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:   PetscFunctionReturn(PETSC_SUCCESS);
225: }

227: static PetscErrorCode ComputeFieldAtParticles_Coulomb(SNES snes, DM sw, PetscReal E[])
228: {
229:   PetscReal  *coords;
230:   PetscInt    dim, d, Np, p, q;
231:   PetscMPIInt size;

233:   PetscFunctionBegin;
234:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)snes), &size));
235:   PetscCheck(size == 1, PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "Coulomb code only works in serial");
236:   PetscCall(DMGetDimension(sw, &dim));
237:   PetscCall(DMSwarmGetLocalSize(sw, &Np));

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

248:       if (p == q) continue;
249:       for (d = 0; d < dim; ++d) rpq[d] = pcoord[d] - qcoord[d];
250:       r = DMPlex_NormD_Internal(dim, rpq);
251:       for (d = 0; d < dim; ++d) pE[d] += rpq[d] / PetscPowRealInt(r, 3);
252:     }
253:   }
254:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
255:   PetscFunctionReturn(PETSC_SUCCESS);
256: }

258: static PetscErrorCode ComputeFieldAtParticles_Primal(SNES snes, DM sw, PetscReal E[])
259: {
260:   DM          dm;
261:   PetscDS     ds;
262:   PetscFE     fe;
263:   Mat         M_p;
264:   Vec         phi, locPhi, rho, f;
265:   PetscReal  *coords, chargeTol = 1e-13;
266:   PetscInt    dim, d, cStart, cEnd, c, Np;
267:   char        oldField[PETSC_MAX_PATH_LEN];
268:   const char *tmp;

270:   PetscFunctionBegin;
271:   PetscCall(DMGetDimension(sw, &dim));
272:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
273:   PetscCall(SNESGetDM(snes, &dm));

275:   PetscCall(DMSwarmVectorGetField(sw, &tmp));
276:   PetscCall(PetscStrncpy(oldField, tmp, PETSC_MAX_PATH_LEN));
277:   PetscCall(DMSwarmVectorDefineField(sw, "w_q"));
278:   PetscCall(DMCreateMassMatrix(sw, dm, &M_p));
279:   PetscCall(DMSwarmVectorDefineField(sw, oldField));

281:   /* Create the charges rho */
282:   PetscCall(DMGetGlobalVector(dm, &rho));
283:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
284:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
285:   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
286:   PetscCall(MatMultTranspose(M_p, f, rho));
287:   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
288:   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
289:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
290:   PetscCall(MatDestroy(&M_p));
291:   {
292:     PetscScalar sum;
293:     PetscInt    n;
294:     PetscReal   phi_0 = 1.; /* (sigma*sigma*sigma)*(timeScale*timeScale)/(m_e*q_e*epsi_0)*/

296:     /* Remove constant from rho */
297:     PetscCall(VecGetSize(rho, &n));
298:     PetscCall(VecSum(rho, &sum));
299:     PetscCall(VecShift(rho, -sum / n));
300:     PetscCall(VecSum(rho, &sum));
301:     PetscCheck(PetscAbsScalar(sum) < chargeTol, PetscObjectComm((PetscObject)sw), PETSC_ERR_PLIB, "Charge should have no DC component: %g", (double)PetscRealPart(sum));
302:     /* Nondimensionalize rho */
303:     PetscCall(VecScale(rho, phi_0));
304:   }
305:   PetscCall(VecViewFromOptions(rho, NULL, "-poisson_rho_view"));

307:   PetscCall(DMGetGlobalVector(dm, &phi));
308:   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
309:   PetscCall(VecSet(phi, 0.0));
310:   PetscCall(SNESSolve(snes, rho, phi));
311:   PetscCall(DMRestoreGlobalVector(dm, &rho));
312:   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));

314:   PetscCall(DMGetLocalVector(dm, &locPhi));
315:   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
316:   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
317:   PetscCall(DMRestoreGlobalVector(dm, &phi));

319:   PetscCall(DMGetDS(dm, &ds));
320:   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
321:   PetscCall(DMSwarmSortGetAccess(sw));
322:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
323:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
324:   for (c = cStart; c < cEnd; ++c) {
325:     PetscTabulation tab;
326:     PetscScalar    *clPhi = NULL;
327:     PetscReal      *pcoord, *refcoord;
328:     PetscReal       v[3], J[9], invJ[9], detJ;
329:     PetscInt       *points;
330:     PetscInt        Ncp, cp;

332:     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
333:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
334:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
335:     for (cp = 0; cp < Ncp; ++cp)
336:       for (d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
337:     PetscCall(DMPlexCoordinatesToReference(dm, c, Ncp, pcoord, refcoord));
338:     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
339:     PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v, J, invJ, &detJ));
340:     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
341:     for (cp = 0; cp < Ncp; ++cp) {
342:       const PetscReal *basisDer = tab->T[1];
343:       const PetscInt   p        = points[cp];

