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, user, user, 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;

268:   PetscFunctionBegin;
269:   PetscCall(DMGetDimension(sw, &dim));
270:   PetscCall(DMSwarmGetLocalSize(sw, &Np));

272:   /* Create the charges rho */
273:   PetscCall(SNESGetDM(snes, &dm));
274:   PetscCall(DMCreateMassMatrix(sw, dm, &M_p));
275:   PetscCall(DMGetGlobalVector(dm, &rho));
276:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
277:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
278:   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
279:   PetscCall(MatMultTranspose(M_p, f, rho));
280:   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
281:   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
282:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
283:   PetscCall(MatDestroy(&M_p));
284:   {
285:     PetscScalar sum;
286:     PetscInt    n;
287:     PetscReal   phi_0 = 1.; /* (sigma*sigma*sigma)*(timeScale*timeScale)/(m_e*q_e*epsi_0)*/

289:     /* Remove constant from rho */
290:     PetscCall(VecGetSize(rho, &n));
291:     PetscCall(VecSum(rho, &sum));
292:     PetscCall(VecShift(rho, -sum / n));
293:     PetscCall(VecSum(rho, &sum));
294:     PetscCheck(PetscAbsScalar(sum) < chargeTol, PetscObjectComm((PetscObject)sw), PETSC_ERR_PLIB, "Charge should have no DC component: %g", (double)PetscRealPart(sum));
295:     /* Nondimensionalize rho */
296:     PetscCall(VecScale(rho, phi_0));
297:   }
298:   PetscCall(VecViewFromOptions(rho, NULL, "-poisson_rho_view"));

300:   PetscCall(DMGetGlobalVector(dm, &phi));
301:   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
302:   PetscCall(VecSet(phi, 0.0));
303:   PetscCall(SNESSolve(snes, rho, phi));
304:   PetscCall(DMRestoreGlobalVector(dm, &rho));
305:   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));

307:   PetscCall(DMGetLocalVector(dm, &locPhi));
308:   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
309:   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
310:   PetscCall(DMRestoreGlobalVector(dm, &phi));

312:   PetscCall(DMGetDS(dm, &ds));
313:   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
314:   PetscCall(DMSwarmSortGetAccess(sw));
315:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
316:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
317:   for (c = cStart; c < cEnd; ++c) {
318:     PetscTabulation tab;
319:     PetscScalar    *clPhi = NULL;
320:     PetscReal      *pcoord, *refcoord;
321:     PetscReal       v[3], J[9], invJ[9], detJ;
322:     PetscInt       *points;
323:     PetscInt        Ncp, cp;

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

338:       for (d = 0; d < dim; ++d) E[p * dim + d] = 0.;
339:       PetscCall(PetscFEFreeInterpolateGradient_Static(fe, basisDer, clPhi, dim, invJ, NULL, cp, &E[p * dim]));
340:       for (d = 0; d < dim; ++d) E[p * dim + d] *= -1.0;
341:     }
342:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
343:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
344:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
345:     PetscCall(PetscTabulationDestroy(&tab));
346:     PetscCall(PetscFree(points));
347:   }
348:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
349:   PetscCall(DMSwarmSortRestoreAccess(sw));
350:   PetscCall(DMRestoreLocalVector(dm, &locPhi));
351:   PetscFunctionReturn(PETSC_SUCCESS);
352: }

354: static PetscErrorCode ComputeFieldAtParticles_Mixed(SNES snes, DM sw, PetscReal E[])
355: {
356:   DM              dm, potential_dm;
357:   IS              potential_IS;
358:   PetscDS         ds;
359:   PetscFE         fe;
360:   PetscFEGeom     feGeometry;
361:   Mat             M_p;
362:   Vec             phi, locPhi, rho, f, temp_rho;
363:   PetscQuadrature q;
364:   PetscReal      *coords, chargeTol = 1e-13;
365:   PetscInt        dim, d, cStart, cEnd, c, Np, fields = 1;

367:   PetscFunctionBegin;
368:   PetscCall(DMGetDimension(sw, &dim));
369:   PetscCall(DMSwarmGetLocalSize(sw, &Np));

371:   /* Create the charges rho */
372:   PetscCall(SNESGetDM(snes, &dm));
373:   PetscCall(DMGetGlobalVector(dm, &rho));
374:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));

