Date: 2022-03-31T04:48:56+00:00

Actual source code: plexland.c

      1: #include <../src/mat/impls/aij/seq/aij.h>
      2: #include <petsc/private/dmpleximpl.h>
      3: #include <petsclandau.h>
      4: #include <petscts.h>
      5: #include <petscdmforest.h>
      6: #include <petscdmcomposite.h>

      8: /* Landau collision operator */

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

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

     22: #if defined(PETSC_HAVE_OPENMP)
     23: #include <omp.h>
     24: #endif

     26: /* vector padding not supported */
     27: #define LANDAU_VL  1

     29: static PetscErrorCode LandauMatMult(Mat A, Vec x, Vec y)
     30: {
     31:   LandauCtx       *ctx;
     32:   PetscContainer  container;

     34:   PetscObjectQuery((PetscObject) A, "LandauCtx", (PetscObject *) &container);
     35:   if (container) {
     36:     PetscContainerGetPointer(container, (void **) &ctx);
     37:     VecScatterBegin(ctx->plex_batch,x,ctx->work_vec,INSERT_VALUES,SCATTER_FORWARD);
     38:     VecScatterEnd(ctx->plex_batch,x,ctx->work_vec,INSERT_VALUES,SCATTER_FORWARD);
     39:     (*ctx->seqaij_mult)(A,ctx->work_vec,y);
     40:     VecCopy(y, ctx->work_vec);
     41:     VecScatterBegin(ctx->plex_batch,ctx->work_vec,y,INSERT_VALUES,SCATTER_REVERSE);
     42:     VecScatterEnd(ctx->plex_batch,ctx->work_vec,y,INSERT_VALUES,SCATTER_REVERSE);
     43:     return 0;
     44:   }
     45:   MatMult(A,x,y);
     46:   return 0;
     47: }

     49: // Computes v3 = v2 + A * v1.
     50: static PetscErrorCode LandauMatMultAdd(Mat A,Vec v1,Vec v2,Vec v3)
     51: {
     52:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "?????");
     53:   LandauMatMult(A,v1,v3);
     54:   VecAYPX(v3,1,v2);
     55:   return 0;
     56: }

     58: static PetscErrorCode LandauMatMultTranspose(Mat A, Vec x, Vec y)
     59: {
     60:   LandauCtx       *ctx;
     61:   PetscContainer  container;

     63:   PetscObjectQuery((PetscObject) A, "LandauCtx", (PetscObject *) &container);
     64:   if (container) {
     65:     PetscContainerGetPointer(container, (void **) &ctx);
     66:     VecScatterBegin(ctx->plex_batch,x,ctx->work_vec,INSERT_VALUES,SCATTER_FORWARD);
     67:     VecScatterEnd(ctx->plex_batch,x,ctx->work_vec,INSERT_VALUES,SCATTER_FORWARD);
     68:     (*ctx->seqaij_multtranspose)(A,ctx->work_vec,y);
     69:     VecCopy(y, ctx->work_vec);
     70:     VecScatterBegin(ctx->plex_batch,ctx->work_vec,y,INSERT_VALUES,SCATTER_REVERSE);
     71:     VecScatterEnd(ctx->plex_batch,ctx->work_vec,y,INSERT_VALUES,SCATTER_REVERSE);
     72:     return 0;
     73:   }
     74:   MatMultTranspose(A,x,y);
     75:   return 0;
     76: }

     78: static PetscErrorCode LandauMatGetDiagonal(Mat A,Vec x)
     79: {
     80:   LandauCtx       *ctx;
     81:   PetscContainer  container;

     83:   PetscObjectQuery((PetscObject) A, "LandauCtx", (PetscObject *) &container);
     84:   if (container) {
     85:     PetscContainerGetPointer(container, (void **) &ctx);
     86:     (*ctx->seqaij_getdiagonal)(A,ctx->work_vec);
     87:     VecScatterBegin(ctx->plex_batch,ctx->work_vec,x,INSERT_VALUES,SCATTER_REVERSE);
     88:     VecScatterEnd(ctx->plex_batch,ctx->work_vec,x,INSERT_VALUES,SCATTER_REVERSE);
     89:     return 0;
     90:   }
     91:   MatGetDiagonal(A, x);
     92:   return 0;
     93: }