345:       for (d = 0; d < dim; ++d) E[p * dim + d] = 0.;
346:       PetscCall(PetscFEFreeInterpolateGradient_Static(fe, basisDer, clPhi, dim, invJ, NULL, cp, &E[p * dim]));
347:       for (d = 0; d < dim; ++d) E[p * dim + d] *= -1.0;
348:     }
349:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
350:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
351:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
352:     PetscCall(PetscTabulationDestroy(&tab));
353:     PetscCall(PetscFree(points));
354:   }
355:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
356:   PetscCall(DMSwarmSortRestoreAccess(sw));
357:   PetscCall(DMRestoreLocalVector(dm, &locPhi));
358:   PetscFunctionReturn(PETSC_SUCCESS);
359: }

361: static PetscErrorCode ComputeFieldAtParticles_Mixed(SNES snes, DM sw, PetscReal E[])
362: {
363:   DM              dm, potential_dm;
364:   IS              potential_IS;
365:   PetscDS         ds;
366:   PetscFE         fe;
367:   PetscFEGeom     feGeometry;
368:   Mat             M_p;
369:   Vec             phi, locPhi, rho, f, temp_rho;
370:   PetscQuadrature q;
371:   PetscReal      *coords, chargeTol = 1e-13;
372:   PetscInt        dim, d, cStart, cEnd, c, Np, fields = 1;
373:   char            oldField[PETSC_MAX_PATH_LEN];
374:   const char     *tmp;

376:   PetscFunctionBegin;
377:   PetscCall(DMGetDimension(sw, &dim));
378:   PetscCall(DMSwarmGetLocalSize(sw, &Np));

380:   /* Create the charges rho */
381:   PetscCall(SNESGetDM(snes, &dm));
382:   PetscCall(DMGetGlobalVector(dm, &rho));
383:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
384:   PetscCall(DMCreateSubDM(dm, 1, &fields, &potential_IS, &potential_dm));

386:   PetscCall(DMSwarmVectorGetField(sw, &tmp));
387:   PetscCall(PetscStrncpy(oldField, tmp, PETSC_MAX_PATH_LEN));
388:   PetscCall(DMSwarmVectorDefineField(sw, "w_q"));
389:   PetscCall(DMCreateMassMatrix(sw, potential_dm, &M_p));
390:   PetscCall(DMSwarmVectorDefineField(sw, oldField));

392:   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
393:   PetscCall(DMGetGlobalVector(potential_dm, &temp_rho));
394:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
395:   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
396:   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
397:   PetscCall(MatMultTranspose(M_p, f, temp_rho));
398:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
399:   PetscCall(MatDestroy(&M_p));
400:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
401:   PetscCall(VecViewFromOptions(rho, NULL, "-poisson_rho_view"));
402:   PetscCall(VecISCopy(rho, potential_IS, SCATTER_FORWARD, temp_rho));
403:   PetscCall(DMRestoreGlobalVector(potential_dm, &temp_rho));
404:   PetscCall(DMDestroy(&potential_dm));
405:   PetscCall(ISDestroy(&potential_IS));
406:   {
407:     PetscScalar sum;
408:     PetscInt    n;
409:     PetscReal   phi_0 = 1.; /*(sigma*sigma*sigma)*(timeScale*timeScale)/(m_e*q_e*epsi_0);*/

411:     /*Remove constant from rho*/
412:     PetscCall(VecGetSize(rho, &n));
413:     PetscCall(VecSum(rho, &sum));
414:     PetscCall(VecShift(rho, -sum / n));
415:     PetscCall(VecSum(rho, &sum));
416:     PetscCheck(PetscAbsScalar(sum) < chargeTol, PetscObjectComm((PetscObject)sw), PETSC_ERR_PLIB, "Charge should have no DC component: %g", (double)PetscRealPart(sum));
417:     /* Nondimensionalize rho */
418:     PetscCall(VecScale(rho, phi_0));
419:   }
420:   PetscCall(DMGetGlobalVector(dm, &phi));
421:   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
422:   PetscCall(VecSet(phi, 0.0));
423:   PetscCall(SNESSolve(snes, NULL, phi));
424:   PetscCall(DMRestoreGlobalVector(dm, &rho));
425:   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));

427:   PetscCall(DMGetLocalVector(dm, &locPhi));
428:   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
429:   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
430:   PetscCall(DMRestoreGlobalVector(dm, &phi));

432:   PetscCall(DMGetDS(dm, &ds));
433:   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
434:   PetscCall(DMSwarmSortGetAccess(sw));
435:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
436:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
437:   for (c = cStart; c < cEnd; ++c) {
438:     PetscTabulation tab;
439:     PetscScalar    *clPhi = NULL;
440:     PetscReal      *pcoord, *refcoord;
441:     PetscReal       v[3], J[9], invJ[9], detJ;
442:     PetscInt       *points;
443:     PetscInt        Ncp, cp;

445:     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
446:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
447:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
448:     for (cp = 0; cp < Ncp; ++cp)
449:       for (d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
450:     PetscCall(DMPlexCoordinatesToReference(dm, c, Ncp, pcoord, refcoord));
451:     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
452:     PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v, J, invJ, &detJ));
453:     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
454:     for (cp = 0; cp < Ncp; ++cp) {
455:       const PetscInt p = points[cp];