376:   PetscCall(DMCreateSubDM(dm, 1, &fields, &potential_IS, &potential_dm));
377:   PetscCall(DMCreateMassMatrix(sw, potential_dm, &M_p));
378:   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
379:   PetscCall(DMGetGlobalVector(potential_dm, &temp_rho));
380:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
381:   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
382:   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
383:   PetscCall(MatMultTranspose(M_p, f, temp_rho));
384:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
385:   PetscCall(MatDestroy(&M_p));
386:   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
387:   PetscCall(VecViewFromOptions(rho, NULL, "-poisson_rho_view"));
388:   PetscCall(VecISCopy(rho, potential_IS, SCATTER_FORWARD, temp_rho));
389:   PetscCall(DMRestoreGlobalVector(potential_dm, &temp_rho));
390:   PetscCall(DMDestroy(&potential_dm));
391:   PetscCall(ISDestroy(&potential_IS));
392:   {
393:     PetscScalar sum;
394:     PetscInt    n;
395:     PetscReal   phi_0 = 1.; /*(sigma*sigma*sigma)*(timeScale*timeScale)/(m_e*q_e*epsi_0);*/

397:     /*Remove constant from rho*/
398:     PetscCall(VecGetSize(rho, &n));
399:     PetscCall(VecSum(rho, &sum));
400:     PetscCall(VecShift(rho, -sum / n));
401:     PetscCall(VecSum(rho, &sum));
402:     PetscCheck(PetscAbsScalar(sum) < chargeTol, PetscObjectComm((PetscObject)sw), PETSC_ERR_PLIB, "Charge should have no DC component: %g", (double)PetscRealPart(sum));
403:     /* Nondimensionalize rho */
404:     PetscCall(VecScale(rho, phi_0));
405:   }
406:   PetscCall(DMGetGlobalVector(dm, &phi));
407:   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
408:   PetscCall(VecSet(phi, 0.0));
409:   PetscCall(SNESSolve(snes, NULL, phi));
410:   PetscCall(DMRestoreGlobalVector(dm, &rho));
411:   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));

413:   PetscCall(DMGetLocalVector(dm, &locPhi));
414:   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
415:   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
416:   PetscCall(DMRestoreGlobalVector(dm, &phi));

418:   PetscCall(DMGetDS(dm, &ds));
419:   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
420:   PetscCall(DMSwarmSortGetAccess(sw));
421:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
422:   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
423:   for (c = cStart; c < cEnd; ++c) {
424:     PetscTabulation tab;
425:     PetscScalar    *clPhi = NULL;
426:     PetscReal      *pcoord, *refcoord;
427:     PetscReal       v[3], J[9], invJ[9], detJ;
428:     PetscInt       *points;
429:     PetscInt        Ncp, cp;

431:     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
432:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
433:     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
434:     for (cp = 0; cp < Ncp; ++cp)
435:       for (d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
436:     PetscCall(DMPlexCoordinatesToReference(dm, c, Ncp, pcoord, refcoord));
437:     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
438:     PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v, J, invJ, &detJ));
439:     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
440:     for (cp = 0; cp < Ncp; ++cp) {
441:       const PetscInt p = points[cp];

443:       for (d = 0; d < dim; ++d) E[p * dim + d] = 0.;
444:       PetscCall(PetscFEGetQuadrature(fe, &q));
445:       PetscCall(PetscFECreateCellGeometry(fe, q, &feGeometry));
446:       PetscCall(PetscFEInterpolateAtPoints_Static(fe, tab, clPhi, &feGeometry, cp, &E[p * dim]));
447:       PetscCall(PetscFEDestroyCellGeometry(fe, &feGeometry));
448:     }
449:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
450:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
451:     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
452:     PetscCall(PetscTabulationDestroy(&tab));
453:     PetscCall(PetscFree(points));
454:   }
455:   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
456:   PetscCall(DMSwarmSortRestoreAccess(sw));
457:   PetscCall(DMRestoreLocalVector(dm, &locPhi));
458:   PetscFunctionReturn(PETSC_SUCCESS);
459: }

461: static PetscErrorCode ComputeFieldAtParticles(SNES snes, DM sw, PetscReal E[])
462: {
463:   AppCtx  *ctx;
464:   PetscInt dim, Np;

466:   PetscFunctionBegin;
469:   PetscAssertPointer(E, 3);
470:   PetscCall(DMGetDimension(sw, &dim));
471:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
472:   PetscCall(DMGetApplicationContext(sw, &ctx));
473:   PetscCall(PetscArrayzero(E, Np * dim));

475:   switch (ctx->em) {
476:   case EM_PRIMAL:
477:     PetscCall(ComputeFieldAtParticles_Primal(snes, sw, E));
478:     break;
479:   case EM_COULOMB:
480:     PetscCall(ComputeFieldAtParticles_Coulomb(snes, sw, E));
481:     break;
482:   case EM_MIXED:
483:     PetscCall(ComputeFieldAtParticles_Mixed(snes, sw, E));
484:     break;
485:   case EM_NONE:
486:     break;
487:   default:
488:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No solver for electrostatic model %s", EMTypes[ctx->em]);
489:   }

