Actual source code: plexland.c

  1: #include <petsc/private/dmpleximpl.h>
  2: #include <petsclandau.h>
  3: #include <petscts.h>
  4: #include <petscdmforest.h>
  5: #include <petscdmcomposite.h>

  7: /* Landau collision operator */

  9: /* relativistic terms */
 10: #if defined(PETSC_USE_REAL_SINGLE)
 11: #define SPEED_OF_LIGHT 2.99792458e8F
 12: #define C_0(v0) (SPEED_OF_LIGHT/v0) /* needed for relativistic tensor on all architectures */
 13: #else
 14: #define SPEED_OF_LIGHT 2.99792458e8
 15: #define C_0(v0) (SPEED_OF_LIGHT/v0) /* needed for relativistic tensor on all architectures */
 16: #endif

 18: #define PETSC_THREAD_SYNC
 19: #include "land_tensors.h"

 21: /* vector padding not supported */
 22: #define LANDAU_VL  1

 24: static PetscErrorCode LandauGPUMapsDestroy(void *ptr)
 25: {
 26:   P4estVertexMaps *maps = (P4estVertexMaps*)ptr;
 27:   PetscErrorCode  ierr;
 29:   // free device data
 30:   if (maps[0].deviceType != LANDAU_CPU) {
 31: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
 32:     if (maps[0].deviceType == LANDAU_KOKKOS) {
 33:       LandauKokkosDestroyMatMaps(maps,  maps[0].numgrids); // imples Kokkos does
 34:     } // else could be CUDA
 35: #elif defined(PETSC_HAVE_CUDA)
 36:     if (maps[0].deviceType == LANDAU_CUDA) {
 37:       LandauCUDADestroyMatMaps(maps, maps[0].numgrids);
 38:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps->deviceType %D ?????",maps->deviceType);
 39: #endif
 40:   }
 41:   // free host data
 42:   for (PetscInt grid=0 ; grid < maps[0].numgrids ; grid++) {
 43:     PetscFree(maps[grid].c_maps);
 44:     PetscFree(maps[grid].gIdx);
 45:   }
 46:   PetscFree(maps);

 48:   return(0);
 49: }
 50: static PetscErrorCode energy_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
 51: {
 52:   PetscReal     v2 = 0;
 54:   /* compute v^2 / 2 */
 55:   for (int i = 0; i < dim; ++i) v2 += x[i]*x[i];
 56:   /* evaluate the Maxwellian */
 57:   u[0] = v2/2;
 58:   return(0);
 59: }

 61: /* needs double */
 62: static PetscErrorCode gamma_m1_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
 63: {
 64:   PetscReal     *c2_0_arr = ((PetscReal*)actx);
 65:   double        u2 = 0, c02 = (double)*c2_0_arr, xx;

 68:   /* compute u^2 / 2 */
 69:   for (int i = 0; i < dim; ++i) u2 += x[i]*x[i];
 70:   /* gamma - 1 = g_eps, for conditioning and we only take derivatives */
 71:   xx = u2/c02;
 72: #if defined(PETSC_USE_DEBUG)
 73:   u[0] = PetscSqrtReal(1. + xx);
 74: #else
 75:   u[0] = xx/(PetscSqrtReal(1. + xx) + 1.) - 1.; // better conditioned. -1 might help condition and only used for derivative
 76: #endif
 77:   return(0);
 78: }

 80: /*
 81:  LandauFormJacobian_Internal - Evaluates Jacobian matrix.

 83:  Input Parameters:
 84:  .  globX - input vector
 85:  .  actx - optional user-defined context
 86:  .  dim - dimension

 88:  Output Parameters:
 89:  .  J0acP - Jacobian matrix filled, not created
 90:  */
 91: static PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, PetscReal shift, void *a_ctx)
 92: {
 93:   LandauCtx         *ctx = (LandauCtx*)a_ctx;
 94:   PetscErrorCode    ierr;
 95:   PetscInt          numCells[LANDAU_MAX_GRIDS],Nq,Nb,Nf[LANDAU_MAX_GRIDS],d,f,fieldA,qj,N,nip_glb;
 96:   PetscQuadrature   quad;
 97:   const PetscReal   *quadWeights;
 98:   PetscTabulation   *Tf; // used for CPU and print info. Same on all grids and all species
 99:   PetscReal         Eq_m[LANDAU_MAX_SPECIES], m_0=ctx->m_0; /* normalize mass -- not needed! */
100:   PetscScalar       *cellClosure=NULL;
101:   const PetscScalar *xdata=NULL;
102:   PetscDS           prob;
103:   //PetscLogDouble    flops;
104:   PetscContainer    container;
105:   P4estVertexMaps   *maps;
106:   PetscSection      section[LANDAU_MAX_GRIDS],globsection[LANDAU_MAX_GRIDS];
107:   Mat               subJ[LANDAU_MAX_GRIDS];

113:   /* check for matrix container for GPU assembly */
114:   PetscLogEventBegin(ctx->events[10],0,0,0,0);
115:   DMGetDS(ctx->plex[0], &prob); // same DS for all grids
116:   PetscDSGetTabulation(prob, &Tf); // Bf, &Df same for all grids
117:   PetscObjectQuery((PetscObject) JacP, "assembly_maps", (PetscObject *) &container);
118:   if (container) {
119:     if (!ctx->gpu_assembly) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"GPU matrix container but no GPU assembly");
120:     PetscContainerGetPointer(container, (void **) &maps);
121:     if (!maps) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"empty GPU matrix container");
122:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) subJ[grid] = NULL;
123:   } else {
124:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
125:       DMCreateMatrix(ctx->plex[grid], &subJ[grid]);
126:     }
127:     maps = NULL;
128:   }
129:   /* DS, Tab and quad is same on all grids */
130:   if (ctx->plex[0] == NULL) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"Plex not created");
131:   PetscFEGetQuadrature(ctx->fe[0], &quad);
132:   PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, &quadWeights); Nb = Nq;
133:   if (Nq >LANDAU_MAX_NQ) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"Order too high. Nq = %D > LANDAU_MAX_NQ (%D)",Nq,LANDAU_MAX_NQ);
134:   if (LANDAU_DIM != dim) SETERRQ2(ctx->comm, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim,LANDAU_DIM);
135:   /* setup each grid */
136:   nip_glb = 0;
137:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
138:     PetscInt cStart, cEnd;
139:     if (ctx->plex[grid] == NULL) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"Plex not created");
140:     DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
141:     numCells[grid] = cEnd - cStart; // grids can have different topology
142:     nip_glb += Nq*numCells[grid];
143:     DMGetLocalSection(ctx->plex[grid], &section[grid]);
144:     DMGetGlobalSection(ctx->plex[grid], &globsection[grid]);
145:     PetscSectionGetNumFields(section[grid], &Nf[grid]);
146:   }
147:   VecGetSize(a_X,&N);
148:   PetscLogEventEnd(ctx->events[10],0,0,0,0);
149:   if (!ctx->initialized) { /* create static point data, Jacobian called first */
150:     PetscReal       *invJ,*ww,*xx,*yy,*zz=NULL,*invJ_a;
151:     PetscInt        outer_ipidx, outer_ej,grid;
152:     PetscFE         fe;

154:     PetscLogEventBegin(ctx->events[7],0,0,0,0);
155:     PetscInfo(ctx->plex[0], "Initialize static data\n");
156:     /* collect f data, first time is for Jacobian, but make mass now */
157:     if (ctx->verbose > 0) {
158:       PetscPrintf(ctx->comm,"%D) %s: %D IPs, %D cells[0], Nb=%D, Nq=%D, dim=%D, Tab: Nb=%D Nf=%D Np=%D cdim=%D N=%D\n",
159:                          0,"FormLandau",nip_glb,numCells[0], Nb, Nq, dim, Tf[0]->Nb, ctx->num_species, Tf[0]->Np, Tf[0]->cdim, N);
160:     }
161:     PetscMalloc4(nip_glb,&ww,nip_glb,&xx,nip_glb,&yy,nip_glb*dim*dim,&invJ_a);
162:     if (dim==3) {
163:       PetscMalloc1(nip_glb,&zz);
164:     }
165:     if (ctx->use_energy_tensor_trick) {
166:       PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &fe);
167:       PetscObjectSetName((PetscObject) fe, "energy");
168:     }
169:     /* init each grid */
170:     for (grid=0, outer_ipidx=0, outer_ej=0 ; grid < ctx->num_grids ; grid++) {
171:       Vec             v2_2 = NULL; // projected function: v^2/2 for non-relativistic, gamma... for relativistic
172:       PetscSection    e_section;
173:       DM              dmEnergy;
174:       PetscInt        cStart, cEnd, ej;

176:       DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
177:       // prep energy trick, get v^2 / 2 vector
178:       if (ctx->use_energy_tensor_trick) {
179:         PetscErrorCode (*energyf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {ctx->use_relativistic_corrections ? gamma_m1_f : energy_f};
180:         Vec            glob_v2;
181:         PetscReal      *c2_0[1], data[1] = {PetscSqr(C_0(ctx->v_0))};

183:         DMClone(ctx->plex[grid], &dmEnergy);
184:         PetscObjectSetName((PetscObject) dmEnergy, "energy");
185:         DMSetField(dmEnergy, 0, NULL, (PetscObject)fe);
186:         DMCreateDS(dmEnergy);
187:         DMGetSection(dmEnergy, &e_section);
188:         DMGetGlobalVector(dmEnergy,&glob_v2);
189:         PetscObjectSetName((PetscObject) glob_v2, "trick");
190:         c2_0[0] = &data[0];
191:         DMProjectFunction(dmEnergy, 0., energyf, (void**)c2_0, INSERT_ALL_VALUES, glob_v2);
192:         DMGetLocalVector(dmEnergy, &v2_2);
193:         VecZeroEntries(v2_2); /* zero BCs so don't set */
194:         DMGlobalToLocalBegin(dmEnergy, glob_v2, INSERT_VALUES, v2_2);
195:         DMGlobalToLocalEnd  (dmEnergy, glob_v2, INSERT_VALUES, v2_2);
196:         DMViewFromOptions(dmEnergy,NULL, "-energy_dm_view");
197:         VecViewFromOptions(glob_v2,NULL, "-energy_vec_view");
198:         DMRestoreGlobalVector(dmEnergy, &glob_v2);
199:       }
200:       /* append part of the IP data for each grid */
201:       for (ej = 0 ; ej < numCells[grid]; ++ej, ++outer_ej) {
202:         PetscScalar *coefs = NULL;
203:         PetscReal    vj[LANDAU_MAX_NQ*LANDAU_DIM],detJj[LANDAU_MAX_NQ], Jdummy[LANDAU_MAX_NQ*LANDAU_DIM*LANDAU_DIM], c0 = C_0(ctx->v_0), c02 = PetscSqr(c0);
204:         invJ = invJ_a + outer_ej * Nq*dim*dim;
205:         DMPlexComputeCellGeometryFEM(ctx->plex[grid], ej+cStart, quad, vj, Jdummy, invJ, detJj);
206:         if (ctx->use_energy_tensor_trick) {
207:           DMPlexVecGetClosure(dmEnergy, e_section, v2_2, ej+cStart, NULL, &coefs);
208:         }
209:         /* create static point data */
210:         for (qj = 0; qj < Nq; qj++, outer_ipidx++) {
211:           const PetscInt gidx = outer_ipidx;
212:           ww    [gidx] = detJj[qj] * quadWeights[qj];
213:           if (dim==2) ww    [gidx] *=              vj[qj * dim + 0];  /* cylindrical coordinate, w/o 2pi */
214:           // get xx, yy, zz
215:           if (ctx->use_energy_tensor_trick) {
216:             double                  refSpaceDer[3],eGradPhi[3];
217:             const PetscReal * const DD = Tf[0]->T[1];
218:             const PetscReal         *Dq = &DD[qj*Nb*dim];
219:             for (int d = 0; d < 3; ++d) refSpaceDer[d] = eGradPhi[d] = 0.0;
220:             for (int b = 0; b < Nb; ++b) {
221:               for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[b*dim+d]*PetscRealPart(coefs[b]);
222:             }
223:             xx[gidx] = 1e10;
224:             if (ctx->use_relativistic_corrections) {
225:               double dg2_c2 = 0;
226:               //for (int d = 0; d < dim; ++d) refSpaceDer[d] *= c02;
227:               for (int d = 0; d < dim; ++d) dg2_c2 += PetscSqr(refSpaceDer[d]);
228:               dg2_c2 *= (double)c02;
229:               if (dg2_c2 >= .999) {
230:                 xx[gidx] = vj[qj * dim + 0]; /* coordinate */
231:                 yy[gidx] = vj[qj * dim + 1];
232:                 if (dim==3) zz[gidx] = vj[qj * dim + 2];
233:                 PetscPrintf(ctx->comm,"Error: %12.5e %D.%D) dg2/c02 = %12.5e x= %12.5e %12.5e %12.5e\n",PetscSqrtReal(xx[gidx]*xx[gidx] + yy[gidx]*yy[gidx] + zz[gidx]*zz[gidx]), ej, qj, dg2_c2, xx[gidx],yy[gidx],zz[gidx]);
234:               } else {
235:                 PetscReal fact = c02/PetscSqrtReal(1. - dg2_c2);
236:                 for (int d = 0; d < dim; ++d) refSpaceDer[d] *= fact;
237:                 // could test with other point u' that (grad - grad') * U (refSpaceDer, refSpaceDer') == 0
238:               }
239:             }
240:             if (xx[gidx] == 1e10) {
241:               for (int d = 0; d < dim; ++d) {
242:                 for (int e = 0 ; e < dim; ++e) {
243:                   eGradPhi[d] += invJ[qj * dim * dim + e*dim+d]*refSpaceDer[e];
244:                 }
245:               }
246:               xx[gidx] = eGradPhi[0];
247:               yy[gidx] = eGradPhi[1];
248:               if (dim==3) zz[gidx] = eGradPhi[2];
249:             }
250:           } else {
251:             xx[gidx] = vj[qj * dim + 0]; /* coordinate */
252:             yy[gidx] = vj[qj * dim + 1];
253:             if (dim==3) zz[gidx] = vj[qj * dim + 2];
254:           }
255:         } /* q */
256:         if (ctx->use_energy_tensor_trick) {
257:           DMPlexVecRestoreClosure(dmEnergy, e_section, v2_2, ej+cStart, NULL, &coefs);
258:         }
259:       } /* ej */
260:       if (ctx->use_energy_tensor_trick) {
261:         DMRestoreLocalVector(dmEnergy, &v2_2);
262:         DMDestroy(&dmEnergy);
263:       }
264:     } /* grid */
265:     if (ctx->use_energy_tensor_trick) {
266:       PetscFEDestroy(&fe);
267:     }

269:     /* cache static data */
270:     if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
271: #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_KOKKOS_KERNELS)
272:       PetscReal invMass[LANDAU_MAX_SPECIES],nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
273:       for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
274:         for (PetscInt ii=ctx->species_offset[grid];ii<ctx->species_offset[grid+1];ii++) {
275:           invMass[ii] = m_0/ctx->masses[ii];
276:           nu_alpha[ii] = PetscSqr(ctx->charges[ii]/m_0)*m_0/ctx->masses[ii];
277:           nu_beta[ii] = PetscSqr(ctx->charges[ii]/ctx->epsilon0)*ctx->lnLam / (8*PETSC_PI) * ctx->t_0*ctx->n_0/PetscPowReal(ctx->v_0,3);
278:         }
279:       }
280:       if (ctx->deviceType == LANDAU_CUDA) {
281: #if defined(PETSC_HAVE_CUDA)
282:         LandauCUDAStaticDataSet(ctx->plex[0], Nq, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset, nu_alpha, nu_beta, invMass, invJ_a, xx, yy, zz, ww, &ctx->SData_d);
283: #else
284:         SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
285: #endif
286:       } else if (ctx->deviceType == LANDAU_KOKKOS) {
287: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
288:         LandauKokkosStaticDataSet(ctx->plex[0], Nq, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset, nu_alpha, nu_beta, invMass,invJ_a,xx,yy,zz,ww,&ctx->SData_d);
289: #else
290:         SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
291: #endif
292:       }
293: #endif
294:       /* free */
295:       PetscFree4(ww,xx,yy,invJ_a);
296:       if (dim==3) {
297:         PetscFree(zz);
298:       }
299:     } else { /* CPU version, just copy in, only use part */
300:       ctx->SData_d.w = (void*)ww;
301:       ctx->SData_d.x = (void*)xx;
302:       ctx->SData_d.y = (void*)yy;
303:       ctx->SData_d.z = (void*)zz;
304:       ctx->SData_d.invJ = (void*)invJ_a;
305:     }
306:     ctx->initialized = PETSC_TRUE;
307:     PetscLogEventEnd(ctx->events[7],0,0,0,0);
308:   } // initialize

310:   if (shift==0) { /* create dynamic point data: f_alpha for closure of each cell (cellClosure[ngrids,ncells[g],f[Nb,ns[g]]]) or xdata */
311:     DM pack;
312:     VecGetDM(a_X, &pack);
313:     if (!pack) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "pack has no DM");
314:     PetscLogEventBegin(ctx->events[1],0,0,0,0);
315:     MatZeroEntries(JacP);
316:     for (fieldA=0;fieldA<ctx->num_species;fieldA++) {
317:       Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
318:       if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
319:     }
320:     if (!ctx->gpu_assembly || !container) {
321:       Vec         locXarray[LANDAU_MAX_GRIDS],globXarray[LANDAU_MAX_GRIDS];
322:       PetscScalar *cellClosure_it;
323:       PetscInt    cellClosure_sz=0;