457:       for (d = 0; d < dim; ++d) E[p * dim + d] = 0.;
458:       PetscCall(PetscFEGetQuadrature(fe, &q));
459:       PetscCall(PetscFECreateCellGeometry(fe, q, &feGeometry));
460:       PetscCall(PetscFEInterpolateAtPoints_Static(fe, tab, clPhi, &feGeometry, cp, &E[p * dim]));
461:       PetscCall(PetscFEDestroyCellGeometry(fe, &feGeometry));
462:     }
463:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
464:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
465:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
466:     PetscCall(PetscTabulationDestroy(&tab));
467:     PetscCall(PetscFree(points));
468:   }
469:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
470:   PetscCall(DMSwarmSortRestoreAccess(sw));
471:   PetscCall(DMRestoreLocalVector(dm, &locPhi));
472:   PetscFunctionReturn(PETSC_SUCCESS);
473: }

475: static PetscErrorCode ComputeFieldAtParticles(SNES snes, DM sw, PetscReal E[])
476: {
477:   AppCtx  *ctx;
478:   PetscInt dim, Np;

480:   PetscFunctionBegin;
483:   PetscAssertPointer(E, 3);
484:   PetscCall(DMGetDimension(sw, &dim));
485:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
486:   PetscCall(DMGetApplicationContext(sw, &ctx));
487:   PetscCall(PetscArrayzero(E, Np * dim));

489:   switch (ctx->em) {
490:   case EM_PRIMAL:
491:     PetscCall(ComputeFieldAtParticles_Primal(snes, sw, E));
492:     break;
493:   case EM_COULOMB:
494:     PetscCall(ComputeFieldAtParticles_Coulomb(snes, sw, E));
495:     break;
496:   case EM_MIXED:
497:     PetscCall(ComputeFieldAtParticles_Mixed(snes, sw, E));
498:     break;
499:   case EM_NONE:
500:     break;
501:   default:
502:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No solver for electrostatic model %s", EMTypes[ctx->em]);
503:   }
504:   PetscFunctionReturn(PETSC_SUCCESS);
505: }

507: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec G, void *ctx)
508: {
509:   DM                 sw;
510:   SNES               snes = ((AppCtx *)ctx)->snes;
511:   const PetscReal   *coords, *vel;
512:   const PetscScalar *u;
513:   PetscScalar       *g;
514:   PetscReal         *E;
515:   PetscInt           dim, d, Np, p;

517:   PetscFunctionBeginUser;
518:   PetscCall(TSGetDM(ts, &sw));
519:   PetscCall(DMGetDimension(sw, &dim));
520:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
521:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
522:   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
523:   PetscCall(VecGetLocalSize(U, &Np));
524:   PetscCall(VecGetArrayRead(U, &u));
525:   PetscCall(VecGetArray(G, &g));

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

529:   Np /= 2 * dim;
530:   for (p = 0; p < Np; ++p) {
531:     const PetscReal x0    = coords[p * dim + 0];
532:     const PetscReal vy0   = vel[p * dim + 1];
533:     const PetscReal omega = vy0 / x0;

535:     for (d = 0; d < dim; ++d) {
536:       g[(p * 2 + 0) * dim + d] = u[(p * 2 + 1) * dim + d];
537:       g[(p * 2 + 1) * dim + d] = E[p * dim + d] - PetscSqr(omega) * u[(p * 2 + 0) * dim + d];
538:     }
539:   }
540:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
541:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
542:   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
543:   PetscCall(VecRestoreArrayRead(U, &u));
544:   PetscCall(VecRestoreArray(G, &g));
545:   PetscFunctionReturn(PETSC_SUCCESS);
546: }

548: /* J_{ij} = dF_i/dx_j
549:    J_p = (  0   1)
550:          (-w^2  0)
551:    TODO Now there is another term with w^2 from the electric field. I think we will need to invert the operator.
552:         Perhaps we can approximate the Jacobian using only the cellwise P-P gradient from Coulomb
553: */
554: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat J, Mat P, void *ctx)
555: {
556:   DM               sw;
557:   const PetscReal *coords, *vel;
558:   PetscInt         dim, d, Np, p, rStart;

560:   PetscFunctionBeginUser;
561:   PetscCall(TSGetDM(ts, &sw));
562:   PetscCall(DMGetDimension(sw, &dim));
563:   PetscCall(VecGetLocalSize(U, &Np));
564:   PetscCall(MatGetOwnershipRange(J, &rStart, NULL));
565:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
566:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
567:   Np /= 2 * dim;
568:   for (p = 0; p < Np; ++p) {
569:     const PetscReal x0      = coords[p * dim + 0];
570:     const PetscReal vy0     = vel[p * dim + 1];
571:     const PetscReal omega   = vy0 / x0;
572:     PetscScalar     vals[4] = {0., 1., -PetscSqr(omega), 0.};