491:   PetscFunctionReturn(PETSC_SUCCESS);
492: }

494: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec G, void *ctx)
495: {
496:   DM                 sw;
497:   SNES               snes = ((AppCtx *)ctx)->snes;
498:   const PetscReal   *coords, *vel;
499:   const PetscScalar *u;
500:   PetscScalar       *g;
501:   PetscReal         *E;
502:   PetscInt           dim, d, Np, p;

504:   PetscFunctionBeginUser;
505:   PetscCall(TSGetDM(ts, &sw));
506:   PetscCall(DMGetDimension(sw, &dim));
507:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
508:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
509:   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
510:   PetscCall(VecGetLocalSize(U, &Np));
511:   PetscCall(VecGetArrayRead(U, &u));
512:   PetscCall(VecGetArray(G, &g));

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

516:   Np /= 2 * dim;
517:   for (p = 0; p < Np; ++p) {
518:     const PetscReal x0    = coords[p * dim + 0];
519:     const PetscReal vy0   = vel[p * dim + 1];
520:     const PetscReal omega = vy0 / x0;

522:     for (d = 0; d < dim; ++d) {
523:       g[(p * 2 + 0) * dim + d] = u[(p * 2 + 1) * dim + d];
524:       g[(p * 2 + 1) * dim + d] = E[p * dim + d] - PetscSqr(omega) * u[(p * 2 + 0) * dim + d];
525:     }
526:   }
527:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
528:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
529:   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
530:   PetscCall(VecRestoreArrayRead(U, &u));
531:   PetscCall(VecRestoreArray(G, &g));
532:   PetscFunctionReturn(PETSC_SUCCESS);
533: }

535: /* J_{ij} = dF_i/dx_j
536:    J_p = (  0   1)
537:          (-w^2  0)
538:    TODO Now there is another term with w^2 from the electric field. I think we will need to invert the operator.
539:         Perhaps we can approximate the Jacobian using only the cellwise P-P gradient from Coulomb
540: */
541: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat J, Mat P, void *ctx)
542: {
543:   DM               sw;
544:   const PetscReal *coords, *vel;
545:   PetscInt         dim, d, Np, p, rStart;

547:   PetscFunctionBeginUser;
548:   PetscCall(TSGetDM(ts, &sw));
549:   PetscCall(DMGetDimension(sw, &dim));
550:   PetscCall(VecGetLocalSize(U, &Np));
551:   PetscCall(MatGetOwnershipRange(J, &rStart, NULL));
552:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
553:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
554:   Np /= 2 * dim;
555:   for (p = 0; p < Np; ++p) {
556:     const PetscReal x0      = coords[p * dim + 0];
557:     const PetscReal vy0     = vel[p * dim + 1];
558:     const PetscReal omega   = vy0 / x0;
559:     PetscScalar     vals[4] = {0., 1., -PetscSqr(omega), 0.};

561:     for (d = 0; d < dim; ++d) {
562:       const PetscInt rows[2] = {(p * 2 + 0) * dim + d + rStart, (p * 2 + 1) * dim + d + rStart};
563:       PetscCall(MatSetValues(J, 2, rows, 2, rows, vals, INSERT_VALUES));
564:     }
565:   }
566:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
567:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
568:   PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
569:   PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
570:   PetscFunctionReturn(PETSC_SUCCESS);
571: }

573: static PetscErrorCode RHSFunctionX(TS ts, PetscReal t, Vec V, Vec Xres, void *ctx)
574: {
575:   DM                 sw;
576:   const PetscScalar *v;
577:   PetscScalar       *xres;
578:   PetscInt           Np, p, dim, d;

580:   PetscFunctionBeginUser;
581:   PetscCall(TSGetDM(ts, &sw));
582:   PetscCall(DMGetDimension(sw, &dim));
583:   PetscCall(VecGetLocalSize(Xres, &Np));
584:   Np /= dim;
585:   PetscCall(VecGetArrayRead(V, &v));
586:   PetscCall(VecGetArray(Xres, &xres));
587:   for (p = 0; p < Np; ++p) {
588:     for (d = 0; d < dim; ++d) xres[p * dim + d] = v[p * dim + d];
589:   }
590:   PetscCall(VecRestoreArrayRead(V, &v));
591:   PetscCall(VecRestoreArray(Xres, &xres));
592:   PetscFunctionReturn(PETSC_SUCCESS);
593: }

595: static PetscErrorCode RHSFunctionV(TS ts, PetscReal t, Vec X, Vec Vres, void *ctx)
596: {
597:   DM                 sw;
598:   SNES               snes = ((AppCtx *)ctx)->snes;
599:   const PetscScalar *x;
600:   const PetscReal   *coords, *vel;
601:   PetscScalar       *vres;
602:   PetscReal         *E;
603:   PetscInt           Np, p, dim, d;