325:       /* count cellClosure size */
326:       for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) cellClosure_sz += Nb*Nf[grid]*numCells[grid];
327:       PetscMalloc1(cellClosure_sz,&cellClosure);
328:       cellClosure_it = cellClosure;
329:       /* for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) { */
330:       /*   DMClearLocalVectors(ctx->plex[grid]); */
331:       /* } */
332:       /* DMClearLocalVectors(pack); */
333:       DMCompositeGetLocalAccessArray(pack, a_X, ctx->num_grids, NULL, locXarray);
334:       DMCompositeGetAccessArray(pack, a_X, ctx->num_grids, NULL, globXarray);
335:       for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
336:         Vec         locX = locXarray[grid], globX = globXarray[grid], locX2;
337:         PetscInt    cStart, cEnd, ei;
338:         VecDuplicate(locX,&locX2);
339:         DMGlobalToLocalBegin(ctx->plex[grid], globX, INSERT_VALUES, locX2);
340:         DMGlobalToLocalEnd  (ctx->plex[grid], globX, INSERT_VALUES, locX2);
341:         DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
342:         for (ei = cStart ; ei < cEnd; ++ei) {
343:           PetscScalar *coef = NULL;
344:           DMPlexVecGetClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef);
345:           PetscMemcpy(cellClosure_it,coef,Nb*Nf[grid]*sizeof(*cellClosure_it)); /* change if LandauIPReal != PetscScalar */
346:           DMPlexVecRestoreClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef);
347:           cellClosure_it += Nb*Nf[grid];
348:         }
349:         VecDestroy(&locX2);
350:       }
351:       if (cellClosure_it-cellClosure != cellClosure_sz) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "iteration wrong %D != cellClosure_sz = %D",cellClosure_it-cellClosure,cellClosure_sz);
352:       DMCompositeRestoreLocalAccessArray(pack, a_X, ctx->num_grids, NULL, locXarray);
353:       DMCompositeRestoreAccessArray(pack, a_X, ctx->num_grids, NULL, globXarray);
354:       xdata = NULL;
355:     } else {
356:       PetscMemType mtype;
357:       VecGetArrayReadAndMemType(a_X,&xdata,&mtype);
358:       if (mtype!=PETSC_MEMTYPE_HOST && ctx->deviceType == LANDAU_CPU) {
359:         SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"CPU run with device data: use -mat_type aij");
360:       }
361:       cellClosure = NULL;
362:     }
363:     PetscLogEventEnd(ctx->events[1],0,0,0,0);
364:   } else xdata = cellClosure = NULL;
365:   /* do it */
366:   if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
367:     if (ctx->deviceType == LANDAU_CUDA) {
368: #if defined(PETSC_HAVE_CUDA)
369:       LandauCUDAJacobian(ctx->plex,Nq,ctx->num_grids,numCells,Eq_m,cellClosure,N,xdata,&ctx->SData_d,ctx->subThreadBlockSize,shift,ctx->events,ctx->mat_offset, ctx->species_offset, subJ, JacP);
370: #else
371:       SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
372: #endif
373:     } else if (ctx->deviceType == LANDAU_KOKKOS) {
374: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
375:       LandauKokkosJacobian(ctx->plex,Nq,ctx->num_grids,numCells,Eq_m,cellClosure,N,xdata,&ctx->SData_d,ctx->subThreadBlockSize,shift,ctx->events,ctx->mat_offset, ctx->species_offset, subJ,JacP);
376: #else
377:       SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
378: #endif
379:     }
380:   } else {   /* CPU version */
381:     PetscInt        IPf_sz = 0;
382:     PetscScalar     coef_buff[LANDAU_MAX_SPECIES*LANDAU_MAX_NQ], *cellClosure_it;
383:     PetscReal       *ff, *dudx, *dudy, *dudz, *invJ, *invJ_a = (PetscReal*)ctx->SData_d.invJ, *xx = (PetscReal*)ctx->SData_d.x, *yy = (PetscReal*)ctx->SData_d.y, *zz = (PetscReal*)ctx->SData_d.z, *ww = (PetscReal*)ctx->SData_d.w;
384:     const PetscReal *const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
385:     PetscReal       Eq_m[LANDAU_MAX_SPECIES], invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
386:     if (shift==0.0) { /* compute dynamic data f and df and init data for Jacobian */
387:       PetscInt IPf_idx = 0;
388:       PetscLogEventBegin(ctx->events[8],0,0,0,0);
389:       /* count IPf size */
390:       for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) IPf_sz += Nq*Nf[grid]*numCells[grid]; // same as closure size
391:       for (fieldA=0;fieldA<ctx->num_species;fieldA++) {
392:         invMass[fieldA] = m_0/ctx->masses[fieldA];
393:         Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
394:         if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
395:         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/m_0)*m_0/ctx->masses[fieldA];
396:         nu_beta[fieldA] = PetscSqr(ctx->charges[fieldA]/ctx->epsilon0)*ctx->lnLam / (8*PETSC_PI) * ctx->t_0*ctx->n_0/PetscPowReal(ctx->v_0,3);
397:       }
398:       PetscMalloc4(IPf_sz, &ff, IPf_sz, &dudx, IPf_sz, &dudy, dim==3 ? IPf_sz : 0, &dudz);
399:       invJ = invJ_a;
400:       cellClosure_it = cellClosure;
401:       for (PetscInt grid = 0 ; grid < ctx->num_grids ; grid++) { // IPf_idx += nip_loc*Nf
402:         PetscInt moffset = ctx->mat_offset[grid], nip_loc = numCells[grid]*Nq, Nfloc = ctx->species_offset[grid+1] - ctx->species_offset[grid];
403:         for (PetscInt ei = 0, jpidx_g = 0; ei < numCells[grid]; ++ei, invJ += Nq*dim*dim, cellClosure_it += Nb*Nfloc) {
404:           PetscScalar *coef;
405:           PetscInt     b,f,q;
406:           PetscReal    u_x[LANDAU_MAX_SPECIES][LANDAU_DIM];
407:           if (cellClosure) {
408:             coef = cellClosure_it; // this is const
409:           } else {
410:             coef = coef_buff;
411:             for (f = 0; f < Nfloc; ++f) {
412:               LandauIdx *const Idxs = &maps[grid].gIdx[ei][f][0];
413:               for (b = 0; b < Nb; ++b) {
414:                 PetscInt idx = Idxs[b];
415:                 if (idx >= 0) {
416:                   coef[f*Nb+b] = xdata[idx+moffset];
417:                 } else {
418:                   idx = -idx - 1;
419:                   coef[f*Nb+b] = 0;
420:                   for (q = 0; q < maps[grid].num_face; q++) {
421:                     PetscInt    id = maps[grid].c_maps[idx][q].gid;
422:                     PetscScalar scale = maps[grid].c_maps[idx][q].scale;
423:                     coef[f*Nb+b] += scale*xdata[id+moffset];
424:                   }
425:                 }
426:               }
427:             }
428:           }
429:           /* get f and df */
430:           for (PetscInt qi = 0; qi < Nq; qi++, jpidx_g++) {
431:             const PetscReal  *Bq = &BB[qi*Nb];
432:             const PetscReal  *Dq = &DD[qi*Nb*dim];
433:             /* get f & df */
434:             for (f = 0; f < Nfloc; ++f) {
435:               const PetscInt idx = IPf_idx + f*nip_loc + jpidx_g;
436:               PetscInt       b, e;
437:               PetscReal      refSpaceDer[LANDAU_DIM];
438:               ff[idx] = 0.0;
439:               for (d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
440:               for (b = 0; b < Nb; ++b) {
441:                 const PetscInt    cidx = b;
442:                 ff[idx] += Bq[cidx]*PetscRealPart(coef[f*Nb+cidx]);
443:                 for (d = 0; d < dim; ++d) refSpaceDer[d] += Dq[cidx*dim+d]*PetscRealPart(coef[f*Nb+cidx]);
444:               }
445:               for (d = 0; d < dim; ++d) {
446:                 for (e = 0, u_x[f][d] = 0.0; e < dim; ++e) {
447:                   u_x[f][d] += invJ[qi * dim * dim + e*dim+d]*refSpaceDer[e];
448:                 }
449:               }
450:             }
451:             for (f=0;f<Nfloc;f++) {
452:               const PetscInt idx = IPf_idx + f*nip_loc + jpidx_g;
453:               dudx[idx] = u_x[f][0];
454:               dudy[idx] = u_x[f][1];
455: #if LANDAU_DIM==3
456:               dudz[idx] = u_x[f][2];
457: #endif
458:             }
459:           } // q
460:         } // ei elem
461:         IPf_idx += nip_loc*Nfloc;
462:       } // grid
463:       if (cellClosure && ((cellClosure_it-cellClosure) != IPf_sz)) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "iteration wrong %D != nip_loc*Nf = %D",cellClosure_it-cellClosure,IPf_sz);
464:       if (IPf_idx != IPf_sz) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "IPf_idx != IPf_sz %D %D",IPf_idx,IPf_sz);
465:       PetscLogEventEnd(ctx->events[8],0,0,0,0);
466:     } // Jacobian setup

468:     /* doit it */
469:     invJ = invJ_a;
470:     for (PetscInt grid = 0, jpidx = 0 ; grid < ctx->num_grids ; grid++) {
471:       const PetscReal * const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
472:       PetscInt                cStart, Nfloc_j = Nf[grid], moffset = ctx->mat_offset[grid], totDim = Nfloc_j*Nq, elemMatSize = totDim*totDim;
473:       PetscScalar             *elemMat;

475:       DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, NULL); // to be safe, for initial DMPlexMatSetClosure
476:       PetscMalloc1(elemMatSize, &elemMat);
477:       for (PetscInt ei = 0; ei < numCells[grid]; ++ei, invJ += Nq*dim*dim) {
478:         PetscMemzero(elemMat, elemMatSize*sizeof(*elemMat));
479:         PetscLogEventBegin(ctx->events[4],0,0,0,0);
480:         for (qj = 0; qj < Nq; ++qj, jpidx++) {
481:           PetscReal               g0[LANDAU_MAX_SPECIES], g2[LANDAU_MAX_SPECIES][LANDAU_DIM], g3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM]; // could make a LANDAU_MAX_SPECIES_GRID ~ number of ions - 1
482:           PetscInt                d,d2,dp,d3,IPf_idx;

484:           if (shift==0.0) {
485:             const PetscReal * const invJj = &invJ[qj*dim*dim];
486:             PetscReal               gg2[LANDAU_MAX_SPECIES][LANDAU_DIM],gg3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM], gg2_temp[LANDAU_DIM], gg3_temp[LANDAU_DIM][LANDAU_DIM];
487:             const PetscReal         vj[3] = {xx[jpidx], yy[jpidx], zz ? zz[jpidx] : 0}, wj = ww[jpidx];
488:             // create g2 & g3
489:             for (d=0;d<dim;d++) { // clear accumulation data D & K
490:               gg2_temp[d] = 0;
491:               for (d2=0;d2<dim;d2++) gg3_temp[d][d2] = 0;
492:             }
493:             /* inner beta reduction */
494:             IPf_idx = 0;
495:             for (PetscInt grid_r = 0, f_off = 0, ipidx = 0; grid_r < ctx->num_grids ; grid_r++, f_off = ctx->species_offset[grid_r]) { // IPf_idx += nip_loc*Nfloc_r
496:               PetscInt  nip_loc_r = numCells[grid_r]*Nq, Nfloc_r = Nf[grid_r];
497:               for (PetscInt ei_r = 0, loc_fdf_idx = 0; ei_r < numCells[grid_r]; ++ei_r) {
498:                 for (PetscInt qi = 0; qi < Nq; qi++, ipidx++, loc_fdf_idx++) {
499:                   const PetscReal wi = ww[ipidx], x = xx[ipidx], y = yy[ipidx];
500:                   PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
501: #if LANDAU_DIM==2
502:                   PetscReal       Ud[2][2], Uk[2][2], mask = (PetscAbs(vj[0]-x) < 100*PETSC_SQRT_MACHINE_EPSILON && PetscAbs(vj[1]-y) < 100*PETSC_SQRT_MACHINE_EPSILON) ? 0. : 1.;
503:                   LandauTensor2D(vj, x, y, Ud, Uk, mask);
504: #else
505:                   PetscReal U[3][3], z = zz[ipidx], mask = (PetscAbs(vj[0]-x) < 100*PETSC_SQRT_MACHINE_EPSILON && PetscAbs(vj[1]-y) < 100*PETSC_SQRT_MACHINE_EPSILON && PetscAbs(vj[2]-z) < 100*PETSC_SQRT_MACHINE_EPSILON) ? 0. : 1.;
506:                   if (ctx->use_relativistic_corrections) {
507:                     LandauTensor3DRelativistic(vj, x, y, z, U, mask, C_0(ctx->v_0));
508:                   } else {
509:                     LandauTensor3D(vj, x, y, z, U, mask);
510:                   }
511: #endif
512:                   for (f = 0; f < Nfloc_r ; ++f) {
513:                     const PetscInt idx = IPf_idx + f*nip_loc_r + loc_fdf_idx;
514:                     temp1[0] += dudx[idx]*nu_beta[f+f_off]*invMass[f+f_off];
515:                     temp1[1] += dudy[idx]*nu_beta[f+f_off]*invMass[f+f_off];
516: #if LANDAU_DIM==3
517:                     temp1[2] += dudz[idx]*nu_beta[f+f_off]*invMass[f+f_off];
518: #endif
519:                     temp2    += ff[idx]*nu_beta[f+f_off];
520:                   }
521:                   temp1[0] *= wi;
522:                   temp1[1] *= wi;
523: #if LANDAU_DIM==3
524:                   temp1[2] *= wi;
525: #endif
526:                   temp2    *= wi;
527: #if LANDAU_DIM==2
528:                   for (d2 = 0; d2 < 2; d2++) {
529:                     for (d3 = 0; d3 < 2; ++d3) {
530:                       /* K = U * grad(f): g2=e: i,A */
531:                       gg2_temp[d2] += Uk[d2][d3]*temp1[d3];
532:                       /* D = -U * (I \kron (fx)): g3=f: i,j,A */
533:                       gg3_temp[d2][d3] += Ud[d2][d3]*temp2;
534:                     }
535:                   }
536: #else
537:                   for (d2 = 0; d2 < 3; ++d2) {
538:                     for (d3 = 0; d3 < 3; ++d3) {
539:                       /* K = U * grad(f): g2 = e: i,A */
540:                       gg2_temp[d2] += U[d2][d3]*temp1[d3];
541:                       /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
542:                       gg3_temp[d2][d3] += U[d2][d3]*temp2;
543:                     }
544:                   }
545: #endif
546:                 } // qi
547:               } // ei_r
548:               IPf_idx += nip_loc_r*Nfloc_r;
549:             } /* grid_r - IPs */
550:             if (IPf_idx != IPf_sz) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "IPf_idx != IPf_sz %D %D",IPf_idx,IPf_sz);
551:             // add alpha and put in gg2/3
552:             for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid]; fieldA < Nfloc_j; ++fieldA) {
553:               for (d2 = 0; d2 < dim; d2++) {
554:                 gg2[fieldA][d2] = gg2_temp[d2]*nu_alpha[fieldA+f_off];
555:                 for (d3 = 0; d3 < dim; d3++) {
556:                   gg3[fieldA][d2][d3] = -gg3_temp[d2][d3]*nu_alpha[fieldA+f_off]*invMass[fieldA+f_off];
557:                 }
558:               }
559:             }
560:             /* add electric field term once per IP */
561:             for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid] ; fieldA < Nfloc_j; ++fieldA) {
562:               gg2[fieldA][dim-1] += Eq_m[fieldA+f_off];
563:             }
564:             /* Jacobian transform - g2, g3 */
565:             for (PetscInt fieldA = 0; fieldA < Nfloc_j; ++fieldA) {
566:               for (d = 0; d < dim; ++d) {
567:                 g2[fieldA][d] = 0.0;
568:                 for (d2 = 0; d2 < dim; ++d2) {
569:                   g2[fieldA][d] += invJj[d*dim+d2]*gg2[fieldA][d2];
570:                   g3[fieldA][d][d2] = 0.0;
571:                   for (d3 = 0; d3 < dim; ++d3) {
572:                     for (dp = 0; dp < dim; ++dp) {
573:                       g3[fieldA][d][d2] += invJj[d*dim + d3]*gg3[fieldA][d3][dp]*invJj[d2*dim + dp];
574:                     }
575:                   }
576:                   g3[fieldA][d][d2] *= wj;
577:                 }
578:                 g2[fieldA][d] *= wj;
579:               }
580:             }
581:           } else { // mass
582:             PetscReal wj = ww[jpidx];
583:             /* Jacobian transform - g0 */
584:             for (fieldA = 0; fieldA < Nfloc_j ; ++fieldA) {
585:               if (dim==2) {
586:                 g0[fieldA] = wj * shift * 2. * PETSC_PI; // move this to below and remove g0
587:               } else {
588:                 g0[fieldA] = wj * shift; // move this to below and remove g0
589:               }
590:             }
591:           }
592:           /* FE matrix construction */
593:           {
594:             PetscInt  fieldA,d,f,d2,g;
595:             const PetscReal *BJq = &BB[qj*Nb], *DIq = &DD[qj*Nb*dim];
596:             /* assemble - on the diagonal (I,I) */
597:             for (fieldA = 0; fieldA < Nfloc_j ; fieldA++) {
598:               for (f = 0; f < Nb ; f++) {
599:                 const PetscInt i = fieldA*Nb + f; /* Element matrix row */
600:                 for (g = 0; g < Nb; ++g) {
601:                   const PetscInt j    = fieldA*Nb + g; /* Element matrix column */
602:                   const PetscInt fOff = i*totDim + j;
603:                   if (shift==0.0) {
604:                     for (d = 0; d < dim; ++d) {
605:                       elemMat[fOff] += DIq[f*dim+d]*g2[fieldA][d]*BJq[g];
606:                       //printf("\t:%d.%d.%d.%d.%d.%d) elemMat=%e += %e %e %e\n",ej,qj,fieldA,f,g,d,elemMat[fOff],DIq[f*dim+d],g2[fieldA][d],BJq[g]);
607:                       for (d2 = 0; d2 < dim; ++d2) {
608:                         elemMat[fOff] += DIq[f*dim + d]*g3[fieldA][d][d2]*DIq[g*dim + d2];
609:                       }
610:                     }
611:                   } else { // mass
612:                     elemMat[fOff] += BJq[f]*g0[fieldA]*BJq[g];
613:                   }
614:                 }
615:               }
616:             }
617:           }
618:         } /* qj loop */
619:         PetscLogEventEnd(ctx->events[4],0,0,0,0);
620:         /* assemble matrix */
621:         PetscLogEventBegin(ctx->events[6],0,0,0,0);
622:         if (!container) {
623:           DMPlexMatSetClosure(ctx->plex[grid], section[grid], globsection[grid], subJ[grid], ei + cStart, elemMat, ADD_VALUES);
624:         } else {  // GPU like assembly for debugging
625:           PetscInt      fieldA,idx,q,f,g,d,nr,nc,rows0[LANDAU_MAX_Q_FACE],cols0[LANDAU_MAX_Q_FACE]={0},rows[LANDAU_MAX_Q_FACE],cols[LANDAU_MAX_Q_FACE];
626:           PetscScalar   vals[LANDAU_MAX_Q_FACE*LANDAU_MAX_Q_FACE],row_scale[LANDAU_MAX_Q_FACE],col_scale[LANDAU_MAX_Q_FACE]={0};
627:           /* assemble - from the diagonal (I,I) in this format for DMPlexMatSetClosure */
628:           for (fieldA = 0; fieldA < Nfloc_j ; fieldA++) {
629:             LandauIdx *const Idxs = &maps[grid].gIdx[ei][fieldA][0];
630:             //printf("\t\t%d) field %d, moffset=%d\n",ei,fieldA,moffset);
631:             for (f = 0; f < Nb ; f++) {
632:               idx = Idxs[f];
633:               if (idx >= 0) {
634:                 nr = 1;
635:                 rows0[0] = idx;
636:                 row_scale[0] = 1.;
637:               } else {
638:                 idx = -idx - 1;
639:                 nr = maps[grid].num_face;
640:                 for (q = 0; q < maps[grid].num_face; q++) {
641:                   rows0[q]     = maps[grid].c_maps[idx][q].gid;
642:                   row_scale[q] = maps[grid].c_maps[idx][q].scale;
643:                 }
644:               }
645:               for (g = 0; g < Nb; ++g) {
646:                 idx = Idxs[g];
647:                 if (idx >= 0) {
648:                   nc = 1;
649:                   cols0[0] = idx;
650:                   col_scale[0] = 1.;
651:                 } else {
652:                   idx = -idx - 1;
653:                   nc = maps[grid].num_face;
654:                   for (q = 0; q < maps[grid].num_face; q++) {
655:                     cols0[q]     = maps[grid].c_maps[idx][q].gid;
656:                     col_scale[q] = maps[grid].c_maps[idx][q].scale;
657:                   }
658:                 }
659:                 const PetscInt    i = fieldA*Nb + f; /* Element matrix row */
660:                 const PetscInt    j = fieldA*Nb + g; /* Element matrix column */
661:                 const PetscScalar Aij = elemMat[i*totDim + j];
662:                 for (q = 0; q < nr; q++) rows[q] = rows0[q] + moffset;
663:                 for (d = 0; d < nc; d++) cols[d] = cols0[d] + moffset;
664:                 for (q = 0; q < nr; q++) {
665:                   for (d = 0; d < nc; d++) {
666:                     vals[q*nc + d] = row_scale[q]*col_scale[d]*Aij;
667:                     //printf("\t\t\t%d) field %d, q=(%d.%d) A(%d.%d) = %g\n",ei,fieldA,f,g,rows[q],cols[d],vals[q*nc + d]);
668:                   }
669:                 }
670:                 MatSetValues(JacP,nr,rows,nc,cols,vals,ADD_VALUES);
671:               }
672:             }
673:           }
674:         }
675:         if (ei==-1) {
676:           PetscErrorCode    ierr2;
677:           ierr2 = PetscPrintf(ctx->comm,"CPU Element matrix\n");CHKERRQ(ierr2);
678:           for (d = 0; d < totDim; ++d) {
679:             for (f = 0; f < totDim; ++f) {ierr2 = PetscPrintf(ctx->comm," %12.5e",  PetscRealPart(elemMat[d*totDim + f]));CHKERRQ(ierr2);}
680:             ierr2 = PetscPrintf(ctx->comm,"\n");CHKERRQ(ierr2);
681:           }
682:           exit(12);
683:         }
684:         PetscLogEventEnd(ctx->events[6],0,0,0,0);
685:       } /* ei cells loop */
686:       PetscFree(elemMat);