574:     for (d = 0; d < dim; ++d) {
575:       const PetscInt rows[2] = {(p * 2 + 0) * dim + d + rStart, (p * 2 + 1) * dim + d + rStart};
576:       PetscCall(MatSetValues(J, 2, rows, 2, rows, vals, INSERT_VALUES));
577:     }
578:   }
579:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
580:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
581:   PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
582:   PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
583:   PetscFunctionReturn(PETSC_SUCCESS);
584: }

586: static PetscErrorCode RHSFunctionX(TS ts, PetscReal t, Vec V, Vec Xres, void *ctx)
587: {
588:   DM                 sw;
589:   const PetscScalar *v;
590:   PetscScalar       *xres;
591:   PetscInt           Np, p, dim, d;

593:   PetscFunctionBeginUser;
594:   PetscCall(TSGetDM(ts, &sw));
595:   PetscCall(DMGetDimension(sw, &dim));
596:   PetscCall(VecGetLocalSize(Xres, &Np));
597:   Np /= dim;
598:   PetscCall(VecGetArrayRead(V, &v));
599:   PetscCall(VecGetArray(Xres, &xres));
600:   for (p = 0; p < Np; ++p) {
601:     for (d = 0; d < dim; ++d) xres[p * dim + d] = v[p * dim + d];
602:   }
603:   PetscCall(VecRestoreArrayRead(V, &v));
604:   PetscCall(VecRestoreArray(Xres, &xres));
605:   PetscFunctionReturn(PETSC_SUCCESS);
606: }

608: static PetscErrorCode RHSFunctionV(TS ts, PetscReal t, Vec X, Vec Vres, void *ctx)
609: {
610:   DM                 sw;
611:   SNES               snes = ((AppCtx *)ctx)->snes;
612:   const PetscScalar *x;
613:   const PetscReal   *coords, *vel;
614:   PetscScalar       *vres;
615:   PetscReal         *E;
616:   PetscInt           Np, p, dim, d;

618:   PetscFunctionBeginUser;
619:   PetscCall(TSGetDM(ts, &sw));
620:   PetscCall(DMGetDimension(sw, &dim));
621:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
622:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
623:   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
624:   PetscCall(VecGetLocalSize(Vres, &Np));
625:   PetscCall(VecGetArrayRead(X, &x));
626:   PetscCall(VecGetArray(Vres, &vres));
627:   PetscCheck(dim == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension must be 2");

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

631:   Np /= dim;
632:   for (p = 0; p < Np; ++p) {
633:     const PetscReal x0    = coords[p * dim + 0];
634:     const PetscReal vy0   = vel[p * dim + 1];
635:     const PetscReal omega = vy0 / x0;

637:     for (d = 0; d < dim; ++d) vres[p * dim + d] = E[p * dim + d] - PetscSqr(omega) * x[p * dim + d];
638:   }
639:   PetscCall(VecRestoreArrayRead(X, &x));
640:   PetscCall(VecRestoreArray(Vres, &vres));
641:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
642:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
643:   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
644:   PetscFunctionReturn(PETSC_SUCCESS);
645: }

647: static PetscErrorCode CreateSolution(TS ts)
648: {
649:   DM       sw;
650:   Vec      u;
651:   PetscInt dim, Np;

653:   PetscFunctionBegin;
654:   PetscCall(TSGetDM(ts, &sw));
655:   PetscCall(DMGetDimension(sw, &dim));
656:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
657:   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
658:   PetscCall(VecSetBlockSize(u, dim));
659:   PetscCall(VecSetSizes(u, 2 * Np * dim, PETSC_DECIDE));
660:   PetscCall(VecSetUp(u));
661:   PetscCall(TSSetSolution(ts, u));
662:   PetscCall(VecDestroy(&u));
663:   PetscFunctionReturn(PETSC_SUCCESS);
664: }

666: static PetscErrorCode SetProblem(TS ts)
667: {
668:   AppCtx *user;
669:   DM      sw;

671:   PetscFunctionBegin;
672:   PetscCall(TSGetDM(ts, &sw));
673:   PetscCall(DMGetApplicationContext(sw, (void **)&user));
674:   // Define unified system for (X, V)
675:   {
676:     Mat      J;
677:     PetscInt dim, Np;

679:     PetscCall(DMGetDimension(sw, &dim));
680:     PetscCall(DMSwarmGetLocalSize(sw, &Np));
681:     PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
682:     PetscCall(MatSetSizes(J, 2 * Np * dim, 2 * Np * dim, PETSC_DECIDE, PETSC_DECIDE));
683:     PetscCall(MatSetBlockSize(J, 2 * dim));
684:     PetscCall(MatSetFromOptions(J));
685:     PetscCall(MatSetUp(J));
686:     PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, user));
687:     PetscCall(TSSetRHSJacobian(ts, J, J, RHSJacobian, user));
688:     PetscCall(MatDestroy(&J));
689:   }
690:   /* Define split system for X and V */
691:   {
692:     Vec             u;
693:     IS              isx, isv, istmp;
694:     const PetscInt *idx;
695:     PetscInt        dim, Np, rstart;