605:   PetscFunctionBeginUser;
606:   PetscCall(TSGetDM(ts, &sw));
607:   PetscCall(DMGetDimension(sw, &dim));
608:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
609:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
610:   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
611:   PetscCall(VecGetLocalSize(Vres, &Np));
612:   PetscCall(VecGetArrayRead(X, &x));
613:   PetscCall(VecGetArray(Vres, &vres));
614:   PetscCheck(dim == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension must be 2");

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

618:   Np /= dim;
619:   for (p = 0; p < Np; ++p) {
620:     const PetscReal x0    = coords[p * dim + 0];
621:     const PetscReal vy0   = vel[p * dim + 1];
622:     const PetscReal omega = vy0 / x0;

624:     for (d = 0; d < dim; ++d) vres[p * dim + d] = E[p * dim + d] - PetscSqr(omega) * x[p * dim + d];
625:   }
626:   PetscCall(VecRestoreArrayRead(X, &x));
627:   PetscCall(VecRestoreArray(Vres, &vres));
628:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
629:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
630:   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
631:   PetscFunctionReturn(PETSC_SUCCESS);
632: }

634: static PetscErrorCode CreateSolution(TS ts)
635: {
636:   DM       sw;
637:   Vec      u;
638:   PetscInt dim, Np;

640:   PetscFunctionBegin;
641:   PetscCall(TSGetDM(ts, &sw));
642:   PetscCall(DMGetDimension(sw, &dim));
643:   PetscCall(DMSwarmGetLocalSize(sw, &Np));
644:   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
645:   PetscCall(VecSetBlockSize(u, dim));
646:   PetscCall(VecSetSizes(u, 2 * Np * dim, PETSC_DECIDE));
647:   PetscCall(VecSetUp(u));
648:   PetscCall(TSSetSolution(ts, u));
649:   PetscCall(VecDestroy(&u));
650:   PetscFunctionReturn(PETSC_SUCCESS);
651: }

653: static PetscErrorCode SetProblem(TS ts)
654: {
655:   AppCtx *user;
656:   DM      sw;

658:   PetscFunctionBegin;
659:   PetscCall(TSGetDM(ts, &sw));
660:   PetscCall(DMGetApplicationContext(sw, (void **)&user));
661:   // Define unified system for (X, V)
662:   {
663:     Mat      J;
664:     PetscInt dim, Np;

666:     PetscCall(DMGetDimension(sw, &dim));
667:     PetscCall(DMSwarmGetLocalSize(sw, &Np));
668:     PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
669:     PetscCall(MatSetSizes(J, 2 * Np * dim, 2 * Np * dim, PETSC_DECIDE, PETSC_DECIDE));
670:     PetscCall(MatSetBlockSize(J, 2 * dim));
671:     PetscCall(MatSetFromOptions(J));
672:     PetscCall(MatSetUp(J));
673:     PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, user));
674:     PetscCall(TSSetRHSJacobian(ts, J, J, RHSJacobian, user));
675:     PetscCall(MatDestroy(&J));
676:   }
677:   /* Define split system for X and V */
678:   {
679:     Vec             u;
680:     IS              isx, isv, istmp;
681:     const PetscInt *idx;
682:     PetscInt        dim, Np, rstart;

684:     PetscCall(TSGetSolution(ts, &u));
685:     PetscCall(DMGetDimension(sw, &dim));
686:     PetscCall(DMSwarmGetLocalSize(sw, &Np));
687:     PetscCall(VecGetOwnershipRange(u, &rstart, NULL));
688:     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 0, 2, &istmp));
689:     PetscCall(ISGetIndices(istmp, &idx));
690:     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isx));
691:     PetscCall(ISRestoreIndices(istmp, &idx));
692:     PetscCall(ISDestroy(&istmp));
693:     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 1, 2, &istmp));
694:     PetscCall(ISGetIndices(istmp, &idx));
695:     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isv));
696:     PetscCall(ISRestoreIndices(istmp, &idx));
697:     PetscCall(ISDestroy(&istmp));
698:     PetscCall(TSRHSSplitSetIS(ts, "position", isx));
699:     PetscCall(TSRHSSplitSetIS(ts, "momentum", isv));
700:     PetscCall(ISDestroy(&isx));
701:     PetscCall(ISDestroy(&isv));
702:     PetscCall(TSRHSSplitSetRHSFunction(ts, "position", NULL, RHSFunctionX, user));
703:     PetscCall(TSRHSSplitSetRHSFunction(ts, "momentum", NULL, RHSFunctionV, user));
704:   }
705:   PetscFunctionReturn(PETSC_SUCCESS);
706: }

708: PetscErrorCode circleSingleX(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
709: {
710:   x[0] = p + 1.;
711:   x[1] = 0.;
712:   return PETSC_SUCCESS;
713: }