     95: static PetscErrorCode LandauGPUMapsDestroy(void *ptr)
     96: {
     97:   P4estVertexMaps *maps = (P4estVertexMaps*)ptr;
     98:   // free device data
     99:   if (maps[0].deviceType != LANDAU_CPU) {
    100: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    101:     if (maps[0].deviceType == LANDAU_KOKKOS) {
    102:       LandauKokkosDestroyMatMaps(maps,  maps[0].numgrids); // imples Kokkos does
    103:     } // else could be CUDA
    104: #elif defined(PETSC_HAVE_CUDA)
    105:     if (maps[0].deviceType == LANDAU_CUDA) {
    106:       LandauCUDADestroyMatMaps(maps, maps[0].numgrids);
    107:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps->deviceType %" PetscInt_FMT " ?????",maps->deviceType);
    108: #endif
    109:   }
    110:   // free host data
    111:   for (PetscInt grid=0 ; grid < maps[0].numgrids ; grid++) {
    112:     PetscFree(maps[grid].c_maps);
    113:     PetscFree(maps[grid].gIdx);
    114:   }
    115:   PetscFree(maps);

    117:   return 0;
    118: }
    119: static PetscErrorCode energy_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
    120: {
    121:   PetscReal     v2 = 0;
    122:   /* compute v^2 / 2 */
    123:   for (int i = 0; i < dim; ++i) v2 += x[i]*x[i];
    124:   /* evaluate the Maxwellian */
    125:   u[0] = v2/2;
    126:   return 0;
    127: }

    129: /* needs double */
    130: static PetscErrorCode gamma_m1_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
    131: {
    132:   PetscReal     *c2_0_arr = ((PetscReal*)actx);
    133:   double        u2 = 0, c02 = (double)*c2_0_arr, xx;

    135:   /* compute u^2 / 2 */
    136:   for (int i = 0; i < dim; ++i) u2 += x[i]*x[i];
    137:   /* gamma - 1 = g_eps, for conditioning and we only take derivatives */
    138:   xx = u2/c02;
    139: #if defined(PETSC_USE_DEBUG)
    140:   u[0] = PetscSqrtReal(1. + xx);
    141: #else
    142:   u[0] = xx/(PetscSqrtReal(1. + xx) + 1.) - 1.; // better conditioned. -1 might help condition and only used for derivative
    143: #endif
    144:   return 0;
    145: }

    147: /*
    148:  LandauFormJacobian_Internal - Evaluates Jacobian matrix.

    150:  Input Parameters:
    151:  .  globX - input vector
    152:  .  actx - optional user-defined context
    153:  .  dim - dimension

    155:  Output Parameters:
    156:  .  J0acP - Jacobian matrix filled, not created
    157:  */
    158: static PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, PetscReal shift, void *a_ctx)
    159: {
    160:   LandauCtx         *ctx = (LandauCtx*)a_ctx;
    161:   PetscInt          numCells[LANDAU_MAX_GRIDS],Nq,Nb;
    162:   PetscQuadrature   quad;
    163:   PetscReal         Eq_m[LANDAU_MAX_SPECIES]; // could be static data w/o quench (ex2)
    164:   PetscScalar       *cellClosure=NULL;
    165:   const PetscScalar *xdata=NULL;
    166:   PetscDS           prob;
    167:   PetscContainer    container;
    168:   P4estVertexMaps   *maps;
    169:   Mat               subJ[LANDAU_MAX_GRIDS*LANDAU_MAX_BATCH_SZ];