697:     PetscCall(TSGetSolution(ts, &u));
698:     PetscCall(DMGetDimension(sw, &dim));
699:     PetscCall(DMSwarmGetLocalSize(sw, &Np));
700:     PetscCall(VecGetOwnershipRange(u, &rstart, NULL));
701:     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 0, 2, &istmp));
702:     PetscCall(ISGetIndices(istmp, &idx));
703:     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isx));
704:     PetscCall(ISRestoreIndices(istmp, &idx));
705:     PetscCall(ISDestroy(&istmp));
706:     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 1, 2, &istmp));
707:     PetscCall(ISGetIndices(istmp, &idx));
708:     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isv));
709:     PetscCall(ISRestoreIndices(istmp, &idx));
710:     PetscCall(ISDestroy(&istmp));
711:     PetscCall(TSRHSSplitSetIS(ts, "position", isx));
712:     PetscCall(TSRHSSplitSetIS(ts, "momentum", isv));
713:     PetscCall(ISDestroy(&isx));
714:     PetscCall(ISDestroy(&isv));
715:     PetscCall(TSRHSSplitSetRHSFunction(ts, "position", NULL, RHSFunctionX, user));
716:     PetscCall(TSRHSSplitSetRHSFunction(ts, "momentum", NULL, RHSFunctionV, user));
717:   }
718:   PetscFunctionReturn(PETSC_SUCCESS);
719: }

721: PetscErrorCode circleSingleX(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
722: {
723:   x[0] = p + 1.;
724:   x[1] = 0.;
725:   return PETSC_SUCCESS;
726: }

728: PetscErrorCode circleSingleV(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar v[], void *ctx)
729: {
730:   v[0] = 0.;
731:   v[1] = PetscSqrtReal(1000. / (p + 1.));
732:   return PETSC_SUCCESS;
733: }

735: /* Put 5 particles into each circle */
736: PetscErrorCode circleMultipleX(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
737: {
738:   const PetscInt  n   = 5;
739:   const PetscReal r0  = (p / n) + 1.;
740:   const PetscReal th0 = (2. * PETSC_PI * (p % n)) / n;

742:   x[0] = r0 * PetscCosReal(th0);
743:   x[1] = r0 * PetscSinReal(th0);
744:   return PETSC_SUCCESS;
745: }

747: /* Put 5 particles into each circle */
748: PetscErrorCode circleMultipleV(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar v[], void *ctx)
749: {
750:   const PetscInt  n     = 5;
751:   const PetscReal r0    = (p / n) + 1.;
752:   const PetscReal th0   = (2. * PETSC_PI * (p % n)) / n;
753:   const PetscReal omega = PetscSqrtReal(1000. / r0) / r0;

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

760: /*
761:   InitializeSolveAndSwarm - Set the solution values to the swarm coordinates and velocities, and also possibly set the initial values.

763:   Input Parameters:
764: + ts         - The TS
765: - useInitial - Flag to also set the initial conditions to the current coordinates and velocities and setup the problem

767:   Output Parameter:
768: . u - The initialized solution vector

770:   Level: advanced

772: .seealso: InitializeSolve()
773: */
774: static PetscErrorCode InitializeSolveAndSwarm(TS ts, PetscBool useInitial)
775: {
776:   DM      sw;
777:   Vec     u, gc, gv, gc0, gv0;
778:   IS      isx, isv;
779:   AppCtx *user;

781:   PetscFunctionBeginUser;
782:   PetscCall(TSGetDM(ts, &sw));
783:   PetscCall(DMGetApplicationContext(sw, &user));
784:   if (useInitial) {
785:     PetscReal v0[1] = {1.};

787:     PetscCall(DMSwarmInitializeCoordinates(sw));
788:     PetscCall(DMSwarmInitializeVelocitiesFromOptions(sw, v0));
789:     PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
790:     PetscCall(TSReset(ts));
791:     PetscCall(CreateSolution(ts));
792:     PetscCall(SetProblem(ts));
793:   }
794:   PetscCall(TSGetSolution(ts, &u));
795:   PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
796:   PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
797:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
798:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initCoordinates", &gc0));
799:   if (useInitial) PetscCall(VecCopy(gc, gc0));
800:   PetscCall(VecISCopy(u, isx, SCATTER_FORWARD, gc));
801:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
802:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initCoordinates", &gc0));
803:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
804:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initVelocity", &gv0));
805:   if (useInitial) PetscCall(VecCopy(gv, gv0));
806:   PetscCall(VecISCopy(u, isv, SCATTER_FORWARD, gv));
807:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
808:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initVelocity", &gv0));
809:   PetscFunctionReturn(PETSC_SUCCESS);
810: }

812: static PetscErrorCode InitializeSolve(TS ts, Vec u)
813: {
814:   PetscFunctionBegin;
815:   PetscCall(TSSetSolution(ts, u));
816:   PetscCall(InitializeSolveAndSwarm(ts, PETSC_TRUE));
817:   PetscFunctionReturn(PETSC_SUCCESS);
818: }