715: PetscErrorCode circleSingleV(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar v[], void *ctx)
716: {
717:   v[0] = 0.;
718:   v[1] = PetscSqrtReal(1000. / (p + 1.));
719:   return PETSC_SUCCESS;
720: }

722: /* Put 5 particles into each circle */
723: PetscErrorCode circleMultipleX(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
724: {
725:   const PetscInt  n   = 5;
726:   const PetscReal r0  = (p / n) + 1.;
727:   const PetscReal th0 = (2. * PETSC_PI * (p % n)) / n;

729:   x[0] = r0 * PetscCosReal(th0);
730:   x[1] = r0 * PetscSinReal(th0);
731:   return PETSC_SUCCESS;
732: }

734: /* Put 5 particles into each circle */
735: PetscErrorCode circleMultipleV(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar v[], void *ctx)
736: {
737:   const PetscInt  n     = 5;
738:   const PetscReal r0    = (p / n) + 1.;
739:   const PetscReal th0   = (2. * PETSC_PI * (p % n)) / n;
740:   const PetscReal omega = PetscSqrtReal(1000. / r0) / r0;

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

747: /*
748:   InitializeSolveAndSwarm - Set the solution values to the swarm coordinates and velocities, and also possibly set the initial values.

750:   Input Parameters:
751: + ts         - The TS
752: - useInitial - Flag to also set the initial conditions to the current coordinates and velocities and setup the problem

754:   Output Parameter:
755: . u - The initialized solution vector

757:   Level: advanced

759: .seealso: InitializeSolve()
760: */
761: static PetscErrorCode InitializeSolveAndSwarm(TS ts, PetscBool useInitial)
762: {
763:   DM      sw;
764:   Vec     u, gc, gv, gc0, gv0;
765:   IS      isx, isv;
766:   AppCtx *user;

768:   PetscFunctionBeginUser;
769:   PetscCall(TSGetDM(ts, &sw));
770:   PetscCall(DMGetApplicationContext(sw, &user));
771:   if (useInitial) {
772:     PetscReal v0[1] = {1.};

774:     PetscCall(DMSwarmInitializeCoordinates(sw));
775:     PetscCall(DMSwarmInitializeVelocitiesFromOptions(sw, v0));
776:     PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
777:     PetscCall(TSReset(ts));
778:     PetscCall(CreateSolution(ts));
779:     PetscCall(SetProblem(ts));
780:   }
781:   PetscCall(TSGetSolution(ts, &u));
782:   PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
783:   PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
784:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
785:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initCoordinates", &gc0));
786:   if (useInitial) PetscCall(VecCopy(gc, gc0));
787:   PetscCall(VecISCopy(u, isx, SCATTER_FORWARD, gc));
788:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
789:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initCoordinates", &gc0));
790:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
791:   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initVelocity", &gv0));
792:   if (useInitial) PetscCall(VecCopy(gv, gv0));
793:   PetscCall(VecISCopy(u, isv, SCATTER_FORWARD, gv));
794:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
795:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initVelocity", &gv0));
796:   PetscFunctionReturn(PETSC_SUCCESS);
797: }

799: static PetscErrorCode InitializeSolve(TS ts, Vec u)
800: {
801:   PetscFunctionBegin;
802:   PetscCall(TSSetSolution(ts, u));
803:   PetscCall(InitializeSolveAndSwarm(ts, PETSC_TRUE));
804:   PetscFunctionReturn(PETSC_SUCCESS);
805: }

807: static PetscErrorCode ComputeError(TS ts, Vec U, Vec E)
808: {
809:   MPI_Comm           comm;
810:   DM                 sw;
811:   AppCtx            *user;
812:   const PetscScalar *u;
813:   const PetscReal   *coords, *vel;
814:   PetscScalar       *e;
815:   PetscReal          t;
816:   PetscInt           dim, Np, p;

818:   PetscFunctionBeginUser;
819:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
820:   PetscCall(TSGetDM(ts, &sw));
821:   PetscCall(DMGetApplicationContext(sw, &user));
822:   PetscCall(DMGetDimension(sw, &dim));
823:   PetscCall(TSGetSolveTime(ts, &t));
824:   PetscCall(VecGetArray(E, &e));
825:   PetscCall(VecGetArrayRead(U, &u));
826:   PetscCall(VecGetLocalSize(U, &Np));
827:   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
828:   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
829:   Np /= 2 * dim;
830:   for (p = 0; p < Np; ++p) {
831:     /* TODO generalize initial conditions and project into plane instead of assuming x-y */
832:     const PetscReal    r0    = DMPlex_NormD_Internal(dim, &coords[p * dim]);
833:     const PetscReal    th0   = PetscAtan2Real(coords[p * dim + 1], coords[p * dim + 0]);
834:     const PetscReal    v0    = DMPlex_NormD_Internal(dim, &vel[p * dim]);
835:     const PetscReal    omega = v0 / r0;
836:     const PetscReal    ct    = PetscCosReal(omega * t + th0);
837:     const PetscReal    st    = PetscSinReal(omega * t + th0);
838:     const PetscScalar *x     = &u[(p * 2 + 0) * dim];
839:     const PetscScalar *v     = &u[(p * 2 + 1) * dim];
840:     const PetscReal    xe[3] = {r0 * ct, r0 * st, 0.0};
841:     const PetscReal    ve[3] = {-v0 * st, v0 * ct, 0.0};
842:     PetscInt           d;