    174:   /* check for matrix container for GPU assembly. Support CPU assembly for debugging */
    176:   PetscLogEventBegin(ctx->events[10],0,0,0,0);
    177:   DMGetDS(ctx->plex[0], &prob); // same DS for all grids
    178:   PetscObjectQuery((PetscObject) JacP, "assembly_maps", (PetscObject *) &container);
    179:   if (container) {
    181:     PetscContainerGetPointer(container, (void **) &maps);
    183:     for (PetscInt i=0;i<ctx->num_grids*ctx->batch_sz;i++) subJ[i] = NULL;
    184:   } else {
    186:     for (PetscInt tid=0 ; tid<ctx->batch_sz ; tid++) {
    187:       for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    188:         DMCreateMatrix(ctx->plex[grid], &subJ[ LAND_PACK_IDX(tid,grid) ]);
    189:       }
    190:     }
    191:     maps = NULL;
    192:   }
    193:   // get dynamic data (Eq is odd, for quench and Spitzer test) for CPU assembly and raw data for Jacobian GPU assembly. Get host numCells[], Nq (yuck)
    194:   PetscFEGetQuadrature(ctx->fe[0], &quad);
    195:   PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL); Nb = Nq;
    197:   // get metadata for collecting dynamic data
    198:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    199:     PetscInt cStart, cEnd;
    201:     DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
    202:     numCells[grid] = cEnd - cStart; // grids can have different topology
    203:   }
    204:   PetscLogEventEnd(ctx->events[10],0,0,0,0);
    205:   if (shift==0) { /* create dynamic point data: f_alpha for closure of each cell (cellClosure[nbatch,ngrids,ncells[g],f[Nb,ns[g]]]) or xdata */
    206:     DM pack;
    207:     VecGetDM(a_X, &pack);
    209:     PetscLogEventBegin(ctx->events[1],0,0,0,0);
    210:     MatZeroEntries(JacP);
    211:     for (PetscInt fieldA=0;fieldA<ctx->num_species;fieldA++) {
    212:       Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
    213:       if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
    214:     }
    215:     if (!ctx->gpu_assembly) {
    216:       Vec          *locXArray,*globXArray;
    217:       PetscScalar  *cellClosure_it;
    218:       PetscInt     cellClosure_sz=0,nDMs,Nf[LANDAU_MAX_GRIDS];
    219:       PetscSection section[LANDAU_MAX_GRIDS],globsection[LANDAU_MAX_GRIDS];
    220:       for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    221:         DMGetLocalSection(ctx->plex[grid], &section[grid]);
    222:         DMGetGlobalSection(ctx->plex[grid], &globsection[grid]);
    223:         PetscSectionGetNumFields(section[grid], &Nf[grid]);
    224:       }
    225:       /* count cellClosure size */
    226:       DMCompositeGetNumberDM(pack,&nDMs);
    227:       for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) cellClosure_sz += Nb*Nf[grid]*numCells[grid];
    228:       PetscMalloc1(cellClosure_sz*ctx->batch_sz,&cellClosure);
    229:       cellClosure_it = cellClosure;
    230:       PetscMalloc(sizeof(*locXArray)*nDMs, &locXArray);
    231:       PetscMalloc(sizeof(*globXArray)*nDMs, &globXArray);
    232:       DMCompositeGetLocalAccessArray(pack, a_X, nDMs, NULL, locXArray);
    233:       DMCompositeGetAccessArray(pack, a_X, nDMs, NULL, globXArray);
    234:       for (PetscInt b_id = 0 ; b_id < ctx->batch_sz ; b_id++) { // OpenMP (once)
    235:         for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
    236:           Vec         locX = locXArray[ LAND_PACK_IDX(b_id,grid) ], globX = globXArray[ LAND_PACK_IDX(b_id,grid) ], locX2;
    237:           PetscInt    cStart, cEnd, ei;
    238:           VecDuplicate(locX,&locX2);
    239:           DMGlobalToLocalBegin(ctx->plex[grid], globX, INSERT_VALUES, locX2);
    240:           DMGlobalToLocalEnd  (ctx->plex[grid], globX, INSERT_VALUES, locX2);
    241:           DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
    242:           for (ei = cStart ; ei < cEnd; ++ei) {
    243:             PetscScalar *coef = NULL;
    244:             DMPlexVecGetClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef);
    245:             PetscMemcpy(cellClosure_it,coef,Nb*Nf[grid]*sizeof(*cellClosure_it)); /* change if LandauIPReal != PetscScalar */
    246:             DMPlexVecRestoreClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef);
    247:             cellClosure_it += Nb*Nf[grid];
    248:           }
    249:           VecDestroy(&locX2);
    250:         }
    251:       }
    253:       DMCompositeRestoreLocalAccessArray(pack, a_X, nDMs, NULL, locXArray);
    254:       DMCompositeRestoreAccessArray(pack, a_X, nDMs, NULL, globXArray);
    255:       PetscFree(locXArray);
    256:       PetscFree(globXArray);
    257:       xdata = NULL;
    258:     } else {
    259:       PetscMemType mtype;
    260:       if (ctx->jacobian_field_major_order) { // get data in batch ordering
    261:         VecScatterBegin(ctx->plex_batch,a_X,ctx->work_vec,INSERT_VALUES,SCATTER_FORWARD);
    262:         VecScatterEnd(ctx->plex_batch,a_X,ctx->work_vec,INSERT_VALUES,SCATTER_FORWARD);
    263:         VecGetArrayReadAndMemType(ctx->work_vec,&xdata,&mtype);
    264:       } else {
    265:         VecGetArrayReadAndMemType(a_X,&xdata,&mtype);
    266:       }
    267:       if (mtype!=PETSC_MEMTYPE_HOST && ctx->deviceType == LANDAU_CPU) {
    268:         SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"CPU run with device data: use -mat_type aij");
    269:       }
    270:       cellClosure = NULL;
    271:     }
    272:     PetscLogEventEnd(ctx->events[1],0,0,0,0);
    273:   } else xdata = cellClosure = NULL;