820: static PetscErrorCode ComputeError(TS ts, Vec U, Vec E)
821: {
822:   MPI_Comm           comm;
823:   DM                 sw;
824:   AppCtx            *user;
825:   const PetscScalar *u;
826:   const PetscReal   *coords, *vel;
827:   PetscScalar       *e;
828:   PetscReal          t;
829:   PetscInt           dim, Np, p;

831:   PetscFunctionBeginUser;
832:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
833:   PetscCall(TSGetDM(ts, &sw));
834:   PetscCall(DMGetApplicationContext(sw, &user));
835:   PetscCall(DMGetDimension(sw, &dim));
836:   PetscCall(TSGetSolveTime(ts, &t));
837:   PetscCall(VecGetArray(E, &e));
838:   PetscCall(VecGetArrayRead(U, &u));
839:   PetscCall(VecGetLocalSize(U, &Np));
840:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
841:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
842:   Np /= 2 * dim;
843:   for (p = 0; p < Np; ++p) {
844:     /* TODO generalize initial conditions and project into plane instead of assuming x-y */
845:     const PetscReal    r0    = DMPlex_NormD_Internal(dim, &coords[p * dim]);
846:     const PetscReal    th0   = PetscAtan2Real(coords[p * dim + 1], coords[p * dim + 0]);
847:     const PetscReal    v0    = DMPlex_NormD_Internal(dim, &vel[p * dim]);
848:     const PetscReal    omega = v0 / r0;
849:     const PetscReal    ct    = PetscCosReal(omega * t + th0);
850:     const PetscReal    st    = PetscSinReal(omega * t + th0);
851:     const PetscScalar *x     = &u[(p * 2 + 0) * dim];
852:     const PetscScalar *v     = &u[(p * 2 + 1) * dim];
853:     const PetscReal    xe[3] = {r0 * ct, r0 * st, 0.0};
854:     const PetscReal    ve[3] = {-v0 * st, v0 * ct, 0.0};
855:     PetscInt           d;

857:     for (d = 0; d < dim; ++d) {
858:       e[(p * 2 + 0) * dim + d] = x[d] - xe[d];
859:       e[(p * 2 + 1) * dim + d] = v[d] - ve[d];
860:     }
861:     if (user->error) {
862:       const PetscReal en   = 0.5 * DMPlex_DotRealD_Internal(dim, v, v);
863:       const PetscReal exen = 0.5 * PetscSqr(v0);
864:       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)));
865:     }
866:   }
867:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
868:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
869:   PetscCall(VecRestoreArrayRead(U, &u));
870:   PetscCall(VecRestoreArray(E, &e));
871:   PetscFunctionReturn(PETSC_SUCCESS);
872: }

874: static PetscErrorCode EnergyMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
875: {
876:   const PetscInt     ostep = ((AppCtx *)ctx)->ostep;
877:   const EMType       em    = ((AppCtx *)ctx)->em;
878:   DM                 sw;
879:   const PetscScalar *u;
880:   PetscReal         *coords, *E;
881:   PetscReal          enKin = 0., enEM = 0.;
882:   PetscInt           dim, d, Np, p, q;

884:   PetscFunctionBeginUser;
885:   if (step % ostep == 0) {
886:     PetscCall(TSGetDM(ts, &sw));
887:     PetscCall(DMGetDimension(sw, &dim));
888:     PetscCall(VecGetArrayRead(U, &u));
889:     PetscCall(VecGetLocalSize(U, &Np));
890:     Np /= 2 * dim;
891:     PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
892:     PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
893:     if (!step) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)ts), "Time     Step Part     Energy\n"));
894:     for (p = 0; p < Np; ++p) {
895:       const PetscReal v2     = DMPlex_DotRealD_Internal(dim, &u[(p * 2 + 1) * dim], &u[(p * 2 + 1) * dim]);
896:       PetscReal      *pcoord = &coords[p * dim];

898:       PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " %5" PetscInt_FMT " %10.4lf\n", (double)t, step, p, (double)(0.5 * v2)));
899:       enKin += 0.5 * v2;
900:       if (em == EM_NONE) {
901:         continue;
902:       } else if (em == EM_COULOMB) {
903:         for (q = p + 1; q < Np; ++q) {
904:           PetscReal *qcoord = &coords[q * dim];
905:           PetscReal  rpq[3], r;
906:           for (d = 0; d < dim; ++d) rpq[d] = pcoord[d] - qcoord[d];
907:           r = DMPlex_NormD_Internal(dim, rpq);
908:           enEM += 1. / r;
909:         }
910:       } else if (em == EM_PRIMAL || em == EM_MIXED) {
911:         for (d = 0; d < dim; ++d) enEM += E[p * dim + d];
912:       }
913:     }
914:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " KE\t    %10.4lf\n", (double)t, step, (double)enKin));
915:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " PE\t    %1.10g\n", (double)t, step, (double)enEM));
916:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " E\t    %10.4lf\n", (double)t, step, (double)(enKin + enEM)));
917:     PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
918:     PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
919:     PetscCall(PetscSynchronizedFlush(PetscObjectComm((PetscObject)ts), NULL));
920:     PetscCall(VecRestoreArrayRead(U, &u));
921:   }
922:   PetscFunctionReturn(PETSC_SUCCESS);
923: }