688:       if (!container) {   // move nest matrix to global JacP
689:         PetscInt          moffset = ctx->mat_offset[grid], nloc, nzl, colbuf[1024], row;
690:         const PetscInt    *cols;
691:         const PetscScalar *vals;
692:         Mat               B = subJ[grid];

694:         MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
695:         MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
696:         MatGetSize(B, &nloc, NULL);
697:         if (nloc != ctx->mat_offset[grid+1] - moffset) SETERRQ2(PetscObjectComm((PetscObject) B), PETSC_ERR_PLIB, "nloc %D != ctx->mat_offset[grid+1] - moffset = %D",nloc,ctx->mat_offset[grid+1] - moffset);
698:         for (int i=0 ; i<nloc ; i++) {
699:           MatGetRow(B,i,&nzl,&cols,&vals);
700:           if (nzl>1024) SETERRQ1(PetscObjectComm((PetscObject) B), PETSC_ERR_PLIB, "Row too big: %D",nzl);
701:           for (int j=0; j<nzl; j++) colbuf[j] = cols[j] + moffset;
702:           row = i + moffset;
703:           MatSetValues(JacP,1,&row,nzl,colbuf,vals,ADD_VALUES);
704:           MatRestoreRow(B,i,&nzl,&cols,&vals);
705:         }
706:         MatDestroy(&subJ[grid]);
707:       }
708:     } /* grid */
709:     if (shift==0.0) { // mass
710:       PetscFree4(ff, dudx, dudy, dudz);
711:     }
712:   } /* CPU version */

714:   /* assemble matrix or vector */
715:   MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);
716:   MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);
717: #define MAP_BF_SIZE (64*LANDAU_DIM*LANDAU_DIM*LANDAU_MAX_Q_FACE*LANDAU_MAX_SPECIES)
718:   if (ctx->gpu_assembly && !container) {
719:     PetscScalar             elemMatrix[LANDAU_MAX_NQ*LANDAU_MAX_NQ*LANDAU_MAX_SPECIES*LANDAU_MAX_SPECIES], *elMat;
720:     pointInterpolationP4est pointMaps[MAP_BF_SIZE][LANDAU_MAX_Q_FACE];
721:     PetscInt                q,eidx,fieldA;
722:     PetscInfo1(ctx->plex[0], "Make GPU maps %D\n",1);
723:     PetscLogEventBegin(ctx->events[2],0,0,0,0);
724:     PetscMalloc(sizeof(*maps)*ctx->num_grids, &maps);
725:     PetscContainerCreate(PETSC_COMM_SELF, &container);
726:     PetscContainerSetPointer(container, (void *)maps);
727:     PetscContainerSetUserDestroy(container, LandauGPUMapsDestroy);
728:     PetscObjectCompose((PetscObject) JacP, "assembly_maps", (PetscObject) container);
729:     PetscContainerDestroy(&container);
730:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
731:       PetscInt cStart, cEnd, ej, Nfloc = Nf[grid], totDim = Nfloc*Nq;
732:       DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
733:       // make maps
734:       maps[grid].d_self = NULL;
735:       maps[grid].num_elements = numCells[grid];
736:       maps[grid].num_face = (PetscInt)(pow(Nq,1./((double)dim))+.001); // Q
737:       maps[grid].num_face = (PetscInt)(pow(maps[grid].num_face,(double)(dim-1))+.001); // Q^2
738:       maps[grid].num_reduced = 0;
739:       maps[grid].deviceType = ctx->deviceType;
740:       maps[grid].numgrids = ctx->num_grids;
741:       // count reduced and get
742:       PetscMalloc(maps[grid].num_elements * sizeof(*maps[grid].gIdx), &maps[grid].gIdx);
743:       for (fieldA=0;fieldA<Nf[grid];fieldA++) {
744:         for (ej = cStart, eidx = 0 ; ej < cEnd; ++ej, ++eidx) {
745:           for (q = 0; q < Nb; ++q) {
746:             PetscInt    numindices,*indices;
747:             PetscScalar *valuesOrig = elMat = elemMatrix;
748:             PetscMemzero(elMat, totDim*totDim*sizeof(*elMat));
749:             elMat[ (fieldA*Nb + q)*totDim + fieldA*Nb + q] = 1;
750:             DMPlexGetClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);
751:             for (f = 0 ; f < numindices ; ++f) { // look for a non-zero on the diagonal
752:               if (PetscAbs(PetscRealPart(elMat[f*numindices + f])) > PETSC_MACHINE_EPSILON) {
753:                 // found it
754:                 if (PetscAbs(PetscRealPart(elMat[f*numindices + f] - 1.)) < PETSC_MACHINE_EPSILON) {
755:                   maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)indices[f]; // normal vertex 1.0
756:                 } else { //found a constraint
757:                   int       jj = 0;
758:                   PetscReal sum = 0;
759:                   const PetscInt ff = f;
760:                   maps[grid].gIdx[eidx][fieldA][q] = -maps[grid].num_reduced - 1; // gid = -(idx+1): idx = -gid - 1
761:                   do {  // constraints are continous in Plex - exploit that here
762:                     int ii;
763:                     for (ii = 0, pointMaps[maps[grid].num_reduced][jj].scale = 0; ii < maps[grid].num_face; ii++) { // DMPlex puts them all together
764:                       if (ff + ii < numindices) {
765:                         pointMaps[maps[grid].num_reduced][jj].scale += PetscRealPart(elMat[f*numindices + ff + ii]);
766:                       }
767:                     }
768:                     sum += pointMaps[maps[grid].num_reduced][jj].scale;
769:                     if (pointMaps[maps[grid].num_reduced][jj].scale == 0) pointMaps[maps[grid].num_reduced][jj].gid = -1; // 3D has Q and Q^2 interps -- all contiguous???
770:                     else                                                  pointMaps[maps[grid].num_reduced][jj].gid = indices[f];
771:                   } while (++jj < maps[grid].num_face && ++f < numindices); // jj is incremented if we hit the end
772:                   while (jj++ < maps[grid].num_face) {
773:                     pointMaps[maps[grid].num_reduced][jj].scale = 0;
774:                     pointMaps[maps[grid].num_reduced][jj].gid = -1;
775:                   }
776:                   if (PetscAbs(sum-1.0) > 10*PETSC_MACHINE_EPSILON) { // debug
777:                     int       d,f;
778:                     PetscReal tmp = 0;
779:                     PetscPrintf(PETSC_COMM_SELF,"\t\t%D.%D.%D) ERROR total I = %22.16e (LANDAU_MAX_Q_FACE=%d, #face=%D)\n",eidx,q,fieldA,sum,LANDAU_MAX_Q_FACE,maps[grid].num_face);
780:                     for (d = 0, tmp = 0; d < numindices; ++d) {
781:                       if (tmp!=0 && PetscAbs(tmp-1.0) > 10*PETSC_MACHINE_EPSILON) {PetscPrintf(PETSC_COMM_WORLD,"%3D) %3D: ",d,indices[d]);}
782:                       for (f = 0; f < numindices; ++f) {
783:                         tmp += PetscRealPart(elMat[d*numindices + f]);
784:                       }
785:                       if (tmp!=0) {PetscPrintf(ctx->comm," | %22.16e\n",tmp);}
786:                     }
787:                   }
788:                   maps[grid].num_reduced++;
789:                   if (maps[grid].num_reduced>=MAP_BF_SIZE) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps[grid].num_reduced %d > %d",maps[grid].num_reduced,MAP_BF_SIZE);
790:                 }
791:                 break;
792:               }
793:             }
794:             // cleanup
795:             DMPlexRestoreClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);
796:             if (elMat != valuesOrig) {DMRestoreWorkArray(ctx->plex[grid], numindices*numindices, MPIU_SCALAR, &elMat);}
797:           }
798:         }
799:       }
800:       // allocate and copy point datamaps[grid].gIdx[eidx][field][q]
801:       PetscMalloc(maps[grid].num_reduced * sizeof(*maps[grid].c_maps), &maps[grid].c_maps);
802:       for (ej = 0; ej < maps[grid].num_reduced; ++ej) {
803:         for (q = 0; q < maps[grid].num_face; ++q) {
804:           maps[grid].c_maps[ej][q].scale = pointMaps[ej][q].scale;
805:           maps[grid].c_maps[ej][q].gid   = pointMaps[ej][q].gid;
806:         }
807:       }
808: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
809:       if (ctx->deviceType == LANDAU_KOKKOS) {
810:         LandauKokkosCreateMatMaps(maps, pointMaps, Nf, Nq, grid); // imples Kokkos does
811:       } // else could be CUDA
812: #endif
813: #if defined(PETSC_HAVE_CUDA)
814:       if (ctx->deviceType == LANDAU_CUDA) {
815:         LandauCUDACreateMatMaps(maps, pointMaps, Nf, Nq, grid);
816:       }
817: #endif
818:     } /* grids */
819:     PetscLogEventEnd(ctx->events[2],0,0,0,0);
820:   } /* first pass with GPU assembly */
821:   /* clean up */
822:   if (cellClosure) {
823:     PetscFree(cellClosure);
824:   }
825:   if (xdata) {
826:     VecRestoreArrayReadAndMemType(a_X,&xdata);
827:   }

829:   return(0);
830: }

832: #if defined(LANDAU_ADD_BCS)
833: static void zero_bc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
834:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
835:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
836:                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
837: {
838:   uexact[0] = 0;
839: }
840: #endif

842: #define MATVEC2(__a,__x,__p) {int i,j; for (i=0.; i<2; i++) {__p[i] = 0; for (j=0.; j<2; j++) __p[i] += __a[i][j]*__x[j]; }}
843: static void CircleInflate(PetscReal r1, PetscReal r2, PetscReal r0, PetscInt num_sections, PetscReal x, PetscReal y,
844:                           PetscReal *outX, PetscReal *outY)
845: {
846:   PetscReal rr = PetscSqrtReal(x*x + y*y), outfact, efact;
847:   if (rr < r1 + PETSC_SQRT_MACHINE_EPSILON) {
848:     *outX = x; *outY = y;
849:   } else {
850:     const PetscReal xy[2] = {x,y}, sinphi=y/rr, cosphi=x/rr;
851:     PetscReal       cth,sth,xyprime[2],Rth[2][2],rotcos,newrr;
852:     if (num_sections==2) {
853:       rotcos = 0.70710678118654;
854:       outfact = 1.5; efact = 2.5;
855:       /* rotate normalized vector into [-pi/4,pi/4) */
856:       if (sinphi >= 0.) {         /* top cell, -pi/2 */
857:         cth = 0.707106781186548; sth = -0.707106781186548;
858:       } else {                    /* bottom cell -pi/8 */
859:         cth = 0.707106781186548; sth = .707106781186548;
860:       }
861:     } else if (num_sections==3) {
862:       rotcos = 0.86602540378443;
863:       outfact = 1.5; efact = 2.5;
864:       /* rotate normalized vector into [-pi/6,pi/6) */
865:       if (sinphi >= 0.5) {         /* top cell, -pi/3 */
866:         cth = 0.5; sth = -0.866025403784439;
867:       } else if (sinphi >= -.5) {  /* mid cell 0 */
868:         cth = 1.; sth = .0;
869:       } else { /* bottom cell +pi/3 */
870:         cth = 0.5; sth = 0.866025403784439;
871:       }
872:     } else if (num_sections==4) {
873:       rotcos = 0.9238795325112;
874:       outfact = 1.5; efact = 3;
875:       /* rotate normalized vector into [-pi/8,pi/8) */
876:       if (sinphi >= 0.707106781186548) {         /* top cell, -3pi/8 */
877:         cth = 0.38268343236509; sth = -0.923879532511287;
878:       } else if (sinphi >= 0.) {                 /* mid top cell -pi/8 */
879:         cth = 0.923879532511287; sth = -.38268343236509;
880:       } else if (sinphi >= -0.707106781186548) { /* mid bottom cell + pi/8 */
881:         cth = 0.923879532511287; sth = 0.38268343236509;
882:       } else {                                   /* bottom cell + 3pi/8 */
883:         cth = 0.38268343236509; sth = .923879532511287;
884:       }
885:     } else {
886:       cth = 0.; sth = 0.; rotcos = 0; efact = 0;
887:     }
888:     Rth[0][0] = cth; Rth[0][1] =-sth;
889:     Rth[1][0] = sth; Rth[1][1] = cth;
890:     MATVEC2(Rth,xy,xyprime);
891:     if (num_sections==2) {
892:       newrr = xyprime[0]/rotcos;
893:     } else {
894:       PetscReal newcosphi=xyprime[0]/rr, rin = r1, rout = rr - rin;
895:       PetscReal routmax = r0*rotcos/newcosphi - rin, nroutmax = r0 - rin, routfrac = rout/routmax;
896:       newrr = rin + routfrac*nroutmax;
897:     }
898:     *outX = cosphi*newrr; *outY = sinphi*newrr;
899:     /* grade */
900:     PetscReal fact,tt,rs,re, rr = PetscSqrtReal(PetscSqr(*outX) + PetscSqr(*outY));
901:     if (rr > r2) { rs = r2; re = r0; fact = outfact;} /* outer zone */
902:     else {         rs = r1; re = r2; fact = efact;} /* electron zone */
903:     tt = (rs + PetscPowReal((rr - rs)/(re - rs),fact) * (re-rs)) / rr;
904:     *outX *= tt;
905:     *outY *= tt;
906:   }
907: }