    275:   /* do it */
    276:   if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
    277:     if (ctx->deviceType == LANDAU_CUDA) {
    278: #if defined(PETSC_HAVE_CUDA)
    279:       LandauCUDAJacobian(ctx->plex,Nq,ctx->batch_sz,ctx->num_grids,numCells,Eq_m,cellClosure,xdata,&ctx->SData_d,shift,ctx->events,ctx->mat_offset, ctx->species_offset, subJ, JacP);
    280: #else
    281:       SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
    282: #endif
    283:     } else if (ctx->deviceType == LANDAU_KOKKOS) {
    284: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    285:       LandauKokkosJacobian(ctx->plex,Nq,ctx->batch_sz,ctx->num_grids,numCells,Eq_m,cellClosure,xdata,&ctx->SData_d,shift,ctx->events,ctx->mat_offset, ctx->species_offset, subJ,JacP);
    286: #else
    287:       SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
    288: #endif
    289:     }
    290:   } else {   /* CPU version */
    291:     PetscTabulation *Tf; // used for CPU and print info. Same on all grids and all species
    292:     PetscInt        ip_offset[LANDAU_MAX_GRIDS+1], ipf_offset[LANDAU_MAX_GRIDS+1], elem_offset[LANDAU_MAX_GRIDS+1],IPf_sz_glb,IPf_sz_tot,num_grids=ctx->num_grids,Nf[LANDAU_MAX_GRIDS];
    293:     PetscReal       *ff, *dudx, *dudy, *dudz, *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;
    294:     PetscReal       Eq_m[LANDAU_MAX_SPECIES], invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
    295:     PetscSection    section[LANDAU_MAX_GRIDS],globsection[LANDAU_MAX_GRIDS];
    296:     PetscScalar     *coo_vals=NULL;
    297:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    298:       DMGetLocalSection(ctx->plex[grid], &section[grid]);
    299:       DMGetGlobalSection(ctx->plex[grid], &globsection[grid]);
    300:       PetscSectionGetNumFields(section[grid], &Nf[grid]);
    301:     }
    302:     /* count IPf size, etc */
    303:     PetscDSGetTabulation(prob, &Tf); // Bf, &Df same for all grids
    304:     const PetscReal *const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
    305:     ip_offset[0] = ipf_offset[0] = elem_offset[0] = 0;
    306:     for (PetscInt grid=0 ; grid<num_grids ; grid++) {
    307:       PetscInt nfloc = ctx->species_offset[grid+1] - ctx->species_offset[grid];
    308:       elem_offset[grid+1] = elem_offset[grid] + numCells[grid];
    309:       ip_offset[grid+1]   = ip_offset[grid]   + numCells[grid]*Nq;
    310:       ipf_offset[grid+1]  = ipf_offset[grid]  + Nq*nfloc*numCells[grid];
    311:     }
    312:     IPf_sz_glb = ipf_offset[num_grids];
    313:     IPf_sz_tot = IPf_sz_glb*ctx->batch_sz;
    314:     // prep COO
    315:     if (ctx->coo_assembly) {
    316:       PetscMalloc1(ctx->SData_d.coo_size,&coo_vals); // allocate every time?
    317:       PetscInfo(ctx->plex[0], "COO Allocate %" PetscInt_FMT " values\n",ctx->SData_d.coo_size);
    318:     }
    319:     if (shift==0.0) { /* compute dynamic data f and df and init data for Jacobian */
    320: #if defined(PETSC_HAVE_THREADSAFETY)
    321:       double         starttime, endtime;
    322:       starttime = MPI_Wtime();
    323: #endif
    324:       PetscLogEventBegin(ctx->events[8],0,0,0,0);
    325:       for (PetscInt fieldA=0;fieldA<ctx->num_species;fieldA++) {
    326:         invMass[fieldA]  = ctx->m_0/ctx->masses[fieldA];
    327:         Eq_m[fieldA]     = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
    328:         if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
    329:         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/ctx->m_0)*ctx->m_0/ctx->masses[fieldA];
    330:         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);
    331:       }