925: static PetscErrorCode SetUpMigrateParticles(TS ts, PetscInt n, PetscReal t, Vec x, PetscBool *flg, void *ctx)
926: {
927:   DM sw;

929:   PetscFunctionBeginUser;
930:   *flg = PETSC_TRUE;
931:   PetscCall(TSGetDM(ts, &sw));
932:   PetscCall(DMViewFromOptions(sw, NULL, "-migrate_view_pre"));
933:   {
934:     Vec u, gc, gv;
935:     IS  isx, isv;

937:     PetscCall(TSGetSolution(ts, &u));
938:     PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
939:     PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
940:     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
941:     PetscCall(VecISCopy(u, isx, SCATTER_REVERSE, gc));
942:     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
943:     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
944:     PetscCall(VecISCopy(u, isv, SCATTER_REVERSE, gv));
945:     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
946:   }
947:   PetscFunctionReturn(PETSC_SUCCESS);
948: }

950: static PetscErrorCode MigrateParticles(TS ts, PetscInt nv, Vec vecsin[], Vec vecsout[], void *ctx)
951: {
952:   DM sw;

954:   PetscFunctionBeginUser;
955:   PetscCall(TSGetDM(ts, &sw));
956:   PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
957:   PetscCall(CreateSolution(ts));
958:   PetscCall(SetProblem(ts));
959:   PetscCall(InitializeSolveAndSwarm(ts, PETSC_FALSE));
960:   PetscFunctionReturn(PETSC_SUCCESS);
961: }

963: int main(int argc, char **argv)
964: {
965:   DM     dm, sw;
966:   TS     ts;
967:   Vec    u;
968:   AppCtx user;

970:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
971:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
972:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
973:   PetscCall(CreatePoisson(dm, &user));
974:   PetscCall(CreateSwarm(dm, &user, &sw));
975:   PetscCall(DMSetApplicationContext(sw, &user));

977:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
978:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
979:   PetscCall(TSSetDM(ts, sw));
980:   PetscCall(TSSetMaxTime(ts, 0.1));
981:   PetscCall(TSSetTimeStep(ts, 0.00001));
982:   PetscCall(TSSetMaxSteps(ts, 100));
983:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
984:   PetscCall(TSMonitorSet(ts, EnergyMonitor, &user, NULL));
985:   PetscCall(TSSetFromOptions(ts));
986:   PetscCall(DMSwarmVectorDefineField(sw, "velocity"));
987:   PetscCall(TSSetComputeInitialCondition(ts, InitializeSolve));
988:   PetscCall(TSSetComputeExactError(ts, ComputeError));
989:   PetscCall(TSSetResize(ts, PETSC_FALSE, SetUpMigrateParticles, MigrateParticles, NULL));

991:   PetscCall(CreateSolution(ts));
992:   PetscCall(TSGetSolution(ts, &u));
993:   PetscCall(TSComputeInitialCondition(ts, u));
994:   PetscCall(TSSolve(ts, NULL));

996:   PetscCall(SNESDestroy(&user.snes));
997:   PetscCall(TSDestroy(&ts));
998:   PetscCall(DMDestroy(&sw));
999:   PetscCall(DMDestroy(&dm));
1000:   PetscCall(PetscFinalize());
1001:   return 0;
1002: }

1004: /*TEST

1006:    build:
1007:      requires: double !complex

1009:    testset:
1010:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1011:      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 \
1012:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1013:            -ts_type basicsymplectic\
1014:            -dm_view -output_step 50 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1015:      test:
1016:        suffix: none_bsi_2d_1
1017:        args: -ts_basicsymplectic_type 1 -em_type none -error
1018:      test:
1019:        suffix: none_bsi_2d_2
1020:        args: -ts_basicsymplectic_type 2 -em_type none -error
1021:      test:
1022:        suffix: none_bsi_2d_3
1023:        args: -ts_basicsymplectic_type 3 -em_type none -error
1024:      test:
1025:        suffix: none_bsi_2d_4
1026:        args: -ts_basicsymplectic_type 4 -em_type none -error
1027:      test:
1028:        suffix: coulomb_bsi_2d_1
1029:        args: -ts_basicsymplectic_type 1
1030:      test:
1031:        suffix: coulomb_bsi_2d_2
1032:        args: -ts_basicsymplectic_type 2
1033:      test:
1034:        suffix: coulomb_bsi_2d_3
1035:        args: -ts_basicsymplectic_type 3
1036:      test:
1037:        suffix: coulomb_bsi_2d_4
1038:        args: -ts_basicsymplectic_type 4