909: static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
910: {
911:   LandauCtx   *ctx = (LandauCtx*)a_ctx;
912:   PetscReal   r = abc[0], z = abc[1];
913:   if (ctx->inflate) {
914:     PetscReal absR, absZ;
915:     absR = PetscAbs(r);
916:     absZ = PetscAbs(z);
917:     CircleInflate(ctx->i_radius[0],ctx->e_radius,ctx->radius[0],ctx->num_sections,absR,absZ,&absR,&absZ); // wrong: how do I know what grid I am on?
918:     r = (r > 0) ? absR : -absR;
919:     z = (z > 0) ? absZ : -absZ;
920:   }
921:   xyz[0] = r;
922:   xyz[1] = z;
923:   if (dim==3) xyz[2] = abc[2];

925:   return(0);
926: }

928: /* create DMComposite of meshes for each species group */
929: static PetscErrorCode LandauDMCreateVMeshes(MPI_Comm comm_self, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM *pack)
930: {
932:   size_t         len;
933:   char           fname[128] = ""; /* we can add a file if we want, for each grid */

936:   /* create DM */
937:   PetscStrlen(fname, &len);
938:   if (len) { // not used, need to loop over grids
939:     PetscInt dim2;
940:     DMPlexCreateFromFile(comm_self, fname, ctx->interpolate, pack);
941:     DMGetDimension(*pack, &dim2);
942:     if (LANDAU_DIM != dim2) SETERRQ2(comm_self, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim2,LANDAU_DIM);
943:   } else { /* p4est, quads */
944:     DMCompositeCreate(comm_self,pack);
945:     /* Create plex mesh of Landau domain */
946:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
947:       PetscReal radius = ctx->radius[grid];
948:       if (!ctx->sphere) {
949:         PetscInt       cells[] = {2,2,2};
950:         PetscReal      lo[] = {-radius,-radius,-radius}, hi[] = {radius,radius,radius};
951:         DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim==2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
952:         if (dim==2) { lo[0] = 0; cells[0] = 1; }
953:         DMPlexCreateBoxMesh(comm_self, dim, PETSC_FALSE, cells, lo, hi, periodicity, PETSC_TRUE, &ctx->plex[grid]); // todo: make composite and create dm[grid] here
954:         DMLocalizeCoordinates(ctx->plex[grid]); /* needed for periodic */
955:         if (dim==3) {PetscObjectSetName((PetscObject) ctx->plex[grid], "cube");}
956:         else {PetscObjectSetName((PetscObject) ctx->plex[grid], "half-plane");}
957:       } else if (dim==2) { // sphere is all wrong. should just have one inner radius
958:         PetscInt       numCells,cells[16][4],i,j;
959:         PetscInt       numVerts;
960:         PetscReal      inner_radius1 = ctx->i_radius[grid], inner_radius2 = ctx->e_radius;
961:         PetscReal      *flatCoords = NULL;
962:         PetscInt       *flatCells = NULL, *pcell;
963:         if (ctx->num_sections==2) {
964: #if 1
965:           numCells = 5;
966:           numVerts = 10;
967:           int cells2[][4] = { {0,1,4,3},
968:                               {1,2,5,4},
969:                               {3,4,7,6},
970:                               {4,5,8,7},
971:                               {6,7,8,9} };
972:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
973:           PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
974:           {
975:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
976:             for (j = 0; j < numVerts-1; j++) {
977:               PetscReal z, r, theta = -PETSC_PI/2 + (j%3) * PETSC_PI/2;
978:               PetscReal rad = (j >= 6) ? inner_radius1 : (j >= 3) ? inner_radius2 : ctx->radius[grid];
979:               z = rad * PetscSinReal(theta);
980:               coords[j][1] = z;
981:               r = rad * PetscCosReal(theta);
982:               coords[j][0] = r;
983:             }
984:             coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
985:           }
986: #else
987:           numCells = 4;
988:           numVerts = 8;
989:           static int     cells2[][4] = {{0,1,2,3},
990:                                         {4,5,1,0},
991:                                         {5,6,2,1},
992:                                         {6,7,3,2}};
993:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
994:           loc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
995:           {
996:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
997:             PetscInt j;
998:             for (j = 0; j < 8; j++) {
999:               PetscReal z, r;
1000:               PetscReal theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3.;
1001:               PetscReal rad = ctx->radius[grid] * ((j < 4) ? 0.5 : 1.0);
1002:               z = rad * PetscSinReal(theta);
1003:               coords[j][1] = z;
1004:               r = rad * PetscCosReal(theta);
1005:               coords[j][0] = r;
1006:             }
1007:           }
1008: #endif
1009:         } else if (ctx->num_sections==3) {
1010:           numCells = 7;
1011:           numVerts = 12;
1012:           int cells2[][4] = { {0,1,5,4},
1013:                               {1,2,6,5},
1014:                               {2,3,7,6},
1015:                               {4,5,9,8},
1016:                               {5,6,10,9},
1017:                               {6,7,11,10},
1018:                               {8,9,10,11} };
1019:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
1020:           PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
1021:           {
1022:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
1023:             for (j = 0; j < numVerts; j++) {
1024:               PetscReal z, r, theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3;
1025:               PetscReal rad = (j >= 8) ? inner_radius1 : (j >= 4) ? inner_radius2 : ctx->radius[grid];
1026:               z = rad * PetscSinReal(theta);
1027:               coords[j][1] = z;
1028:               r = rad * PetscCosReal(theta);
1029:               coords[j][0] = r;
1030:             }
1031:           }
1032:         } else if (ctx->num_sections==4) {
1033:           numCells = 10;
1034:           numVerts = 16;
1035:           int cells2[][4] = { {0,1,6,5},
1036:                               {1,2,7,6},
1037:                               {2,3,8,7},
1038:                               {3,4,9,8},
1039:                               {5,6,11,10},
1040:                               {6,7,12,11},
1041:                               {7,8,13,12},
1042:                               {8,9,14,13},
1043:                               {10,11,12,15},
1044:                               {12,13,14,15}};
1045:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
1046:           PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
1047:           {
1048:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
1049:             for (j = 0; j < numVerts-1; j++) {
1050:               PetscReal z, r, theta = -PETSC_PI/2 + (j%5) * PETSC_PI/4;
1051:               PetscReal rad = (j >= 10) ? inner_radius1 : (j >= 5) ? inner_radius2 : ctx->radius[grid];
1052:               z = rad * PetscSinReal(theta);
1053:               coords[j][1] = z;
1054:               r = rad * PetscCosReal(theta);
1055:               coords[j][0] = r;
1056:             }
1057:             coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
1058:           }
1059:         } else {
1060:           numCells = 0;
1061:           numVerts = 0;
1062:         }
1063:         for (j = 0, pcell = flatCells; j < numCells; j++, pcell += 4) {
1064:           pcell[0] = cells[j][0]; pcell[1] = cells[j][1];
1065:           pcell[2] = cells[j][2]; pcell[3] = cells[j][3];
1066:         }
1067:         DMPlexCreateFromCellListPetsc(comm_self,2,numCells,numVerts,4,ctx->interpolate,flatCells,2,flatCoords,&ctx->plex[grid]);
1068:         PetscFree2(flatCoords,flatCells);
1069:         PetscObjectSetName((PetscObject) ctx->plex[grid], "semi-circle");
1070:       } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Velocity space meshes does not support cubed sphere");

1072:       DMSetFromOptions(ctx->plex[grid]);
1073:     } // grid loop
1074:     PetscObjectSetOptionsPrefix((PetscObject)*pack,prefix);
1075:     DMSetFromOptions(*pack);

1077:     { /* convert to p4est (or whatever), wait for discretization to create pack */
1078:       char      convType[256];
1079:       PetscBool flg;
1080:       PetscOptionsBegin(ctx->comm, prefix, "Mesh conversion options", "DMPLEX");
1081:       PetscOptionsFList("-dm_landau_type","Convert DMPlex to another format (p4est)","plexland.c",DMList,DMPLEX,convType,256,&flg);
1082:       PetscOptionsEnd();
1083:       if (flg) {
1084:         ctx->use_p4est = PETSC_TRUE; /* flag for Forest */
1085:         for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
1086:           DM dmforest;
1087:           DMConvert(ctx->plex[grid],convType,&dmforest);
1088:           if (dmforest) {
1089:             PetscBool isForest;
1090:             PetscObjectSetOptionsPrefix((PetscObject)dmforest,prefix);
1091:             DMIsForest(dmforest,&isForest);
1092:             if (isForest) {
1093:               if (ctx->sphere && ctx->inflate) {
1094:                 DMForestSetBaseCoordinateMapping(dmforest,GeometryDMLandau,ctx);
1095:               }
1096:               if (dmforest->prealloc_only != ctx->plex[grid]->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dmforest),PETSC_ERR_PLIB,"plex->prealloc_only != dm->prealloc_only");
1097:               DMDestroy(&ctx->plex[grid]);
1098:               ctx->plex[grid] = dmforest; // Forest for adaptivity
1099:             } else SETERRQ(ctx->comm, PETSC_ERR_USER, "Converted to non Forest?");
1100:           } else SETERRQ(ctx->comm, PETSC_ERR_USER, "Convert failed?");
1101:         }
1102:       } else ctx->use_p4est = PETSC_FALSE; /* flag for Forest */
1103:     }
1104:   } /* non-file */
1105:   DMSetDimension(*pack, dim);
1106:   PetscObjectSetName((PetscObject) *pack, "Mesh");
1107:   DMSetApplicationContext(*pack, ctx);

1109:   return(0);
1110: }

1112: static PetscErrorCode SetupDS(DM pack, PetscInt dim, PetscInt grid, LandauCtx *ctx)
1113: {
1114:   PetscErrorCode  ierr;
1115:   PetscInt        ii,i0;
1116:   char            buf[256];
1117:   PetscSection    section;

1120:   for (ii = ctx->species_offset[grid], i0 = 0 ; ii < ctx->species_offset[grid+1] ; ii++, i0++) {
1121:     if (ii==0) PetscSNPrintf(buf, 256, "e");
1122:     else {PetscSNPrintf(buf, 256, "i%D", ii);}
1123:     /* Setup Discretization - FEM */
1124:     PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &ctx->fe[ii]);
1125:     PetscObjectSetName((PetscObject) ctx->fe[ii], buf);
1126:     DMSetField(ctx->plex[grid], i0, NULL, (PetscObject) ctx->fe[ii]);
1127:   }
1128:   DMCreateDS(ctx->plex[grid]);
1129:   DMGetSection(ctx->plex[grid], &section);
1130:   for (PetscInt ii = ctx->species_offset[grid], i0 = 0 ; ii < ctx->species_offset[grid+1] ; ii++, i0++) {
1131:     if (ii==0) PetscSNPrintf(buf, 256, "se");
1132:     else PetscSNPrintf(buf, 256, "si%D", ii);
1133:     PetscSectionSetComponentName(section, i0, 0, buf);
1134:   }
1135:   return(0);
1136: }

1138: /* Define a Maxwellian function for testing out the operator. */

1140: /* Using cartesian velocity space coordinates, the particle */
1141: /* density, [1/m^3], is defined according to */

1143: /* $$ n=\int_{R^3} dv^3 \left(\frac{m}{2\pi T}\right)^{3/2}\exp [- mv^2/(2T)] $$ */

1145: /* Using some constant, c, we normalize the velocity vector into a */
1146: /* dimensionless variable according to v=c*x. Thus the density, $n$, becomes */

1148: /* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */

1150: /* Defining $\theta=2T/mc^2$, we thus find that the probability density */
1151: /* for finding the particle within the interval in a box dx^3 around x is */

1153: /* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */

1155: typedef struct {
1156:   PetscReal v_0;
1157:   PetscReal kT_m;
1158:   PetscReal n;
1159:   PetscReal shift;
1160: } MaxwellianCtx;

1162: static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
1163: {
1164:   MaxwellianCtx *mctx = (MaxwellianCtx*)actx;
1165:   PetscInt      i;
1166:   PetscReal     v2 = 0, theta = 2*mctx->kT_m/(mctx->v_0*mctx->v_0); /* theta = 2kT/mc^2 */
1168:   /* compute the exponents, v^2 */
1169:   for (i = 0; i < dim; ++i) v2 += x[i]*x[i];
1170:   /* evaluate the Maxwellian */
1171:   u[0] = mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
1172:   if (mctx->shift!=0.) {
1173:     v2 = 0;
1174:     for (i = 0; i < dim-1; ++i) v2 += x[i]*x[i];
1175:     v2 += (x[dim-1]-mctx->shift)*(x[dim-1]-mctx->shift);
1176:     /* evaluate the shifted Maxwellian */
1177:     u[0] += mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
1178:   }
1179:   return(0);
1180: }

1182: /*@
1183:  LandauAddMaxwellians - Add a Maxwellian distribution to a state

1185:  Collective on X

1187:  Input Parameters:
1188:  .   dm - The mesh (local)
1189:  +   time - Current time
1190:  -   temps - Temperatures of each species (global)
1191:  .   ns - Number density of each species (global)
1192:  -   grid - index into current grid - just used for offset into temp and ns
1193:  +   actx - Landau context

1195:  Output Parameter:
1196:  .   X  - The state (local to this grid)

1198:  Level: beginner

1200:  .keywords: mesh
1201:  .seealso: LandauCreateVelocitySpace()
1202:  @*/
1203: PetscErrorCode LandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], PetscInt grid, void *actx)
1204: {
1205:   LandauCtx      *ctx = (LandauCtx*)actx;
1206:   PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *);
1207:   PetscErrorCode ierr,ii,i0;
1208:   PetscInt       dim;
1209:   MaxwellianCtx  *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];

1212:   DMGetDimension(dm, &dim);
1213:   if (!ctx) { DMGetApplicationContext(dm, &ctx); }
1214:   for (ii = ctx->species_offset[grid], i0 = 0 ; ii < ctx->species_offset[grid+1] ; ii++, i0++) {
1215:     mctxs[i0] = &data[i0];
1216:     data[i0].v_0 = ctx->v_0; // v_0 same for whole grid
1217:     data[i0].kT_m = ctx->k*temps[ii]/ctx->masses[ii]; /* kT/m */
1218:     data[i0].n = ns[ii];
1219:     initu[i0] = maxwellian;
1220:     data[i0].shift = 0;
1221:   }
1222:   data[0].shift = ctx->electronShift;
1223:   /* need to make ADD_ALL_VALUES work - TODO */
1224:   DMProjectFunction(dm, time, initu, (void**)mctxs, INSERT_ALL_VALUES, X);
1225:   return(0);
1226: }

1228: /*
1229:  LandauSetInitialCondition - Addes Maxwellians with context

1231:  Collective on X

1233:  Input Parameters:
1234:  .   dm - The mesh
1235:  -   grid - index into current grid - just used for offset into temp and ns
1236:  +   actx - Landau context with T and n

1238:  Output Parameter:
1239:  .   X  - The state

1241:  Level: beginner

1243:  .keywords: mesh
1244:  .seealso: LandauCreateVelocitySpace(), LandauAddMaxwellians()
1245:  */
1246: static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, PetscInt grid, void *actx)
1247: {
1248:   LandauCtx        *ctx = (LandauCtx*)actx;
1251:   if (!ctx) { DMGetApplicationContext(dm, &ctx); }
1252:   VecZeroEntries(X);
1253:   LandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, grid, ctx);
1254:   return(0);
1255: }

1257: // adapt a level once. Forest in/out
1258: static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscInt type, PetscInt grid, LandauCtx *ctx, DM *newForest)
1259: {
1260:   DM               forest, plex, adaptedDM = NULL;
1261:   PetscDS          prob;
1262:   PetscBool        isForest;
1263:   PetscQuadrature  quad;
1264:   PetscInt         Nq, *Nb, cStart, cEnd, c, dim, qj, k;
1265:   DMLabel          adaptLabel = NULL;
1266:   PetscErrorCode   ierr;