844:     for (d = 0; d < dim; ++d) {
845:       e[(p * 2 + 0) * dim + d] = x[d] - xe[d];
846:       e[(p * 2 + 1) * dim + d] = v[d] - ve[d];
847:     }
848:     if (user->error) {
849:       const PetscReal en   = 0.5 * DMPlex_DotRealD_Internal(dim, v, v);
850:       const PetscReal exen = 0.5 * PetscSqr(v0);
851:       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)));
852:     }
853:   }
854:   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
855:   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
856:   PetscCall(VecRestoreArrayRead(U, &u));
857:   PetscCall(VecRestoreArray(E, &e));
858:   PetscFunctionReturn(PETSC_SUCCESS);
859: }

861: static PetscErrorCode EnergyMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
862: {
863:   const PetscInt     ostep = ((AppCtx *)ctx)->ostep;
864:   const EMType       em    = ((AppCtx *)ctx)->em;
865:   DM                 sw;
866:   const PetscScalar *u;
867:   PetscReal         *coords, *E;
868:   PetscReal          enKin = 0., enEM = 0.;
869:   PetscInt           dim, d, Np, p, q;

871:   PetscFunctionBeginUser;
872:   if (step % ostep == 0) {
873:     PetscCall(TSGetDM(ts, &sw));
874:     PetscCall(DMGetDimension(sw, &dim));
875:     PetscCall(VecGetArrayRead(U, &u));
876:     PetscCall(VecGetLocalSize(U, &Np));
877:     Np /= 2 * dim;
878:     PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
879:     PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
880:     if (!step) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)ts), "Time     Step Part     Energy\n"));
881:     for (p = 0; p < Np; ++p) {
882:       const PetscReal v2     = DMPlex_DotRealD_Internal(dim, &u[(p * 2 + 1) * dim], &u[(p * 2 + 1) * dim]);
883:       PetscReal      *pcoord = &coords[p * dim];

885:       PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " %5" PetscInt_FMT " %10.4lf\n", (double)t, step, p, (double)(0.5 * v2)));
886:       enKin += 0.5 * v2;
887:       if (em == EM_NONE) {
888:         continue;
889:       } else if (em == EM_COULOMB) {
890:         for (q = p + 1; q < Np; ++q) {
891:           PetscReal *qcoord = &coords[q * dim];
892:           PetscReal  rpq[3], r;
893:           for (d = 0; d < dim; ++d) rpq[d] = pcoord[d] - qcoord[d];
894:           r = DMPlex_NormD_Internal(dim, rpq);
895:           enEM += 1. / r;
896:         }
897:       } else if (em == EM_PRIMAL || em == EM_MIXED) {
898:         for (d = 0; d < dim; ++d) enEM += E[p * dim + d];
899:       }
900:     }
901:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " KE\t    %10.4lf\n", (double)t, step, (double)enKin));
902:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " PE\t    %1.10g\n", (double)t, step, (double)enEM));
903:     PetscCall(PetscSynchronizedPrintf(PetscObjectComm((PetscObject)ts), "%.6lf %4" PetscInt_FMT " E\t    %10.4lf\n", (double)t, step, (double)(enKin + enEM)));
904:     PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
905:     PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
906:     PetscCall(PetscSynchronizedFlush(PetscObjectComm((PetscObject)ts), NULL));
907:     PetscCall(VecRestoreArrayRead(U, &u));
908:   }
909:   PetscFunctionReturn(PETSC_SUCCESS);
910: }

912: static PetscErrorCode SetUpMigrateParticles(TS ts, PetscInt n, PetscReal t, Vec x, PetscBool *flg, void *ctx)
913: {
914:   DM sw;

916:   PetscFunctionBeginUser;
917:   *flg = PETSC_TRUE;
918:   PetscCall(TSGetDM(ts, &sw));
919:   PetscCall(DMViewFromOptions(sw, NULL, "-migrate_view_pre"));
920:   {
921:     Vec u, gc, gv;
922:     IS  isx, isv;