1040:    testset:
1041:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1042:      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 \
1043:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1044:            -ts_type basicsymplectic\
1045:            -em_type primal -em_pc_type svd\
1046:            -dm_view -output_step 50 -error -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10\
1047:            -petscspace_degree 2 -petscfe_default_quadrature_order 3 -sigma 1.0e-8 -timeScale 2.0e-14
1048:      test:
1049:        suffix: poisson_bsi_2d_1
1050:        args: -ts_basicsymplectic_type 1
1051:      test:
1052:        suffix: poisson_bsi_2d_2
1053:        args: -ts_basicsymplectic_type 2
1054:      test:
1055:        suffix: poisson_bsi_2d_3
1056:        args: -ts_basicsymplectic_type 3
1057:      test:
1058:        suffix: poisson_bsi_2d_4
1059:        args: -ts_basicsymplectic_type 4

1061:    testset:
1062:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1063:      args: -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1064:            -ts_type theta -ts_theta_theta 0.5 -ts_convergence_estimate -convest_num_refine 2 \
1065:              -mat_type baij -ksp_error_if_not_converged -em_pc_type svd\
1066:            -dm_view -output_step 50 -error -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10\
1067:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14
1068:      test:
1069:        suffix: im_2d_0
1070:        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

1072:    testset:
1073:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1074:      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 \
1075:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV -dm_swarm_num_species 1\
1076:            -ts_type basicsymplectic -ts_convergence_estimate -convest_num_refine 2 \
1077:            -em_snes_type ksponly -em_pc_type svd -em_type primal -petscspace_degree 1\
1078:            -dm_view -output_step 50\
1079:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 1.0 -ts_max_steps 10
1080:      test:
1081:        suffix: bsi_2d_mesh_1
1082:        args: -ts_basicsymplectic_type 4
1083:      test:
1084:        suffix: bsi_2d_mesh_1_par_2
1085:        nsize: 2
1086:        args: -ts_basicsymplectic_type 4
1087:      test:
1088:        suffix: bsi_2d_mesh_1_par_3
1089:        nsize: 3
1090:        args: -ts_basicsymplectic_type 4
1091:      test:
1092:        suffix: bsi_2d_mesh_1_par_4
1093:        nsize: 4
1094:        args: -ts_basicsymplectic_type 4 -dm_swarm_num_particles 0,0,2,0

1096:    testset:
1097:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1098:      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 \
1099:            -dm_swarm_num_particles 10 -dm_swarm_coordinate_function circleMultipleX -dm_swarm_velocity_function circleMultipleV \
1100:            -ts_convergence_estimate -convest_num_refine 2 \
1101:              -em_pc_type lu\
1102:            -dm_view -output_step 50 -error\
1103:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1104:      test:
1105:        suffix: bsi_2d_multiple_1
1106:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 1
1107:      test:
1108:        suffix: bsi_2d_multiple_2
1109:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 2
1110:      test:
1111:        suffix: bsi_2d_multiple_3
1112:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 3 -ts_dt 0.001
1113:      test:
1114:        suffix: im_2d_multiple_0
1115:        args: -ts_type theta -ts_theta_theta 0.5 \
1116:                -mat_type baij -ksp_error_if_not_converged -em_pc_type lu

1118:    testset:
1119:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1120:      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 \
1121:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1122:            -em_pc_type fieldsplit -ksp_rtol 1e-10 -em_ksp_type preonly -em_type mixed -em_ksp_error_if_not_converged\
1123:            -dm_view -output_step 50 -error -dm_refine 0\
1124:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1125:      test:
1126:        suffix: bsi_4_rt_1
1127:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 4\
1128:              -pc_fieldsplit_detect_saddle_point\
1129:              -pc_type fieldsplit\
1130:              -pc_fieldsplit_type schur\
1131:              -pc_fieldsplit_schur_precondition full \
1132:              -field_petscspace_degree 2\
1133:              -field_petscfe_default_quadrature_order 1\
1134:              -field_petscspace_type sum \
1135:              -field_petscspace_variables 2 \
1136:              -field_petscspace_components 2 \
1137:              -field_petscspace_sum_spaces 2 \
1138:              -field_petscspace_sum_concatenate true \
1139:              -field_sumcomp_0_petscspace_variables 2 \
1140:              -field_sumcomp_0_petscspace_type tensor \
1141:              -field_sumcomp_0_petscspace_tensor_spaces 2 \
1142:              -field_sumcomp_0_petscspace_tensor_uniform false \
1143:              -field_sumcomp_0_tensorcomp_0_petscspace_degree 1 \
1144:              -field_sumcomp_0_tensorcomp_1_petscspace_degree 0 \
1145:              -field_sumcomp_1_petscspace_variables 2 \
1146:              -field_sumcomp_1_petscspace_type tensor \
1147:              -field_sumcomp_1_petscspace_tensor_spaces 2 \
1148:              -field_sumcomp_1_petscspace_tensor_uniform false \
1149:              -field_sumcomp_1_tensorcomp_0_petscspace_degree 0 \
1150:              -field_sumcomp_1_tensorcomp_1_petscspace_degree 1 \
1151:              -field_petscdualspace_form_degree -1 \
1152:              -field_petscdualspace_order 1 \
1153:              -field_petscdualspace_lagrange_trimmed true\
1154:              -ksp_gmres_restart 500

1156: TEST*/