1269:   forest = ctx->plex[grid];
1270:   DMCreateDS(forest);
1271:   DMGetDS(forest, &prob);
1272:   DMGetDimension(forest, &dim);
1273:   DMIsForest(forest, &isForest);
1274:   if (!isForest) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"! Forest");
1275:   DMConvert(forest, DMPLEX, &plex);
1276:   DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
1277:   DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);
1278:   PetscFEGetQuadrature(fem, &quad);
1279:   PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);
1280:   if (Nq >LANDAU_MAX_NQ) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"Order too high. Nq = %D > LANDAU_MAX_NQ (%D)",Nq,LANDAU_MAX_NQ);
1281:   PetscDSGetDimensions(prob, &Nb);
1282:   if (type==4) {
1283:     for (c = cStart; c < cEnd; c++) {
1284:       DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);
1285:     }
1286:     PetscInfo1(sol, "Phase:%s: Uniform refinement\n","adaptToleranceFEM");
1287:   } else if (type==2) {
1288:     PetscInt  rCellIdx[8], eCellIdx[64], iCellIdx[64], eMaxIdx = -1, iMaxIdx = -1, nr = 0, nrmax = (dim==3) ? 8 : 2;
1289:     PetscReal minRad = PETSC_INFINITY, r, eMinRad = PETSC_INFINITY, iMinRad = PETSC_INFINITY;
1290:     for (c = 0; c < 64; c++) { eCellIdx[c] = iCellIdx[c] = -1; }
1291:     for (c = cStart; c < cEnd; c++) {
1292:       PetscReal    tt, v0[LANDAU_MAX_NQ*3], detJ[LANDAU_MAX_NQ];
1293:       DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ);
1294:       for (qj = 0; qj < Nq; ++qj) {
1295:         tt = PetscSqr(v0[dim*qj+0]) + PetscSqr(v0[dim*qj+1]) + PetscSqr(((dim==3) ? v0[dim*qj+2] : 0));
1296:         r = PetscSqrtReal(tt);
1297:         if (r < minRad - PETSC_SQRT_MACHINE_EPSILON*10.) {
1298:           minRad = r;
1299:           nr = 0;
1300:           rCellIdx[nr++]= c;
1301:           PetscInfo4(sol, "\t\tPhase: adaptToleranceFEM Found first inner r=%e, cell %D, qp %D/%D\n", r, c, qj+1, Nq);
1302:         } else if ((r-minRad) < PETSC_SQRT_MACHINE_EPSILON*100. && nr < nrmax) {
1303:           for (k=0;k<nr;k++) if (c == rCellIdx[k]) break;
1304:           if (k==nr) {
1305:             rCellIdx[nr++]= c;
1306:             PetscInfo5(sol, "\t\t\tPhase: adaptToleranceFEM Found another inner r=%e, cell %D, qp %D/%D, d=%e\n", r, c, qj+1, Nq, r-minRad);
1307:           }
1308:         }
1309:         if (ctx->sphere) {
1310:           if ((tt=r-ctx->e_radius) > 0) {
1311:             PetscInfo2(sol, "\t\t\t %D cell r=%g\n",c,tt);
1312:             if (tt < eMinRad - PETSC_SQRT_MACHINE_EPSILON*100.) {
1313:               eMinRad = tt;
1314:               eMaxIdx = 0;
1315:               eCellIdx[eMaxIdx++] = c;
1316:             } else if (eMaxIdx > 0 && (tt-eMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != eCellIdx[eMaxIdx-1]) {
1317:               eCellIdx[eMaxIdx++] = c;
1318:             }
1319:           }
1320:           if ((tt=r-ctx->i_radius[grid]) > 0) {
1321:             if (tt < iMinRad - 1.e-5) {
1322:               iMinRad = tt;
1323:               iMaxIdx = 0;
1324:               iCellIdx[iMaxIdx++] = c;
1325:             } else if (iMaxIdx > 0 && (tt-iMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != iCellIdx[iMaxIdx-1]) {
1326:               iCellIdx[iMaxIdx++] = c;
1327:             }
1328:           }
1329:         }
1330:       }
1331:     }
1332:     for (k=0;k<nr;k++) {
1333:       DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE);
1334:     }
1335:     if (ctx->sphere) {
1336:       for (c = 0; c < eMaxIdx; c++) {
1337:         DMLabelSetValue(adaptLabel, eCellIdx[c], DM_ADAPT_REFINE);
1338:         PetscInfo3(sol, "\t\tPhase:%s: refine sphere e cell %D r=%g\n","adaptToleranceFEM",eCellIdx[c],eMinRad);
1339:       }
1340:       for (c = 0; c < iMaxIdx; c++) {
1341:         DMLabelSetValue(adaptLabel, iCellIdx[c], DM_ADAPT_REFINE);
1342:         PetscInfo3(sol, "\t\tPhase:%s: refine sphere i cell %D r=%g\n","adaptToleranceFEM",iCellIdx[c],iMinRad);
1343:       }
1344:     }
1345:     PetscInfo4(sol, "Phase:%s: Adaptive refine origin cells %D,%D r=%g\n","adaptToleranceFEM",rCellIdx[0],rCellIdx[1],minRad);
1346:   } else if (type==0 || type==1 || type==3) { /* refine along r=0 axis */
1347:     PetscScalar  *coef = NULL;
1348:     Vec          coords;
1349:     PetscInt     csize,Nv,d,nz;
1350:     DM           cdm;
1351:     PetscSection cs;
1352:     DMGetCoordinatesLocal(forest, &coords);
1353:     DMGetCoordinateDM(forest, &cdm);
1354:     DMGetLocalSection(cdm, &cs);
1355:     for (c = cStart; c < cEnd; c++) {
1356:       PetscInt doit = 0, outside = 0;
1357:       DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef);
1358:       Nv = csize/dim;
1359:       for (nz = d = 0; d < Nv; d++) {
1360:         PetscReal z = PetscRealPart(coef[d*dim + (dim-1)]), x = PetscSqr(PetscRealPart(coef[d*dim + 0])) + ((dim==3) ? PetscSqr(PetscRealPart(coef[d*dim + 1])) : 0);
1361:         x = PetscSqrtReal(x);
1362:         if (x < PETSC_MACHINE_EPSILON*10. && PetscAbs(z)<PETSC_MACHINE_EPSILON*10.) doit = 1;             /* refine origin */
1363:         else if (type==0 && (z < -PETSC_MACHINE_EPSILON*10. || z > ctx->re_radius+PETSC_MACHINE_EPSILON*10.)) outside++;   /* first pass don't refine bottom */
1364:         else if (type==1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) outside++; /* don't refine outside electron refine radius */
1365:         else if (type==3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) outside++; /* don't refine outside ion refine radius */
1366:         if (x < PETSC_MACHINE_EPSILON*10.) nz++;
1367:       }
1368:       DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef);
1369:       if (doit || (outside<Nv && nz)) {
1370:         DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);
1371:       }
1372:     }
1373:     PetscInfo1(sol, "Phase:%s: RE refinement\n","adaptToleranceFEM");
1374:   }
1375:   DMDestroy(&plex);
1376:   DMAdaptLabel(forest, adaptLabel, &adaptedDM);
1377:   DMLabelDestroy(&adaptLabel);
1378:   *newForest = adaptedDM;
1379:   if (adaptedDM) {
1380:     if (isForest) {
1381:       DMForestSetAdaptivityForest(adaptedDM,NULL); // ????
1382:     } else exit(33); // ???????
1383:     DMConvert(adaptedDM, DMPLEX, &plex);
1384:     DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
1385:     PetscInfo2(sol, "\tPhase: adaptToleranceFEM: %D cells, %d total quadrature points\n",cEnd-cStart,Nq*(cEnd-cStart));
1386:     DMDestroy(&plex);
1387:   } else  *newForest = NULL;
1388:   return(0);
1389: }

1391: // forest goes in (ctx->plex[grid]), plex comes out
1392: static PetscErrorCode adapt(PetscInt grid, LandauCtx *ctx, Vec *uu)
1393: {
1394:   PetscErrorCode  ierr;
1395:   PetscInt        adaptIter;

1398:   PetscInt  type, limits[5] = {(grid==0) ? ctx->numRERefine : 0, (grid==0) ? ctx->nZRefine1 : 0, ctx->numAMRRefine[grid], (grid==0) ? ctx->nZRefine2 : 0,ctx->postAMRRefine[grid]};
1399:   for (type=0;type<5;type++) {
1400:     for (adaptIter = 0; adaptIter<limits[type];adaptIter++) {
1401:       DM  newForest = NULL;
1402:       adaptToleranceFEM(ctx->fe[0], *uu, type, grid, ctx, &newForest);
1403:       if (newForest)  {
1404:         DMDestroy(&ctx->plex[grid]);
1405:         VecDestroy(uu);
1406:         DMCreateGlobalVector(newForest,uu);
1407:         PetscObjectSetName((PetscObject) *uu, "uAMR");
1408:         LandauSetInitialCondition(newForest, *uu, grid, ctx);
1409:         ctx->plex[grid] = newForest;
1410:       } else {
1411:         exit(4); // can happen with no AMR and post refinement
1412:       }
1413:     }
1414:   }
1415:   return(0);
1416: }

1418: static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
1419: {
1420:   PetscErrorCode    ierr;
1421:   PetscBool         flg, sph_flg;
1422:   PetscInt          ii,nt,nm,nc,num_species_grid[LANDAU_MAX_GRIDS];
1423:   PetscReal         v0_grid[LANDAU_MAX_GRIDS];
1424:   DM                dummy;

1427:   DMCreate(ctx->comm,&dummy);
1428:   /* get options - initialize context */
1429:   ctx->verbose = 1;
1430:   ctx->interpolate = PETSC_TRUE;
1431:   ctx->gpu_assembly = PETSC_TRUE;
1432:   ctx->aux_bool = PETSC_FALSE;
1433:   ctx->electronShift = 0;
1434:   ctx->M = NULL;
1435:   ctx->J = NULL;
1436:   /* geometry and grids */
1437:   ctx->sphere = PETSC_FALSE;
1438:   ctx->inflate = PETSC_FALSE;
1439:   ctx->aux_bool = PETSC_FALSE;
1440:   ctx->use_p4est = PETSC_FALSE;
1441:   ctx->num_sections = 3; /* 2, 3 or 4 */
1442:   for (PetscInt grid=0;grid<LANDAU_MAX_GRIDS;grid++) {
1443:     ctx->radius[grid] = 5.; /* thermal radius (velocity) */
1444:     ctx->numAMRRefine[grid] = 5;
1445:     ctx->postAMRRefine[grid] = 0;
1446:     ctx->species_offset[grid+1] = 1; // one species default
1447:     num_species_grid[grid] = 0;
1448:     ctx->plex[grid] = NULL;     /* cache as expensive to Convert */
1449:     v0_grid[grid] = 1;
1450:   }
1451:   ctx->species_offset[0] = 0;
1452:   ctx->re_radius = 0.;
1453:   ctx->vperp0_radius1 = 0;
1454:   ctx->vperp0_radius2 = 0;
1455:   ctx->nZRefine1 = 0;
1456:   ctx->nZRefine2 = 0;
1457:   ctx->numRERefine = 0;
1458:   num_species_grid[0] = 1; // one species default
1459:   /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
1460:   ctx->charges[0] = -1;  /* electron charge (MKS) */
1461:   ctx->masses[0] = 1/1835.469965278441013; /* temporary value in proton mass */
1462:   ctx->n[0] = 1;
1463:   ctx->v_0 = 1; /* thermal velocity, we could start with a scale != 1 */
1464:   ctx->thermal_temps[0] = 1;
1465:   /* constants, etc. */
1466:   ctx->epsilon0 = 8.8542e-12; /* permittivity of free space (MKS) F/m */
1467:   ctx->k = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
1468:   ctx->lnLam = 10;         /* cross section ratio large - small angle collisions */
1469:   ctx->n_0 = 1.e20;        /* typical plasma n, but could set it to 1 */
1470:   ctx->Ez = 0;
1471:   ctx->subThreadBlockSize = 1; /* for device and maybe OMP */
1472:   ctx->numConcurrency = 1; /* for device */
1473:   ctx->times[0] = 0;
1474:   ctx->initialized = PETSC_FALSE; // doit first time
1475:   ctx->use_matrix_mass = PETSC_FALSE; /* fast but slightly fragile */
1476:   ctx->use_relativistic_corrections = PETSC_FALSE;
1477:   ctx->use_energy_tensor_trick = PETSC_FALSE; /* Use Eero's trick for energy conservation v --> grad(v^2/2) */
1478:   ctx->SData_d.w = NULL;
1479:   ctx->SData_d.x = NULL;
1480:   ctx->SData_d.y = NULL;
1481:   ctx->SData_d.z = NULL;
1482:   ctx->SData_d.invJ = NULL;
1483:   PetscOptionsBegin(ctx->comm, prefix, "Options for Fokker-Plank-Landau collision operator", "none");
1484:   {
1485:     char opstring[256];
1486: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1487:     ctx->deviceType = LANDAU_KOKKOS;
1488:     PetscStrcpy(opstring,"kokkos");
1489: #if defined(PETSC_HAVE_CUDA)
1490:     ctx->subThreadBlockSize = 16;
1491: #endif
1492: #elif defined(PETSC_HAVE_CUDA)
1493:     ctx->deviceType = LANDAU_CUDA;
1494:     PetscStrcpy(opstring,"cuda");
1495: #else
1496:     ctx->deviceType = LANDAU_CPU;
1497:     PetscStrcpy(opstring,"cpu");
1498:     ctx->subThreadBlockSize = 0;
1499: #endif
1500:     PetscOptionsString("-dm_landau_device_type","Use kernels on 'cpu', 'cuda', or 'kokkos'","plexland.c",opstring,opstring,256,NULL);
1501:     PetscStrcmp("cpu",opstring,&flg);
1502:     if (flg) {
1503:       ctx->deviceType = LANDAU_CPU;
1504:       ctx->subThreadBlockSize = 0;
1505:     } else {
1506:       PetscStrcmp("cuda",opstring,&flg);
1507:       if (flg) {
1508:         ctx->deviceType = LANDAU_CUDA;
1509:         ctx->subThreadBlockSize = 0;
1510:       } else {
1511:         PetscStrcmp("kokkos",opstring,&flg);
1512:         if (flg) ctx->deviceType = LANDAU_KOKKOS;
1513:         else SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_device_type %s",opstring);
1514:       }
1515:     }
1516:   }

1518:   PetscOptionsReal("-dm_landau_electron_shift","Shift in thermal velocity of electrons","none",ctx->electronShift,&ctx->electronShift, NULL);
1519:   PetscOptionsInt("-dm_landau_verbose", "Level of verbosity output", "plexland.c", ctx->verbose, &ctx->verbose, NULL);
1520:   PetscOptionsReal("-dm_landau_Ez","Initial parallel electric field in unites of Conner-Hastie criticle field","plexland.c",ctx->Ez,&ctx->Ez, NULL);
1521:   PetscOptionsReal("-dm_landau_n_0","Normalization constant for number density","plexland.c",ctx->n_0,&ctx->n_0, NULL);
1522:   PetscOptionsReal("-dm_landau_ln_lambda","Cross section parameter","plexland.c",ctx->lnLam,&ctx->lnLam, NULL);
1523:   PetscOptionsBool("-dm_landau_use_mataxpy_mass", "Use fast but slightly fragile MATAXPY to add mass term", "plexland.c", ctx->use_matrix_mass, &ctx->use_matrix_mass, NULL);
1524:   PetscOptionsBool("-dm_landau_use_relativistic_corrections", "Use relativistic corrections", "plexland.c", ctx->use_relativistic_corrections, &ctx->use_relativistic_corrections, NULL);
1525:   PetscOptionsBool("-dm_landau_use_energy_tensor_trick", "Use Eero's trick of using grad(v^2/2) instead of v as args to Landau tensor to conserve energy with relativistic corrections and Q1 elements", "plexland.c", ctx->use_energy_tensor_trick, &ctx->use_energy_tensor_trick, NULL);