924:     PetscCall(TSGetSolution(ts, &u));
925:     PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
926:     PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
927:     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
928:     PetscCall(VecISCopy(u, isx, SCATTER_REVERSE, gc));
929:     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
930:     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
931:     PetscCall(VecISCopy(u, isv, SCATTER_REVERSE, gv));
932:     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
933:   }
934:   PetscFunctionReturn(PETSC_SUCCESS);
935: }

937: static PetscErrorCode MigrateParticles(TS ts, PetscInt nv, Vec vecsin[], Vec vecsout[], void *ctx)
938: {
939:   DM sw;

941:   PetscFunctionBeginUser;
942:   PetscCall(TSGetDM(ts, &sw));
943:   PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
944:   PetscCall(CreateSolution(ts));
945:   PetscCall(SetProblem(ts));
946:   PetscCall(InitializeSolveAndSwarm(ts, PETSC_FALSE));
947:   PetscFunctionReturn(PETSC_SUCCESS);
948: }

950: int main(int argc, char **argv)
951: {
952:   DM     dm, sw;
953:   TS     ts;
954:   Vec    u;
955:   AppCtx user;

957:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
958:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
959:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
960:   PetscCall(CreatePoisson(dm, &user));
961:   PetscCall(CreateSwarm(dm, &user, &sw));
962:   PetscCall(DMSetApplicationContext(sw, &user));

964:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
965:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
966:   PetscCall(TSSetDM(ts, sw));
967:   PetscCall(TSSetMaxTime(ts, 0.1));
968:   PetscCall(TSSetTimeStep(ts, 0.00001));
969:   PetscCall(TSSetMaxSteps(ts, 100));
970:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
971:   PetscCall(TSMonitorSet(ts, EnergyMonitor, &user, NULL));
972:   PetscCall(TSSetFromOptions(ts));
973:   PetscCall(DMSwarmVectorDefineField(sw, "velocity"));
974:   PetscCall(TSSetComputeInitialCondition(ts, InitializeSolve));
975:   PetscCall(TSSetComputeExactError(ts, ComputeError));
976:   PetscCall(TSSetResize(ts, SetUpMigrateParticles, MigrateParticles, NULL));

978:   PetscCall(CreateSolution(ts));
979:   PetscCall(TSGetSolution(ts, &u));
980:   PetscCall(TSComputeInitialCondition(ts, u));
981:   PetscCall(TSSolve(ts, NULL));

983:   PetscCall(SNESDestroy(&user.snes));
984:   PetscCall(TSDestroy(&ts));
985:   PetscCall(DMDestroy(&sw));
986:   PetscCall(DMDestroy(&dm));
987:   PetscCall(PetscFinalize());
988:   return 0;
989: }

991: /*TEST

993:    build:
994:      requires: double !complex

996:    testset:
997:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
998:      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 \
999:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1000:            -ts_type basicsymplectic\
1001:            -dm_view -output_step 50 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1002:      test:
1003:        suffix: none_bsi_2d_1
1004:        args: -ts_basicsymplectic_type 1 -em_type none -error
1005:      test:
1006:        suffix: none_bsi_2d_2
1007:        args: -ts_basicsymplectic_type 2 -em_type none -error
1008:      test:
1009:        suffix: none_bsi_2d_3
1010:        args: -ts_basicsymplectic_type 3 -em_type none -error
1011:      test:
1012:        suffix: none_bsi_2d_4
1013:        args: -ts_basicsymplectic_type 4 -em_type none -error
1014:      test:
1015:        suffix: coulomb_bsi_2d_1
1016:        args: -ts_basicsymplectic_type 1
1017:      test:
1018:        suffix: coulomb_bsi_2d_2
1019:        args: -ts_basicsymplectic_type 2
1020:      test:
1021:        suffix: coulomb_bsi_2d_3
1022:        args: -ts_basicsymplectic_type 3
1023:      test:
1024:        suffix: coulomb_bsi_2d_4
1025:        args: -ts_basicsymplectic_type 4

1027:    testset:
1028:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1029:      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 \
1030:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1031:            -ts_type basicsymplectic\
1032:            -em_type primal -em_pc_type svd\
1033:            -dm_view -output_step 50 -error -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10\
1034:            -petscspace_degree 2 -petscfe_default_quadrature_order 3 -sigma 1.0e-8 -timeScale 2.0e-14
1035:      test:
1036:        suffix: poisson_bsi_2d_1
1037:        args: -ts_basicsymplectic_type 1
1038:      test:
1039:        suffix: poisson_bsi_2d_2
1040:        args: -ts_basicsymplectic_type 2
1041:      test:
1042:        suffix: poisson_bsi_2d_3
1043:        args: -ts_basicsymplectic_type 3
1044:      test:
1045:        suffix: poisson_bsi_2d_4
1046:        args: -ts_basicsymplectic_type 4

