enEM)));
930:     PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
931:     PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
932:     PetscCall(PetscSynchronizedFlush(PetscObjectComm((PetscObject)ts), NULL));
933:     PetscCall(VecRestoreArrayRead(U, &u));
934:   }
935:   PetscFunctionReturn(PETSC_SUCCESS);
936: }

938: static PetscErrorCode SetUpMigrateParticles(TS ts, PetscInt n, PetscReal t, Vec x, PetscBool *flg, void *ctx)
939: {
940:   DM sw;

942:   PetscFunctionBeginUser;
943:   *flg = PETSC_TRUE;
944:   PetscCall(TSGetDM(ts, &sw));
945:   PetscCall(DMViewFromOptions(sw, NULL, "-migrate_view_pre"));
946:   {
947:     Vec u, gc, gv;
948:     IS  isx, isv;

950:     PetscCall(TSGetSolution(ts, &u));
951:     PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
952:     PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
953:     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
954:     PetscCall(VecISCopy(u, isx, SCATTER_REVERSE, gc));
955:     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
956:     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
957:     PetscCall(VecISCopy(u, isv, SCATTER_REVERSE, gv));
958:     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
959:   }
960:   PetscFunctionReturn(PETSC_SUCCESS);
961: }

963: static PetscErrorCode MigrateParticles(TS ts, PetscInt nv, Vec vecsin[], Vec vecsout[], void *ctx)
964: {
965:   DM sw;

967:   PetscFunctionBeginUser;
968:   PetscCall(TSGetDM(ts, &sw));
969:   PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
970:   PetscCall(CreateSolution(ts));
971:   PetscCall(SetProblem(ts));
972:   PetscCall(InitializeSolveAndSwarm(ts, PETSC_FALSE));
973:   PetscFunctionReturn(PETSC_SUCCESS);
974: }

976: int main(int argc, char **argv)
977: {
978:   DM     dm, sw;
979:   TS     ts;
980:   Vec    u;
981:   AppCtx user;

983:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
984:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
985:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
986:   PetscCall(CreatePoisson(dm, &user));
987:   PetscCall(CreateSwarm(dm, &user, &sw));
988:   PetscCall(DMSetApplicationContext(sw, &user));

990:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
991:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
992:   PetscCall(TSSetDM(ts, sw));
993:   PetscCall(TSSetMaxTime(ts, 0.1));
994:   PetscCall(TSSetTimeStep(ts, 0.00001));
995:   PetscCall(TSSetMaxSteps(ts, 100));
996:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
997:   PetscCall(TSMonitorSet(ts, EnergyMonitor, &user, NULL));
998:   PetscCall(TSSetFromOptions(ts));
999:   PetscCall(TSSetComputeInitialCondition(ts, InitializeSolve));
1000:   PetscCall(TSSetComputeExactError(ts, ComputeError));
1001:   PetscCall(TSSetResize(ts, PETSC_FALSE, SetUpMigrateParticles, MigrateParticles, NULL));

1003:   PetscCall(CreateSolution(ts));
1004:   PetscCall(TSGetSolution(ts, &u));
1005:   PetscCall(TSComputeInitialCondition(ts, u));
1006:   PetscCall(TSSolve(ts, NULL));

1008:   PetscCall(SNESDestroy(&user.snes));
1009:   PetscCall(TSDestroy(&ts));
1010:   PetscCall(DMDestroy(&sw));
1011:   PetscCall(DMDestroy(&dm));
1012:   PetscCall(PetscFinalize());
1013:   return 0;
1014: }

1016: /*TEST

1018:    build:
1019:      requires: double !complex

1021:    testset:
1022:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1023:      args: -dm_plex_dim 2 -dm_plex_simplex 0 -dm_plex_box_faces 1,1 -dm_plex_box_lower -5,-5 -dm_plex_box_upper 5,5 \
1024:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1025:            -ts_type basicsymplectic\
1026:            -dm_view -output_step 50 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1027:      test:
1028:        suffix: none_bsi_2d_1
1029:        args: -ts_basicsymplectic_type 1 -em_type none -error
1030:      test:
1031:        suffix: none_bsi_2d_2
1032:        args: -ts_basicsymplectic_type 2 -em_type none -error
1033:      test:
1034:        suffix: none_bsi_2d_3
1035:        args: -ts_basicsymplectic_type 3 -em_type none -error
1036:      test:
1037:        suffix: none_bsi_2d_4
1038:        args: -ts_basicsymplectic_type 4 -em_type none -error
1039:      test:
1040:        suffix: coulomb_bsi_2d_1
1041:        args: -ts_basicsymplectic_type 1
1042:      test:
1043:        suffix: coulomb_bsi_2d_2
1044:        args: -ts_basicsymplectic_type 2
1045:      test:
1046:        suffix: coulomb_bsi_2d_3
1047:        args: -ts_basicsymplectic_type 3
1048:      test:
1049:        suffix: coulomb_bsi_2d_4
1050:        args: -ts_basicsymplectic_type 4

1052:    testset:
1053:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1054:      args: -dm_plex_dim 2 -dm_plex_simplex 0 -dm_plex_box_faces 1,1 -dm_plex_box_lower -5,-5 -dm_plex_box_upper 5,5 \
1055:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1056:            -ts_type basicsymplectic\
1057:            -em_type primal -em_pc_type svd\
1058:            -dm_view -output_step 50 -error -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10\
1059:            -petscspace_degree 2 -petscfe_default_quadrature_order 3 -sigma 1.0e-8 -timeScale 2.0e-14
1060:      test:
1061:        suffix: poisson_bsi_2d_1
1062:        args: -ts_basicsymplectic_type 1
1063:      test:
1064:        suffix: poisson_bsi_2d_2
1065:        args: -ts_basicsymplectic_type 2
1066:      test:
1067:        suffix: poisson_bsi_2d_3
1068:        args: -ts_basicsymplectic_type 3
1069:      test:
1070:        suffix: poisson_bsi_2d_4
1071:        args: -ts_basicsymplectic_type 4