1527:   /* get num species with temperature*/
1528:   {
1529:     PetscReal arr[100];
1530:     nt = 100;
1531:     PetscOptionsRealArray("-dm_landau_thermal_temps", "Temperature of each species [e,i_0,i_1,...] in keV", "plexland.c", arr, &nt, &flg);
1532:     if (flg && nt > LANDAU_MAX_SPECIES) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"-thermal_temps ,t1,t2,.. number of species %D > MAX %D",nt,LANDAU_MAX_SPECIES);
1533:   }
1534:   nt = LANDAU_MAX_SPECIES;
1535:   for (ii=1;ii<LANDAU_MAX_SPECIES;ii++) {
1536:     ctx->thermal_temps[ii] = 1.;
1537:     ctx->charges[ii] = 1;
1538:     ctx->masses[ii] = 1;
1539:     ctx->n[ii] = (ii==1) ? 1 : 0;
1540:   }
1541:   PetscOptionsRealArray("-dm_landau_thermal_temps", "Temperature of each species [e,i_0,i_1,...] in keV (must be set to set number of species)", "plexland.c", ctx->thermal_temps, &nt, &flg);
1542:   if (flg) {
1543:     PetscInfo1(dummy, "num_species set to number of thermal temps provided (%D)\n",nt);
1544:     ctx->num_species = nt;
1545:   } else SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
1546:   for (ii=0;ii<ctx->num_species;ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
1547:   nm = LANDAU_MAX_SPECIES-1;
1548:   PetscOptionsRealArray("-dm_landau_ion_masses", "Mass of each species in units of proton mass [i_0=2,i_1=40...]", "plexland.c", &ctx->masses[1], &nm, &flg);
1549:   if (flg && nm != ctx->num_species-1) {
1550:     SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"num ion masses %D != num species %D",nm,ctx->num_species-1);
1551:   }
1552:   nm = LANDAU_MAX_SPECIES;
1553:   PetscOptionsRealArray("-dm_landau_n", "Normalized (by -n_0) number density of each species", "plexland.c", ctx->n, &nm, &flg);
1554:   if (flg && nm != ctx->num_species) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"wrong num n: %D != num species %D",nm,ctx->num_species);
1555:   ctx->n_0 *= ctx->n[0]; /* normalized number density */
1556:   for (ii=1;ii<ctx->num_species;ii++) ctx->n[ii] = ctx->n[ii]/ctx->n[0];
1557:   ctx->n[0] = 1;
1558:   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
1559:   ctx->masses[0] = 9.10938356e-31; /* electron mass kg (should be about right already) */
1560:   ctx->m_0 = ctx->masses[0]; /* arbitrary reference mass, electrons */
1561:   nc = LANDAU_MAX_SPECIES-1;
1562:   PetscOptionsRealArray("-dm_landau_ion_charges", "Charge of each species in units of proton charge [i_0=2,i_1=18,...]", "plexland.c", &ctx->charges[1], &nc, &flg);
1563:   if (flg && nc != ctx->num_species-1) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"num charges %D != num species %D",nc,ctx->num_species-1);
1564:   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
1565:   /* geometry and grids */
1566:   nt = LANDAU_MAX_GRIDS;
1567:   PetscOptionsIntArray("-dm_landau_num_species_grid","Number of species on each grid: [ 1, ....] or [S, 0 ....] for single grid","plexland.c", num_species_grid, &nt, &flg);
1568:   if (flg) {
1569:     ctx->num_grids = nt;
1570:     for (ii=nt=0;ii<ctx->num_grids;ii++) nt += num_species_grid[ii];
1571:     if (ctx->num_species != nt) SETERRQ4(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_num_species_grid: sum %D != num_species = %D. %D grids (check that number of grids <= LANDAU_MAX_GRIDS = %D)",nt,ctx->num_species,ctx->num_grids,LANDAU_MAX_GRIDS);
1572:   } else {
1573:     ctx->num_grids = 1; // go back to a single grid run
1574:     num_species_grid[0] = ctx->num_species;
1575:   }
1576:   for (ctx->species_offset[0] = ii = 0; ii < ctx->num_grids ; ii++) ctx->species_offset[ii+1] = ctx->species_offset[ii] + num_species_grid[ii];
1577:   if (ctx->species_offset[ctx->num_grids] != ctx->num_species) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"ctx->species_offset[ctx->num_grids] %D != ctx->num_species = %D ???????????",ctx->species_offset[ctx->num_grids],ctx->num_species);
1578:   for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
1579:     int iii = ctx->species_offset[grid]; // normalize with first (arbitrary) species on grid
1580:     v0_grid[grid] *= PetscSqrtReal(ctx->k*ctx->thermal_temps[iii]/ctx->masses[iii]); /* arbitrary units for non-dimensionalization: mean velocity in 1D of first species on grid */
1581:   }
1582:   ii = 0;
1583:   //PetscOptionsInt("-dm_landau_v0_grid", "Index of grid to use for setting v_0 (electrons are default). Not recommended to change", "plexland.c", ii, &ii, NULL);
1584:   ctx->v_0 = v0_grid[ii]; /* arbitrary units for non dimensionalization: mean velocity in 1D of first species on grid */
1585:   ctx->t_0 = 8*PETSC_PI*PetscSqr(ctx->epsilon0*ctx->m_0/PetscSqr(ctx->charges[0]))/ctx->lnLam/ctx->n_0*PetscPowReal(ctx->v_0,3); /* note, this t_0 makes nu[0,0]=1 */
1586:   /* domain */
1587:   nt = LANDAU_MAX_GRIDS;
1588:   PetscOptionsRealArray("-dm_landau_domain_radius","Phase space size in units of thermal velocity of grid","plexland.c",ctx->radius,&nt, &flg);
1589:   if (flg && nt < ctx->num_grids) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_domain_radius: given %D radius != number grids %D",nt,ctx->num_grids);
1590:   for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
1591:     if (flg && ctx->radius[grid] <= 0) { /* negative is ratio of c */
1592:       if (ctx->radius[grid] == 0) ctx->radius[grid] = 0.75;
1593:       else ctx->radius[grid] = -ctx->radius[grid];
1594:       ctx->radius[grid] = ctx->radius[grid]*SPEED_OF_LIGHT/ctx->v_0; // use any species on grid to normalize (v_0 same for all on grid)
1595:       PetscInfo2(dummy, "Change domain radius to %e for grid %D\n",ctx->radius[grid],grid);
1596:     }
1597:     ctx->radius[grid] *= v0_grid[grid]/ctx->v_0; // scale domain by thermal radius relative to v_0
1598:   }
1599:   /* amr parametres */
1600:   nt = LANDAU_MAX_GRIDS;
1601:   PetscOptionsIntArray("-dm_landau_amr_levels_max", "Number of AMR levels of refinement around origin, after (RE) refinements along z", "plexland.c", ctx->numAMRRefine, &nt, &flg);
1602:   if (flg && nt < ctx->num_grids) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_amr_levels_max: given %D != number grids %D",nt,ctx->num_grids);
1603:   nt = LANDAU_MAX_GRIDS;
1604:   PetscOptionsIntArray("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &nt, &flg);
1605:   for (ii=1;ii<ctx->num_grids;ii++)  ctx->postAMRRefine[ii] = ctx->postAMRRefine[0]; // all grids the same now
1606:   PetscOptionsInt("-dm_landau_amr_re_levels", "Number of levels to refine along v_perp=0, z>0", "plexland.c", ctx->numRERefine, &ctx->numRERefine, &flg);
1607:   PetscOptionsInt("-dm_landau_amr_z_refine1",  "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine1, &ctx->nZRefine1, &flg);
1608:   PetscOptionsInt("-dm_landau_amr_z_refine2",  "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine2, &ctx->nZRefine2, &flg);
1609:   PetscOptionsReal("-dm_landau_re_radius","velocity range to refine on positive (z>0) r=0 axis for runaways","plexland.c",ctx->re_radius,&ctx->re_radius, &flg);
1610:   PetscOptionsReal("-dm_landau_z_radius1","velocity range to refine r=0 axis (for electrons)","plexland.c",ctx->vperp0_radius1,&ctx->vperp0_radius1, &flg);
1611:   PetscOptionsReal("-dm_landau_z_radius2","velocity range to refine r=0 axis (for ions) after origin AMR","plexland.c",ctx->vperp0_radius2, &ctx->vperp0_radius2, &flg);
1612:   /* spherical domain (not used) */
1613:   PetscOptionsInt("-dm_landau_num_sections", "Number of tangential section in (2D) grid, 2, 3, of 4", "plexland.c", ctx->num_sections, &ctx->num_sections, NULL);
1614:   PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, &sph_flg);
1615:   PetscOptionsBool("-dm_landau_inflate", "With sphere, inflate for curved edges", "plexland.c", ctx->inflate, &ctx->inflate, &flg);
1616:   PetscOptionsReal("-dm_landau_e_radius","Electron thermal velocity, used for circular meshes","plexland.c",ctx->e_radius, &ctx->e_radius, &flg);
1617:   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an e radius but did not set sphere, user error really */
1618:   if (!flg) {
1619:     ctx->e_radius = 1.5*PetscSqrtReal(8*ctx->k*ctx->thermal_temps[0]/ctx->masses[0]/PETSC_PI)/ctx->v_0;
1620:   }
1621:   nt = LANDAU_MAX_GRIDS;
1622:   PetscOptionsRealArray("-dm_landau_i_radius","Ion thermal velocity, used for circular meshes","plexland.c",ctx->i_radius, &nt, &flg);
1623:   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE;
1624:   if (!flg) {
1625:     ctx->i_radius[0] = 1.5*PetscSqrtReal(8*ctx->k*ctx->thermal_temps[1]/ctx->masses[1]/PETSC_PI)/ctx->v_0; // need to correct for ion grid domain
1626:   }
1627:   if (flg && ctx->num_grids != nt) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_i_radius: %D != num_species = %D",nt,ctx->num_grids);
1628:   if (ctx->sphere && ctx->e_radius <= ctx->i_radius[0]) SETERRQ3(ctx->comm,PETSC_ERR_ARG_WRONG,"bad radii: %g < %g < %g",ctx->i_radius[0],ctx->e_radius,ctx->radius[0]);
1629:   /* processing options */
1630:   PetscOptionsInt("-dm_landau_sub_thread_block_size", "Number of threads in Kokkos integration point subblock", "plexland.c", ctx->subThreadBlockSize, &ctx->subThreadBlockSize, NULL);
1631:   PetscOptionsBool("-dm_landau_gpu_assembly", "Assemble Jacobian on GPU", "plexland.c", ctx->gpu_assembly, &ctx->gpu_assembly, NULL);
1632:   PetscOptionsInt("-dm_landau_num_thread_teams", "The number of other concurrent runs to make room for", "plexland.c", ctx->numConcurrency, &ctx->numConcurrency, NULL);

1634:   PetscOptionsEnd();
1635:   for (ii=ctx->num_species;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] = ctx->thermal_temps[ii]  = ctx->charges[ii] = 0;
1636:   if (ctx->verbose > 0) {
1637:     PetscPrintf(ctx->comm, "masses:        e=%10.3e; ions in proton mass units:   %10.3e %10.3e ...\n",ctx->masses[0],ctx->masses[1]/1.6720e-27,ctx->num_species>2 ? ctx->masses[2]/1.6720e-27 : 0);
1638:     PetscPrintf(ctx->comm, "charges:       e=%10.3e; charges in elementary units: %10.3e %10.3e\n", ctx->charges[0],-ctx->charges[1]/ctx->charges[0],ctx->num_species>2 ? -ctx->charges[2]/ctx->charges[0] : 0);
1639:     PetscPrintf(ctx->comm, "thermal T (K): e=%10.3e i=%10.3e %10.3e. v_0=%10.3e (%10.3ec) n_0=%10.3e t_0=%10.3e, %s, %s\n", ctx->thermal_temps[0], ctx->thermal_temps[1], (ctx->num_species>2) ? ctx->thermal_temps[2] : 0, ctx->v_0, ctx->v_0/SPEED_OF_LIGHT, ctx->n_0, ctx->t_0, ctx->use_relativistic_corrections ? "relativistic" : "classical", ctx->use_energy_tensor_trick ? "Use trick" : "Intuitive");
1640:     PetscPrintf(ctx->comm, "Domain radius (AMR levels) grid %D: %10.3e (%D) ",0,ctx->radius[0],ctx->numAMRRefine[0]);
1641:     for (ii=1;ii<ctx->num_grids;ii++) PetscPrintf(ctx->comm, ", %D: %10.3e (%D) ",ii,ctx->radius[ii],ctx->numAMRRefine[ii]);
1642:     PetscPrintf(ctx->comm,"\n");
1643:   }
1644:   DMDestroy(&dummy);
1645:   {
1646:     PetscMPIInt    rank;
1647:     MPI_Comm_rank(ctx->comm, &rank);
1648:     /* PetscLogStage  setup_stage; */
1649:     PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[11]); /* 11 */
1650:     PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[0]); /* 0 */
1651:     PetscLogEventRegister("Landau Mass", DM_CLASSID, &ctx->events[9]); /* 9 */
1652:     PetscLogEventRegister(" Preamble", DM_CLASSID, &ctx->events[10]); /* 10 */
1653:     PetscLogEventRegister(" static IP Data", DM_CLASSID, &ctx->events[7]); /* 7 */
1654:     PetscLogEventRegister(" dynamic IP-Jac", DM_CLASSID, &ctx->events[1]); /* 1 */
1655:     PetscLogEventRegister(" Kernel-init", DM_CLASSID, &ctx->events[3]); /* 3 */
1656:     PetscLogEventRegister(" Jac-f-df (GPU)", DM_CLASSID, &ctx->events[8]); /* 8 */
1657:     PetscLogEventRegister(" Kernel (GPU)", DM_CLASSID, &ctx->events[4]); /* 4 */
1658:     PetscLogEventRegister(" Copy to CPU", DM_CLASSID, &ctx->events[5]); /* 5 */
1659:     PetscLogEventRegister(" Jac-assemble", DM_CLASSID, &ctx->events[6]); /* 6 */
1660:     PetscLogEventRegister(" Jac asmbl setup", DM_CLASSID, &ctx->events[2]); /* 2 */
1661:     PetscLogEventRegister(" Other", DM_CLASSID, &ctx->events[13]); /* 13 */

1663:     if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
1664:       PetscOptionsClearValue(NULL,"-snes_converged_reason");
1665:       PetscOptionsClearValue(NULL,"-ksp_converged_reason");
1666:       PetscOptionsClearValue(NULL,"-snes_monitor");
1667:       PetscOptionsClearValue(NULL,"-ksp_monitor");
1668:       PetscOptionsClearValue(NULL,"-ts_monitor");
1669:       PetscOptionsClearValue(NULL,"-ts_adapt_monitor");
1670:       PetscOptionsClearValue(NULL,"-dm_landau_amr_dm_view");
1671:       PetscOptionsClearValue(NULL,"-dm_landau_amr_vec_view");
1672:       PetscOptionsClearValue(NULL,"-dm_landau_mass_dm_view");
1673:       PetscOptionsClearValue(NULL,"-dm_landau_mass_view");
1674:       PetscOptionsClearValue(NULL,"-dm_landau_jacobian_view");
1675:       PetscOptionsClearValue(NULL,"-dm_landau_mat_view");
1676:       PetscOptionsClearValue(NULL,"-");
1677:       PetscOptionsClearValue(NULL,"-info");
1678:     }
1679:   }
1680:   return(0);
1681: }

1683: /*@C
1684:  LandauCreateVelocitySpace - Create a DMPlex velocity space mesh

1686:  Collective on comm

1688:  Input Parameters:
1689:  +   comm  - The MPI communicator
1690:  .   dim - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
1691:  -   prefix - prefix for options (not tested)

1693:  Output Parameter:
1694:  .   pack  - The DM object representing the mesh
1695:  +   X - A vector (user destroys)
1696:  -   J - Optional matrix (object destroys)

1698:  Level: beginner

1700:  .keywords: mesh
1701:  .seealso: DMPlexCreate(), LandauDestroyVelocitySpace()
1702:  @*/
1703: PetscErrorCode LandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *pack)
1704: {
1706:   LandauCtx      *ctx;
1707:   PetscBool      prealloc_only,flg;
1708:   Vec            Xsub[LANDAU_MAX_GRIDS];

1711:   if (dim!=2 && dim!=3) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Only 2D and 3D supported");
1712:   PetscNew(&ctx);
1713:   ctx->comm = comm; /* used for diagnostics and global errors */
1714:   /* process options */
1715:   ProcessOptions(ctx,prefix);
1716:   if (dim==2) ctx->use_relativistic_corrections = PETSC_FALSE;
1717:   /* Create Mesh */
1718:   LandauDMCreateVMeshes(PETSC_COMM_SELF, dim, prefix, ctx, pack); // creates grids (Forest of AMR)
1719:   prealloc_only = (*pack)->prealloc_only;
1720:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
1721:     /* create FEM */
1722:     SetupDS(ctx->plex[grid],dim,grid,ctx);
1723:     /* set initial state */
1724:     DMCreateGlobalVector(ctx->plex[grid],&Xsub[grid]);
1725:     PetscObjectSetName((PetscObject) Xsub[grid], "u_orig");
1726:     /* initial static refinement, no solve */
1727:     LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, ctx);
1728:     /* forest refinement - forest goes in (if forest), plex comes out */
1729:     if (ctx->use_p4est) {
1730:       DM plex;
1731:       adapt(grid,ctx,&Xsub[grid]); // forest goes in, plex comes out
1732:       if (ctx->plex[grid]->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)pack),PETSC_ERR_PLIB,"ctx->plex[grid]->prealloc_only != prealloc_only");
1733:       DMViewFromOptions(ctx->plex[grid],NULL,"-dm_landau_amr_dm_view"); // need to differentiate - todo
1734:       VecViewFromOptions(Xsub[grid], NULL, "-dm_landau_amr_vec_view");
1735:       // convert to plex, all done with this level
1736:       DMConvert(ctx->plex[grid], DMPLEX, &plex);
1737:       DMDestroy(&ctx->plex[grid]);
1738:       ctx->plex[grid] = plex;
1739:     }
1740:     DMCompositeAddDM(*pack,ctx->plex[grid]);
1741:     DMSetApplicationContext(ctx->plex[grid], ctx);
1742:   }
1743:   DMSetApplicationContext(*pack, ctx);
1744:   PetscOptionsInsertString(NULL,"-dm_preallocate_only");
1745:   DMSetFromOptions(*pack);
1746:   DMCreateMatrix(*pack, &ctx->J);
1747:   PetscOptionsInsertString(NULL,"-dm_preallocate_only false");
1748:   MatSetOption(ctx->J, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);
1749:   MatSetOption(ctx->J, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);
1750:   PetscObjectSetName((PetscObject)ctx->J, "Jac");
1751:   if (J) *J = ctx->J;
1752:   // construct X, copy data in
1753:   DMCreateGlobalVector(*pack,X);
1754:   for (PetscInt grid=0, idx = 0 ; grid < ctx->num_grids ; grid++) {
1755:     PetscInt          n;
1756:     PetscScalar const *values;
1757:     VecGetLocalSize(Xsub[grid],&n);
1758:     VecGetArrayRead(Xsub[grid],&values);
1759:     for (int i=0; i<n; i++, idx++) {
1760:       VecSetValue(*X,idx,values[i],INSERT_VALUES);
1761:     }
1762:     VecRestoreArrayRead(Xsub[grid],&values);
1763:     VecDestroy(&Xsub[grid]);
1764:   }