1048:    testset:
1049:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1050:      args: -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1051:            -ts_type theta -ts_theta_theta 0.5 -ts_convergence_estimate -convest_num_refine 2 \
1052:              -mat_type baij -ksp_error_if_not_converged -em_pc_type svd\
1053:            -dm_view -output_step 50 -error -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10\
1054:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14
1055:      test:
1056:        suffix: im_2d_0
1057:        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

1059:    testset:
1060:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1061:      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 \
1062:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV -dm_swarm_num_species 1\
1063:            -ts_type basicsymplectic -ts_convergence_estimate -convest_num_refine 2 \
1064:            -em_snes_type ksponly -em_pc_type svd -em_type primal -petscspace_degree 1\
1065:            -dm_view -output_step 50\
1066:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 1.0 -ts_max_steps 10
1067:      test:
1068:        suffix: bsi_2d_mesh_1
1069:        args: -ts_basicsymplectic_type 4
1070:      test:
1071:        suffix: bsi_2d_mesh_1_par_2
1072:        nsize: 2
1073:        args: -ts_basicsymplectic_type 4
1074:      test:
1075:        suffix: bsi_2d_mesh_1_par_3
1076:        nsize: 3
1077:        args: -ts_basicsymplectic_type 4
1078:      test:
1079:        suffix: bsi_2d_mesh_1_par_4
1080:        nsize: 4
1081:        args: -ts_basicsymplectic_type 4 -dm_swarm_num_particles 0,0,2,0

1083:    testset:
1084:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1085:      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 \
1086:            -dm_swarm_num_particles 10 -dm_swarm_coordinate_function circleMultipleX -dm_swarm_velocity_function circleMultipleV \
1087:            -ts_convergence_estimate -convest_num_refine 2 \
1088:              -em_pc_type lu\
1089:            -dm_view -output_step 50 -error\
1090:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1091:      test:
1092:        suffix: bsi_2d_multiple_1
1093:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 1
1094:      test:
1095:        suffix: bsi_2d_multiple_2
1096:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 2
1097:      test:
1098:        suffix: bsi_2d_multiple_3
1099:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 3 -ts_dt 0.001
1100:      test:
1101:        suffix: im_2d_multiple_0
1102:        args: -ts_type theta -ts_theta_theta 0.5 \
1103:                -mat_type baij -ksp_error_if_not_converged -em_pc_type lu

1105:    testset:
1106:      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
1107:      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 \
1108:            -dm_swarm_num_particles 2 -dm_swarm_coordinate_function circleSingleX -dm_swarm_velocity_function circleSingleV \
1109:            -em_pc_type fieldsplit -ksp_rtol 1e-10 -em_ksp_type preonly -em_type mixed -em_ksp_error_if_not_converged\
1110:            -dm_view -output_step 50 -error -dm_refine 0\
1111:            -pc_type svd -sigma 1.0e-8 -timeScale 2.0e-14 -ts_dt 0.01 -ts_max_time 10.0 -ts_max_steps 10
1112:      test:
1113:        suffix: bsi_4_rt_1
1114:        args: -ts_type basicsymplectic -ts_basicsymplectic_type 4\
1115:              -pc_fieldsplit_detect_saddle_point\
1116:              -pc_type fieldsplit\
1117:              -pc_fieldsplit_type schur\
1118:              -pc_fieldsplit_schur_precondition full \
1119:              -field_petscspace_degree 2\
1120:              -field_petscfe_default_quadrature_order 1\
1121:              -field_petscspace_type sum \
1122:              -field_petscspace_variables 2 \
1123:              -field_petscspace_components 2 \
1124:              -field_petscspace_sum_spaces 2 \
1125:              -field_petscspace_sum_concatenate true \
1126:              -field_sumcomp_0_petscspace_variables 2 \
1127:              -field_sumcomp_0_petscspace_type tensor \
1128:              -field_sumcomp_0_petscspace_tensor_spaces 2 \
1129:              -field_sumcomp_0_petscspace_tensor_uniform false \
1130:              -field_sumcomp_0_tensorcomp_0_petscspace_degree 1 \
1131:              -field_sumcomp_0_tensorcomp_1_petscspace_degree 0 \
1132:              -field_sumcomp_1_petscspace_variables 2 \
1133:              -field_sumcomp_1_petscspace_type tensor \
1134:              -field_sumcomp_1_petscspace_tensor_spaces 2 \
1135:              -field_sumcomp_1_petscspace_tensor_uniform false \
1136:              -field_sumcomp_1_tensorcomp_0_petscspace_degree 0 \
1137:              -field_sumcomp_1_tensorcomp_1_petscspace_degree 1 \
1138:              -field_petscdualspace_form_degree -1 \
1139:              -field_petscdualspace_order 1 \
1140:              -field_petscdualspace_lagrange_trimmed true\
1141:              -ksp_gmres_restart 500

1143: TEST*/