1073:    testset:
1074:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1075:      args: -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1076:            -ts_type theta -ts_theta_theta 0.5 -ts_convergence_estimate -convest_num_refine 2 \
1077:              -mat_type baij -ksp_error_if_not_converged -em_pc_type svd\
1078:            -dm_view -output_step 50 -error -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10\
1079:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14
1080:      test:
1081:        suffix: im_2d_0
1082:        args: -dm_plex_dim 2 -dm_plex_simplex 0 -dm_plex_box_faces 1,1 -dm_plex_box_lower -5,-5 -dm_plex_box_upper 5,5

1084:    testset:
1085:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1086:      args: -dm_plex_dim 2 -dm_plex_simplex 0 -dm_plex_box_faces 10,10 -dm_plex_box_lower -5,-5 -dm_plex_box_upper 5,5 -petscpartitioner_type simple \
1087:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV -dm_swarm_num_species 1\
1088:            -ts_type basicsymplectic -ts_convergence_estimate -convest_num_refine 2 \
1089:            -em_snes_type ksponly -em_pc_type svd -em_type primal -petscspace_degree 1\
1090:            -dm_view -output_step 50\
1091:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 1.0 -ts_max_steps 10
1092:      test:
1093:        suffix: bsi_2d_mesh_1
1094:        args: -ts_basicsymplectic_type 4
1095:      test:
1096:        suffix: bsi_2d_mesh_1_par_2
1097:        nsize: 2
1098:        args: -ts_basicsymplectic_type 4
1099:      test:
1100:        suffix: bsi_2d_mesh_1_par_3
1101:        nsize: 3
1102:        args: -ts_basicsymplectic_type 4
1103:      test:
1104:        suffix: bsi_2d_mesh_1_par_4
1105:        nsize: 4
1106:        args: -ts_basicsymplectic_type 4 -dm_swarm_num_particles 0,0,2,0

1108:    testset:
1109:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1110:      args: -dm_plex_dim 2 -dm_plex_simplex 0 -dm_plex_box_faces 10,10 -dm_plex_box_lower -5,-5 -dm_plex_box_upper 5,5 \
1111:            -dm_swarm_num_particles 10 -dm_swarm_coordinate_function circleMultipleX -dm_swarm_velocity_function circleMultipleV \
1112:            -ts_convergence_estimate -convest_num_refine 2 \
1113:              -em_pc_type lu\
1114:            -dm_view -output_step 50 -error\
1115:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1116:      test:
1117:        suffix: bsi_2d_multiple_1
1118:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 1
1119:      test:
1120:        suffix: bsi_2d_multiple_2
1121:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 2
1122:      test:
1123:        suffix: bsi_2d_multiple_3
1124:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 3 -ts_dt 0.001
1125:      test:
1126:        suffix: im_2d_multiple_0
1127:        args: -ts_type theta -ts_theta_theta 0.5 \
1128:                -mat_type baij -ksp_error_if_not_converged -em_pc_type lu

1130:    testset:
1131:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1132:      args: -dm_plex_dim 2 -dm_plex_simplex 0 -dm_plex_box_faces 2,2 -dm_plex_box_lower -5,-5 -dm_plex_box_upper 5,5 \
1133:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1134:            -em_pc_type fieldsplit -ksp_rtol 1e-10 -em_ksp_type preonly -em_type mixed -em_ksp_error_if_not_converged\
1135:            -dm_view -output_step 50 -error -dm_refine 0\
1136:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1137:      test:
1138:        suffix: bsi_4_rt_1
1139:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 4\
1140:              -pc_fieldsplit_detect_saddle_point\
1141:              -pc_type fieldsplit\
1142:              -pc_fieldsplit_type schur\
1143:              -pc_fieldsplit_schur_precondition full \
1144:              -field_petscspace_degree 2\
1145:              -field_petscfe_default_quadrature_order 1\
1146:              -field_petscspace_type sum \
1147:              -field_petscspace_variables 2 \
1148:              -field_petscspace_components 2 \
1149:              -field_petscspace_sum_spaces 2 \
1150:              -field_petscspace_sum_concatenate true \
1151:              -field_sumcomp_0_petscspace_variables 2 \
1152:              -field_sumcomp_0_petscspace_type tensor \
1153:              -field_sumcomp_0_petscspace_tensor_spaces 2 \
1154:              -field_sumcomp_0_petscspace_tensor_uniform false \
1155:              -field_sumcomp_0_tensorcomp_0_petscspace_degree 1 \
1156:              -field_sumcomp_0_tensorcomp_1_petscspace_degree 0 \
1157:              -field_sumcomp_1_petscspace_variables 2 \
1158:              -field_sumcomp_1_petscspace_type tensor \
1159:              -field_sumcomp_1_petscspace_tensor_spaces 2 \
1160:              -field_sumcomp_1_petscspace_tensor_uniform false \
1161:              -field_sumcomp_1_tensorcomp_0_petscspace_degree 0 \
1162:              -field_sumcomp_1_tensorcomp_1_petscspace_degree 1 \
1163:              -field_petscdualspace_form_degree -1 \
1164:              -field_petscdualspace_order 1 \
1165:              -field_petscdualspace_lagrange_trimmed true\
1166:              -ksp_gmres_restart 500

1168: TEST*/