1766:   /* check for types that we need */
1767:   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
1768:     if (ctx->deviceType == LANDAU_CUDA) {
1769:       PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");
1770:       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must use '-dm_mat_type aijcusparse -dm_vec_type cuda' for GPU assembly and Cuda");
1771:     } else if (ctx->deviceType == LANDAU_KOKKOS) {
1772:       PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,MATAIJKOKKOS,"");
1773: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1774:       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for GPU assembly and Kokkos");
1775: #else
1776:       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must configure with '--download-kokkos-kernels=1' for GPU assembly and Kokkos");
1777: #endif
1778:     }
1779:   }
1780:   return(0);
1781: }

1783: /*@
1784:  LandauDestroyVelocitySpace - Destroy a DMPlex velocity space mesh

1786:  Collective on dm

1788:  Input/Output Parameters:
1789:  .   dm - the dm to destroy

1791:  Level: beginner

1793:  .keywords: mesh
1794:  .seealso: LandauCreateVelocitySpace()
1795:  @*/
1796: PetscErrorCode LandauDestroyVelocitySpace(DM *dm)
1797: {
1798:   PetscErrorCode ierr,ii;
1799:   LandauCtx      *ctx;
1800:   PetscContainer container = NULL;
1802:   DMGetApplicationContext(*dm, &ctx);
1803:   PetscObjectQuery((PetscObject)ctx->J,"coloring", (PetscObject*)&container);
1804:   if (container) {
1805:     PetscContainerDestroy(&container);
1806:   }
1807:   MatDestroy(&ctx->M);
1808:   MatDestroy(&ctx->J);
1809:   for (ii=0;ii<ctx->num_species;ii++) {
1810:     PetscFEDestroy(&ctx->fe[ii]);
1811:   }
1812:   if (ctx->deviceType == LANDAU_CUDA) {
1813: #if defined(PETSC_HAVE_CUDA)
1814:     LandauCUDAStaticDataClear(&ctx->SData_d);
1815: #else
1816:     SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
1817: #endif
1818:   } else if (ctx->deviceType == LANDAU_KOKKOS) {
1819: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1820:     LandauKokkosStaticDataClear(&ctx->SData_d);
1821: #else
1822:     SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
1823: #endif
1824:   } else {
1825:     if (ctx->SData_d.x) { /* in a CPU run */
1826:       PetscReal *invJ = (PetscReal*)ctx->SData_d.invJ, *xx = (PetscReal*)ctx->SData_d.x, *yy = (PetscReal*)ctx->SData_d.y, *zz = (PetscReal*)ctx->SData_d.z, *ww = (PetscReal*)ctx->SData_d.w;
1827:       PetscFree4(ww,xx,yy,invJ);
1828:       if (zz) {
1829:         PetscFree(zz);
1830:       }
1831:     }
1832:   }
1833:   if (ctx->times[0] > 0) {
1834:     PetscPrintf(ctx->comm, "Landau Operator       %d 1.0 %10.3e ....\n",10000,ctx->times[0]);
1835:   }
1836:   for (PetscInt grid=0 ; grid < ctx->num_grids ; grid++) {
1837:     DMDestroy(&ctx->plex[grid]);
1838:   }
1839:   PetscFree(ctx);
1840:   DMDestroy(dm);
1841:   return(0);
1842: }

1844: /* < v, ru > */
1845: static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1846:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1847:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1848:                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1849: {
1850:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1851:   f0[0] = u[ii];
1852: }

1854: /* < v, ru > */
1855: static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1856:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1857:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1858:                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1859: {
1860:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
1861:   f0[0] = x[jj]*u[ii]; /* x momentum */
1862: }

1864: static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1865:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1866:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1867:                     PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1868: {
1869:   PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
1870:   double tmp1 = 0.;
1871:   for (i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1872:   f0[0] = tmp1*u[ii];
1873: }

1875: static PetscErrorCode gamma_n_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *actx)
1876: {
1877:   const PetscReal *c2_0_arr = ((PetscReal*)actx);
1878:   const PetscReal c02 = c2_0_arr[0];

1881:   for (int s = 0 ; s < Nf ; s++) {
1882:     PetscReal tmp1 = 0.;
1883:     for (int i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1884: #if defined(PETSC_USE_DEBUG)
1885:     u[s] = PetscSqrtReal(1. + tmp1/c02);//  u[0] = PetscSqrtReal(1. + xx);
1886: #else
1887:     {
1888:       PetscReal xx = tmp1/c02;
1889:       u[s] = xx/(PetscSqrtReal(1. + xx) + 1.); // better conditioned = xx/(PetscSqrtReal(1. + xx) + 1.)
1890:     }
1891: #endif
1892:   }
1893:   return(0);
1894: }

1896: /* < v, ru > */
1897: static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1898:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1899:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1900:                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1901: {
1902:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1903:   f0[0] = 2.*PETSC_PI*x[0]*u[ii];
1904: }

1906: /* < v, ru > */
1907: static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1908:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1909:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1910:                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1911: {
1912:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1913:   f0[0] = 2.*PETSC_PI*x[0]*x[1]*u[ii];
1914: }

1916: static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1917:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1918:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1919:                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1920: {
1921:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1922:   f0[0] =  2.*PETSC_PI*x[0]*(x[0]*x[0] + x[1]*x[1])*u[ii];
1923: }

1925: /*@
1926:  LandauPrintNorms - collects moments and prints them

1928:  Collective on dm

1930:  Input Parameters:
1931:  +   X  - the state
1932:  -   stepi - current step to print

1934:  Level: beginner

1936:  .keywords: mesh
1937:  .seealso: LandauCreateVelocitySpace()
1938:  @*/
1939: PetscErrorCode LandauPrintNorms(Vec X, PetscInt stepi)
1940: {
1942:   LandauCtx      *ctx;
1943:   PetscDS        prob;
1944:   DM             pack;
1945:   PetscInt       cStart, cEnd, dim, ii, i0;
1946:   PetscScalar    xmomentumtot=0, ymomentumtot=0, zmomentumtot=0, energytot=0, densitytot=0, tt[LANDAU_MAX_SPECIES];
1947:   PetscScalar    xmomentum[LANDAU_MAX_SPECIES],  ymomentum[LANDAU_MAX_SPECIES],  zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
1948:   Vec            globXArray[LANDAU_MAX_GRIDS];

1951:   VecGetDM(X, &pack);
1952:   if (!pack) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Vector has no DM");
1953:   DMGetDimension(pack, &dim);
1954:   if (dim!=2 && dim!=3) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim= %D",dim);
1955:   DMGetApplicationContext(pack, &ctx);
1956:   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1957:   /* print momentum and energy */
1958:   DMCompositeGetAccessArray(pack, X, ctx->num_grids, NULL, globXArray);
1959:   for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
1960:     Vec Xloc = globXArray[grid];
1961:     DMGetDS(ctx->plex[grid], &prob);
1962:     for (ii=ctx->species_offset[grid],i0=0;ii<ctx->species_offset[grid+1];ii++,i0++) {
1963:       PetscScalar user[2] = { (PetscScalar)i0, (PetscScalar)ctx->charges[ii]};
1964:       PetscDSSetConstants(prob, 2, user);
1965:       if (dim==2) { /* 2/3X + 3V (cylindrical coordinates) */
1966:         PetscDSSetObjective(prob, 0, &f0_s_rden);
1967:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1968:         density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1969:         PetscDSSetObjective(prob, 0, &f0_s_rmom);
1970:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1971:         zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1972:         PetscDSSetObjective(prob, 0, &f0_s_rv2);
1973:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1974:         energy[ii] = tt[0]*0.5*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1975:         zmomentumtot += zmomentum[ii];
1976:         energytot  += energy[ii];
1977:         densitytot += density[ii];
1978:         PetscPrintf(ctx->comm, "%3D) species-%D: charge density= %20.13e z-momentum= %20.13e energy= %20.13e",stepi,ii,PetscRealPart(density[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));
1979:       } else { /* 2/3Xloc + 3V */
1980:         PetscDSSetObjective(prob, 0, &f0_s_den);
1981:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1982:         density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1983:         PetscDSSetObjective(prob, 0, &f0_s_mom);
1984:         user[1] = 0;
1985:         PetscDSSetConstants(prob, 2, user);
1986:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1987:         xmomentum[ii]  = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1988:         user[1] = 1;
1989:         PetscDSSetConstants(prob, 2, user);
1990:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1991:         ymomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1992:         user[1] = 2;
1993:         PetscDSSetConstants(prob, 2, user);
1994:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
1995:         zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1996:         if (ctx->use_relativistic_corrections) {
1997:           /* gamma * M * f */
1998:           if (ii==0 && grid==0) { // do all at once
1999:             Vec            Mf, globGamma, globMfarray[LANDAU_MAX_GRIDS], globGammaArray[LANDAU_MAX_GRIDS];
2000:             PetscErrorCode (*gammaf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {gamma_n_f};
2001:             PetscReal      *c2_0[1], data[1];

2003:             VecDuplicate(X,&globGamma);
2004:             VecDuplicate(X,&Mf);
2005:             /* M * f */
2006:             MatMult(ctx->M,X,Mf);
2007:             /* gamma */
2008:             DMCompositeGetAccessArray(pack, globGamma, ctx->num_grids, NULL, globGammaArray);
2009:             for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) { // yes a grid loop in a grid loop to print nice
2010:               Vec v1 = globGammaArray[grid];
2011:               data[0] = PetscSqr(C_0(ctx->v_0));
2012:               c2_0[0] = &data[0];
2013:               DMProjectFunction(ctx->plex[grid], 0., gammaf, (void**)c2_0, INSERT_ALL_VALUES, v1);
2014:             }
2015:             DMCompositeRestoreAccessArray(pack, globGamma, ctx->num_grids, NULL, globGammaArray);
2016:             /* gamma * Mf */
2017:             DMCompositeGetAccessArray(pack, globGamma, ctx->num_grids, NULL, globGammaArray);
2018:             DMCompositeGetAccessArray(pack, Mf, ctx->num_grids, NULL, globMfarray);
2019:             for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) { // yes a grid loop in a grid loop to print nice
2020:               PetscInt Nf = ctx->species_offset[grid+1] - ctx->species_offset[grid], N, bs;
2021:               Vec      Mfsub = globMfarray[grid], Gsub = globGammaArray[grid], v1, v2;
2022:               // get each component
2023:               VecGetSize(Mfsub,&N);
2024:               VecCreate(ctx->comm,&v1);
2025:               VecSetSizes(v1,PETSC_DECIDE,N/Nf);
2026:               VecCreate(ctx->comm,&v2);
2027:               VecSetSizes(v2,PETSC_DECIDE,N/Nf);
2028:               VecSetFromOptions(v1); // ???
2029:               VecSetFromOptions(v2);
2030:               // get each component
2031:               VecGetBlockSize(Gsub,&bs);
2032:               if (bs != Nf) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "bs %D != num_species %D in Gsub",bs,Nf);
2033:               VecGetBlockSize(Mfsub,&bs);
2034:               if (bs != Nf) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "bs %D != num_species %D",bs,Nf);
2035:               for (int i=0, ix=ctx->species_offset[grid] ; i<Nf ; i++, ix++) {
2036:                 PetscScalar val;
2037:                 VecStrideGather(Gsub,i,v1,INSERT_VALUES);
2038:                 VecStrideGather(Mfsub,i,v2,INSERT_VALUES);
2039:                 VecDot(v1,v2,&val);
2040:                 energy[ix] = PetscRealPart(val)*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ix];
2041:               }
2042:               VecDestroy(&v1);
2043:               VecDestroy(&v2);
2044:             } /* grids */
2045:             DMCompositeRestoreAccessArray(pack, globGamma, ctx->num_grids, NULL, globGammaArray);
2046:             DMCompositeRestoreAccessArray(pack, Mf, ctx->num_grids, NULL, globMfarray);
2047:             VecDestroy(&globGamma);
2048:             VecDestroy(&Mf);
2049:           }
2050:         } else {
2051:           PetscDSSetObjective(prob, 0, &f0_s_v2);
2052:           DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
2053:           energy[ii]    = 0.5*tt[0]*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
2054:         }
2055:         PetscPrintf( ctx->comm, "%3D) species %D: density=%20.13e, x-momentum=%20.13e, y-momentum=%20.13e, z-momentum=%20.13e, energy=%21.13e",
2056:                             stepi,ii,PetscRealPart(density[ii]),PetscRealPart(xmomentum[ii]),PetscRealPart(ymomentum[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));
2057:         xmomentumtot += xmomentum[ii];
2058:         ymomentumtot += ymomentum[ii];
2059:         zmomentumtot += zmomentum[ii];
2060:         energytot  += energy[ii];
2061:         densitytot += density[ii];
2062:       }
2063:       if (ctx->num_species>1) PetscPrintf(ctx->comm, "\n");
2064:     }
2065:   }
2066:   DMCompositeRestoreAccessArray(pack, X, ctx->num_grids, NULL, globXArray);
2067:   /* totals */
2068:   DMPlexGetHeightStratum(ctx->plex[0],0,&cStart,&cEnd);
2069:   if (ctx->num_species>1) {
2070:     if (dim==2) {
2071:       PetscPrintf(ctx->comm, "\t%3D) Total: charge density=%21.13e, momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %D cells on electron grid)",
2072:                          stepi,(double)PetscRealPart(densitytot),(double)PetscRealPart(zmomentumtot),(double)PetscRealPart(energytot),(double)(ctx->masses[1]/ctx->masses[0]),cEnd-cStart);
2073:     } else {
2074:       PetscPrintf(ctx->comm, "\t%3D) Total: charge density=%21.13e, x-momentum=%21.13e, y-momentum=%21.13e, z-momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %D cells)",
2075:                          stepi,(double)PetscRealPart(densitytot),(double)PetscRealPart(xmomentumtot),(double)PetscRealPart(ymomentumtot),(double)PetscRealPart(zmomentumtot),(double)PetscRealPart(energytot),(double)(ctx->masses[1]/ctx->masses[0]),cEnd-cStart);
2076:     }
2077:   } else {
2078:     PetscPrintf(ctx->comm, " -- %D cells",cEnd-cStart);
2079:   }
2080:   if (ctx->verbose > 1) {PetscPrintf(ctx->comm,", %D sub (vector) threads\n",ctx->subThreadBlockSize);}
2081:   else {PetscPrintf(ctx->comm,"\n");}
2082:   return(0);
2083: }

2085: static PetscErrorCode destroy_coloring (void *is)
2086: {
2087:   ISColoring tmp = (ISColoring)is;
2088:   return ISColoringDestroy(&tmp);
2089: }

2091: /*@
2092:  LandauCreateColoring - create a coloring and add to matrix (Landau context used just for 'print' flag, should be in DMPlex)

2094:  Collective on JacP

2096:  Input Parameters:
2097:  +   JacP  - matrix to add coloring to
2098:  -   plex - The DM

2100:  Output Parameter:
2101:  .   container  - Container with coloring

2103:  Level: beginner

2105:  .keywords: mesh
2106:  .seealso: LandauCreateVelocitySpace()
2107:  @*/
2108: PetscErrorCode LandauCreateColoring(Mat JacP, DM plex, PetscContainer *container)
2109: {
2110:   PetscErrorCode  ierr;
2111:   PetscInt        dim,cell,i,ej,nc,Nv,totDim,numGCells,cStart,cEnd;
2112:   ISColoring      iscoloring = NULL;
2113:   Mat             G,Q;
2114:   PetscScalar     ones[128];
2115:   MatColoring     mc;
2116:   IS             *is;
2117:   PetscInt        csize,colour,j,k;
2118:   const PetscInt *indices;
2119:   PetscInt       numComp[1];
2120:   PetscInt       numDof[4];
2121:   PetscFE        fe;
2122:   DM             colordm;
2123:   PetscSection   csection, section, globalSection;
2124:   PetscDS        prob;
2125:   LandauCtx      *ctx;

2128:   DMGetApplicationContext(plex, &ctx);
2129:   DMGetLocalSection(plex, &section);
2130:   DMGetGlobalSection(plex, &globalSection);
2131:   DMGetDimension(plex, &dim);
2132:   DMGetDS(plex, &prob);
2133:   PetscDSGetTotalDimension(prob, &totDim);
2134:   DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
2135:   numGCells = cEnd - cStart;
2136:   /* create cell centered DM */
2137:   DMClone(plex, &colordm);
2138:   PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, "color_", PETSC_DECIDE, &fe);
2139:   PetscObjectSetName((PetscObject) fe, "color");
2140:   DMSetField(colordm, 0, NULL, (PetscObject)fe);
2141:   PetscFEDestroy(&fe);
2142:   for (i = 0; i < (dim+1); ++i) numDof[i] = 0;
2143:   numDof[dim] = 1;
2144:   numComp[0] = 1;
2145:   DMPlexCreateSection(colordm, NULL, numComp, numDof, 0, NULL, NULL, NULL, NULL, &csection);
2146:   PetscSectionSetFieldName(csection, 0, "color");
2147:   DMSetLocalSection(colordm, csection);
2148:   DMViewFromOptions(colordm,NULL,"-color_dm_view");
2149:   /* get vertex to element map Q and colroing graph G */
2150:   MatGetSize(JacP,NULL,&Nv);
2151:   MatCreateAIJ(PETSC_COMM_SELF,PETSC_DECIDE,PETSC_DECIDE,numGCells,Nv,totDim,NULL,0,NULL,&Q);
2152:   for (i=0;i<128;i++) ones[i] = 1.0;
2153:   for (cell = cStart, ej = 0 ; cell < cEnd; ++cell, ++ej) {
2154:     PetscInt numindices,*indices;
2155:     DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);
2156:     if (numindices>128) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many indices. %D > %D",numindices,128);
2157:     MatSetValues(Q,1,&ej,numindices,indices,ones,ADD_VALUES);
2158:     DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);
2159:   }
2160:   MatAssemblyBegin(Q, MAT_FINAL_ASSEMBLY);
2161:   MatAssemblyEnd(Q, MAT_FINAL_ASSEMBLY);
2162:   MatMatTransposeMult(Q,Q,MAT_INITIAL_MATRIX,4.0,&G);
2163:   PetscObjectSetName((PetscObject) Q, "Q");
2164:   PetscObjectSetName((PetscObject) G, "coloring graph");
2165:   MatViewFromOptions(G,NULL,"-coloring_mat_view");
2166:   MatViewFromOptions(Q,NULL,"-coloring_mat_view");
2167:   MatDestroy(&Q);
2168:   /* coloring */
2169:   MatColoringCreate(G,&mc);
2170:   MatColoringSetDistance(mc,1);
2171:   MatColoringSetType(mc,MATCOLORINGJP);
2172:   MatColoringSetFromOptions(mc);
2173:   MatColoringApply(mc,&iscoloring);
2174:   MatColoringDestroy(&mc);
2175:   /* view */
2176:   ISColoringViewFromOptions(iscoloring,NULL,"-coloring_is_view");
2177:   ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);
2178:   if (ctx && ctx->verbose > 2) {
2179:     PetscViewer    viewer;
2180:     Vec            color_vec, eidx_vec;
2181:     DMGetGlobalVector(colordm, &color_vec);
2182:     DMGetGlobalVector(colordm, &eidx_vec);
2183:     for (colour=0; colour<nc; colour++) {
2184:       ISGetLocalSize(is[colour],&csize);
2185:       ISGetIndices(is[colour],&indices);
2186:       for (j=0; j<csize; j++) {
2187:         PetscScalar v = (PetscScalar)colour;
2188:         k = indices[j];
2189:         VecSetValues(color_vec,1,&k,&v,INSERT_VALUES);
2190:         v = (PetscScalar)k;
2191:         VecSetValues(eidx_vec,1,&k,&v,INSERT_VALUES);
2192:       }
2193:       ISRestoreIndices(is[colour],&indices);
2194:     }
2195:     /* view */
2196:     PetscViewerVTKOpen(ctx->comm, "color.vtu", FILE_MODE_WRITE, &viewer);
2197:     PetscObjectSetName((PetscObject) color_vec, "color");
2198:     VecView(color_vec, viewer);
2199:     PetscViewerDestroy(&viewer);
2200:     PetscViewerVTKOpen(ctx->comm, "eidx.vtu", FILE_MODE_WRITE, &viewer);
2201:     PetscObjectSetName((PetscObject) eidx_vec, "element-idx");
2202:     VecView(eidx_vec, viewer);
2203:     PetscViewerDestroy(&viewer);
2204:     DMRestoreGlobalVector(colordm, &color_vec);
2205:     DMRestoreGlobalVector(colordm, &eidx_vec);
2206:   }
2207:   PetscSectionDestroy(&csection);
2208:   DMDestroy(&colordm);
2209:   ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);
2210:   MatDestroy(&G);
2211:   /* stash coloring */
2212:   PetscContainerCreate(PETSC_COMM_SELF, container);
2213:   PetscContainerSetPointer(*container,(void*)iscoloring);
2214:   PetscContainerSetUserDestroy(*container, destroy_coloring);
2215:   PetscObjectCompose((PetscObject)JacP,"coloring",(PetscObject)*container);
2216:   if (ctx && ctx->verbose > 0) {
2217:     PetscPrintf(ctx->comm, "Made coloring with %D colors\n", nc);
2218:   }
2219:   return(0);
2220: }

2222: PetscErrorCode LandauAssembleOpenMP(PetscInt cStart, PetscInt cEnd, PetscInt totDim, DM plex, PetscSection section, PetscSection globalSection, Mat JacP, PetscScalar elemMats[], PetscContainer container)
2223: {
2224:   PetscErrorCode  ierr;
2225:   IS             *is;
2226:   PetscInt        nc,colour,j;
2227:   const PetscInt *clr_idxs;
2228:   ISColoring      iscoloring;
2230:   PetscContainerGetPointer(container,(void**)&iscoloring);
2231:   ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);
2232:   for (colour=0; colour<nc; colour++) {
2233:     PetscInt    *idx_arr[1024]; /* need to make dynamic for general use */
2234:     PetscScalar *new_el_mats[1024];
2235:     PetscInt     idx_size[1024],csize;
2236:     ISGetLocalSize(is[colour],&csize);
2237:     if (csize>1024) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many elements in color. %D > %D",csize,1024);
2238:     ISGetIndices(is[colour],&clr_idxs);
2239:     /* get indices and mats */
2240:     for (j=0; j<csize; j++) {
2241:       PetscInt    cell = cStart + clr_idxs[j];
2242:       PetscInt    numindices,*indices;
2243:       PetscScalar *elMat = &elemMats[clr_idxs[j]*totDim*totDim];
2244:       PetscScalar *valuesOrig = elMat;
2245:       DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);
2246:       idx_size[j] = numindices;
2247:       PetscMalloc2(numindices,&idx_arr[j],numindices*numindices,&new_el_mats[j]);
2248:       PetscMemcpy(idx_arr[j],indices,numindices*sizeof(*idx_arr[j]));
2249:       PetscMemcpy(new_el_mats[j],elMat,numindices*numindices*sizeof(*new_el_mats[j]));
2250:       DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);
2251:       if (elMat != valuesOrig) {DMRestoreWorkArray(plex, numindices*numindices, MPIU_SCALAR, &elMat);}
2252:     }
2253:     /* assemble matrix */
2254:     for (j=0; j<csize; j++) {
2255:       PetscInt    numindices = idx_size[j], *indices = idx_arr[j];
2256:       PetscScalar *elMat = new_el_mats[j];
2257:       MatSetValues(JacP,numindices,indices,numindices,indices,elMat,ADD_VALUES);
2258:     }
2259:     /* free */
2260:     ISRestoreIndices(is[colour],&clr_idxs);
2261:     for (j=0; j<csize; j++) {
2262:       PetscFree2(idx_arr[j],new_el_mats[j]);
2263:     }
2264:   }
2265:   ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);
2266:   return(0);
2267: }

2269: /* < v, u > */
2270: static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux,
2271:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2272:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2273:                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
2274: {
2275:   g0[0] = 1.;
2276: }

2278: /* < v, u > */
2279: static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux,
2280:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2281:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2282:                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
2283: {
2284:   g0[0] = 2.*PETSC_PI*x[0];
2285: }

2287: /*@
2288:  LandauCreateMassMatrix - Create mass matrix for Landau

2290:  Collective on pack

2292:  Input Parameters:
2293:  . pack     - the DM object

2295:  Output Parameters:
2296:  . Amat - The mass matrix (optional), mass matrix is added to the DM context

2298:  Level: beginner

2300:  .keywords: mesh
2301:  .seealso: LandauCreateVelocitySpace()
2302:  @*/
2303: PetscErrorCode LandauCreateMassMatrix(DM pack, Mat *Amat)
2304: {
2305:   DM             mass_pack,massDM[LANDAU_MAX_GRIDS];
2306:   PetscDS        prob;
2307:   PetscInt       ii,dim,N1=1,N2;
2309:   LandauCtx      *ctx;
2310:   Mat            packM,subM[LANDAU_MAX_GRIDS];

2315:   DMGetApplicationContext(pack, &ctx);
2316:   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2317:   DMGetDimension(pack, &dim);
2318:   DMCompositeCreate(PetscObjectComm((PetscObject) pack),&mass_pack);
2319:   /* create pack mass matrix */
2320:   for (PetscInt grid=0, ix=0 ; grid<ctx->num_grids ; grid++) {
2321:     DMClone(ctx->plex[grid], &massDM[grid]);
2322:     DMCopyFields(ctx->plex[grid], massDM[grid]);
2323:     DMCreateDS(massDM[grid]);
2324:     DMGetDS(massDM[grid], &prob);
2325:     //for (ii=0;ii<ctx->num_species;ii++) {
2326:     for (ix=0, ii=ctx->species_offset[grid];ii<ctx->species_offset[grid+1];ii++,ix++) {
2327:       if (dim==3) {PetscDSSetJacobian(prob, ix, ix, g0_1, NULL, NULL, NULL);}
2328:       else        {PetscDSSetJacobian(prob, ix, ix, g0_r, NULL, NULL, NULL);}
2329:     }
2330:     DMCompositeAddDM(mass_pack,massDM[grid]);
2331:     DMCreateMatrix(massDM[grid], &subM[grid]);
2332:   }
2333:   PetscOptionsInsertString(NULL,"-dm_preallocate_only");
2334:   DMSetFromOptions(mass_pack);
2335:   DMCreateMatrix(mass_pack, &packM);
2336:   PetscOptionsInsertString(NULL,"-dm_preallocate_only false");
2337:   MatSetOption(packM, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);
2338:   MatSetOption(packM, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);
2339:   DMViewFromOptions(mass_pack,NULL,"-dm_landau_mass_dm_view");
2340:   DMDestroy(&mass_pack);
2341:   /* make mass matrix for each block */
2342:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
2343:     Vec locX;
2344:     DM  plex = massDM[grid];
2345:     DMGetLocalVector(plex, &locX);
2346:     /* Mass matrix is independent of the input, so no need to fill locX */
2347:     DMPlexSNESComputeJacobianFEM(plex, locX, subM[grid], subM[grid], ctx);
2348:     DMRestoreLocalVector(plex, &locX);
2349:     DMDestroy(&massDM[grid]);
2350:   }
2351:   MatGetSize(ctx->J, &N1, NULL);
2352:   MatGetSize(packM, &N2, NULL);
2353:   if (N1 != N2) SETERRQ2(PetscObjectComm((PetscObject) pack), PETSC_ERR_PLIB, "Incorrect matrix sizes: |Jacobian| = %D, |Mass|=%D",N1,N2);
2354:   /* assemble block diagonals */
2355:   ctx->mat_offset[0] = 0;
2356:   for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
2357:     PetscInt          nloc, nzl, colbuf[1024], row;
2358:     const PetscInt    *cols;
2359:     const PetscScalar *vals;
2360:     Mat               B = subM[grid];

2362:     MatGetSize(B, &nloc, NULL);
2363:     for (int i=0 ; i<nloc ; i++) {
2364:       MatGetRow(B,i,&nzl,&cols,&vals);
2365:       if (nzl>1024) SETERRQ1(PetscObjectComm((PetscObject) pack), PETSC_ERR_PLIB, "Row too big: %D",nzl);
2366:       for (int j=0; j<nzl; j++) colbuf[j] = cols[j] + ctx->mat_offset[grid];
2367:       row = i + ctx->mat_offset[grid];
2368:       MatSetValues(packM,1,&row,nzl,colbuf,vals,INSERT_VALUES);
2369:       MatRestoreRow(B,i,&nzl,&cols,&vals);
2370:     }
2371:     MatDestroy(&subM[grid]);
2372:     ctx->mat_offset[grid+1] = ctx->mat_offset[grid] + nloc;
2373:   }
2374:   MatAssemblyBegin(packM,MAT_FINAL_ASSEMBLY);
2375:   MatAssemblyEnd(packM,MAT_FINAL_ASSEMBLY);
2376:   PetscObjectSetName((PetscObject)packM, "mass");
2377:   MatViewFromOptions(packM,NULL,"-dm_landau_mass_view");
2378:   ctx->M = packM; /* this could be a noop, a = a */
2379:   if (Amat) *Amat = packM;
2380:   return(0);
2381: }

2383: /*@
2384:  LandauIFunction - TS residual calculation

2386:  Collective on ts

2388:  Input Parameters:
2389:  +   TS  - The time stepping context
2390:  .   time_dummy - current time (not used)
2391:  -   X - Current state
2392:  +   X_t - Time derivative of current state
2393:  .   actx - Landau context

2395:  Output Parameter:
2396:  .   F  - The residual

2398:  Level: beginner

2400:  .keywords: mesh
2401:  .seealso: LandauCreateVelocitySpace(), LandauIJacobian()
2402:  @*/
2403: PetscErrorCode LandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
2404: {
2406:   LandauCtx      *ctx=(LandauCtx*)actx;
2407:   PetscInt       dim;
2408:   DM             pack;
2409: #if defined(PETSC_HAVE_THREADSAFETY)
2410:   double         starttime, endtime;
2411: #endif

2414:   TSGetDM(ts,&pack);
2415:   DMGetApplicationContext(pack, &ctx);
2416:   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2417:   PetscLogEventBegin(ctx->events[11],0,0,0,0);
2418:   PetscLogEventBegin(ctx->events[0],0,0,0,0);
2419: #if defined(PETSC_HAVE_THREADSAFETY)
2420:   starttime = MPI_Wtime();
2421: #endif
2422:   DMGetDimension(pack, &dim);
2423:   if (!ctx->aux_bool) {
2424:     PetscInfo3(ts, "Create Landau Jacobian t=%g X=%p %s\n",time_dummy,X_t,ctx->aux_bool ? " -- seems to be in line search" : "");
2425:     LandauFormJacobian_Internal(X,ctx->J,dim,0.0,(void*)ctx);
2426:     MatViewFromOptions(ctx->J, NULL, "-dm_landau_jacobian_view");
2427:     ctx->aux_bool = PETSC_TRUE;
2428:   } else {
2429:     PetscInfo(ts, "Skip forming Jacobian, has not changed (should check norm)\n");
2430:   }
2431:   /* mat vec for op */
2432:   MatMult(ctx->J,X,F); /* C*f */
2433:   /* add time term */
2434:   if (X_t) {
2435:     MatMultAdd(ctx->M,X_t,F,F);
2436:   }
2437: #if defined(PETSC_HAVE_THREADSAFETY)
2438:   endtime = MPI_Wtime();
2439:   ctx->times[0] += (endtime - starttime);
2440: #endif
2441:   PetscLogEventEnd(ctx->events[0],0,0,0,0);
2442:   PetscLogEventEnd(ctx->events[11],0,0,0,0);
2443:   return(0);
2444: }
2445: static PetscErrorCode MatrixNfDestroy(void *ptr)
2446: {
2447:   PetscInt *nf = (PetscInt *)ptr;
2448:   PetscErrorCode  ierr;
2450:   PetscFree(nf);
2451:   return(0);
2452: }
2453: /*@
2454:  LandauIJacobian - TS Jacobian construction

2456:  Collective on ts

2458:  Input Parameters:
2459:  +   TS  - The time stepping context
2460:  .   time_dummy - current time (not used)
2461:  -   X - Current state
2462:  +   U_tdummy - Time derivative of current state (not used)
2463:  .   shift - shift for du/dt term
2464:  -   actx - Landau context

2466:  Output Parameter:
2467:  .   Amat  - Jacobian
2468:  +   Pmat  - same as Amat

2470:  Level: beginner

2472:  .keywords: mesh
2473:  .seealso: LandauCreateVelocitySpace(), LandauIFunction()
2474:  @*/
2475: PetscErrorCode LandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
2476: {
2478:   LandauCtx      *ctx=(LandauCtx*)actx;
2479:   PetscInt       dim;
2480:   DM             pack;
2481:   PetscContainer container;
2482: #if defined(PETSC_HAVE_THREADSAFETY)
2483:   double         starttime, endtime;
2484: #endif

2487:   TSGetDM(ts,&pack);
2488:   DMGetApplicationContext(pack, &ctx);
2489:   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2490:   if (Amat!=Pmat || Amat!=ctx->J) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Amat!=Pmat || Amat!=ctx->J");
2491:   DMGetDimension(pack, &dim);
2492:   /* get collision Jacobian into A */
2493:   PetscLogEventBegin(ctx->events[11],0,0,0,0);
2494:   PetscLogEventBegin(ctx->events[9],0,0,0,0);
2495: #if defined(PETSC_HAVE_THREADSAFETY)
2496:   starttime = MPI_Wtime();
2497: #endif
2498:   PetscInfo2(ts, "Adding just mass to Jacobian t=%g, shift=%g\n",(double)time_dummy,(double)shift);
2499:   if (shift==0.0) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "zero shift");
2500:   if (!ctx->aux_bool) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "wrong state");
2501:   if (!ctx->use_matrix_mass) {
2502:     LandauFormJacobian_Internal(X,ctx->J,dim,shift,(void*)ctx);
2503:     MatViewFromOptions(ctx->J, NULL, "-dm_landau_mat_view");
2504:   } else { /* add mass */
2505:     MatAXPY(Pmat,shift,ctx->M,SAME_NONZERO_PATTERN);
2506:   }
2507:   ctx->aux_bool = PETSC_FALSE;
2508:   /* set number species in Jacobian */
2509:   PetscObjectQuery((PetscObject) ctx->J, "Nf", (PetscObject *) &container);
2510:   if (!container) {
2511:     PetscInt *pNf;
2512:     PetscContainerCreate(PETSC_COMM_SELF, &container);
2513:     PetscMalloc(sizeof(*pNf), &pNf);
2514:     *pNf = ctx->num_species + 1000*ctx->numConcurrency;
2515:     PetscContainerSetPointer(container, (void *)pNf);
2516:     PetscContainerSetUserDestroy(container, MatrixNfDestroy);
2517:     PetscObjectCompose((PetscObject)ctx->J, "Nf", (PetscObject) container);
2518:     PetscContainerDestroy(&container);
2519:   }
2520: #if defined(PETSC_HAVE_THREADSAFETY)
2521:   endtime = MPI_Wtime();
2522:   ctx->times[0] += (endtime - starttime);
2523: #endif
2524:   PetscLogEventEnd(ctx->events[9],0,0,0,0);
2525:   PetscLogEventEnd(ctx->events[11],0,0,0,0);
2526:   return(0);
2527: }