    332:       PetscMalloc4(IPf_sz_tot, &ff, IPf_sz_tot, &dudx, IPf_sz_tot, &dudy, dim==3 ? IPf_sz_tot : 0, &dudz);
    333:       // F df/dx
    334:       for (PetscInt tid = 0 ; tid < ctx->batch_sz*elem_offset[num_grids] ; tid++) { // for each element
    335:         const PetscInt b_Nelem = elem_offset[num_grids], b_elem_idx = tid%b_Nelem, b_id = tid/b_Nelem; // b_id == OMP thd_id in batch
    336:         // find my grid:
    337:         PetscInt       grid = 0;
    338:         while (b_elem_idx >= elem_offset[grid+1]) grid++; // yuck search for grid
    339:         {
    340:           const PetscInt     loc_nip = numCells[grid]*Nq, loc_Nf = ctx->species_offset[grid+1] - ctx->species_offset[grid], loc_elem = b_elem_idx - elem_offset[grid];
    341:           const PetscInt     moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset); //b_id*b_N + ctx->mat_offset[grid];
    342:           PetscScalar        *coef, coef_buff[LANDAU_MAX_SPECIES*LANDAU_MAX_NQ];
    343:           PetscReal          *invJe  = &invJ_a[(ip_offset[grid] + loc_elem*Nq)*dim*dim]; // ingJ is static data on batch 0
    344:           PetscInt           b,f,q;
    345:           if (cellClosure) {
    346:             coef = &cellClosure[b_id*IPf_sz_glb + ipf_offset[grid] + loc_elem*Nb*loc_Nf]; // this is const
    347:           } else {
    348:             coef = coef_buff;
    349:             for (f = 0; f < loc_Nf; ++f) {
    350:               LandauIdx *const Idxs = &maps[grid].gIdx[loc_elem][f][0];
    351:               for (b = 0; b < Nb; ++b) {
    352:                 PetscInt idx = Idxs[b];
    353:                 if (idx >= 0) {
    354:                   coef[f*Nb+b] = xdata[idx+moffset];
    355:                 } else {
    356:                   idx = -idx - 1;
    357:                   coef[f*Nb+b] = 0;
    358:                   for (q = 0; q < maps[grid].num_face; q++) {
    359:                     PetscInt    id    = maps[grid].c_maps[idx][q].gid;
    360:                     PetscScalar scale = maps[grid].c_maps[idx][q].scale;
    361:                     coef[f*Nb+b] += scale*xdata[id+moffset];
    362:                   }
    363:                 }
    364:               }
    365:             }
    366:           }
    367:           /* get f and df */
    368:           for (PetscInt qi = 0; qi < Nq; qi++) {
    369:             const PetscReal  *invJ = &invJe[qi*dim*dim];
    370:             const PetscReal  *Bq   = &BB[qi*Nb];
    371:             const PetscReal  *Dq   = &DD[qi*Nb*dim];
    372:             PetscReal        u_x[LANDAU_DIM];
    373:             /* get f & df */
    374:             for (f = 0; f < loc_Nf; ++f) {
    375:               const PetscInt idx = b_id*IPf_sz_glb + ipf_offset[grid] + f*loc_nip + loc_elem*Nq + qi;
    376:               PetscInt       b, e;
    377:               PetscReal      refSpaceDer[LANDAU_DIM];
    378:               ff[idx] = 0.0;
    379:               for (int d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
    380:               for (b = 0; b < Nb; ++b) {
    381:                 const PetscInt    cidx = b;
    382:                 ff[idx] += Bq[cidx]*PetscRealPart(coef[f*Nb+cidx]);
    383:                 for (int d = 0; d < dim; ++d) {
    384:                   refSpaceDer[d] += Dq[cidx*dim+d]*PetscRealPart(coef[f*Nb+cidx]);
    385:                 }
    386:               }
    387:               for (int d = 0; d < LANDAU_DIM; ++d) {
    388:                 for (e = 0, u_x[d] = 0.0; e < LANDAU_DIM; ++e) {
    389:                   u_x[d] += invJ[e*dim+d]*refSpaceDer[e];
    390:                 }
    391:               }
    392:               dudx[idx] = u_x[0];
    393:               dudy[idx] = u_x[1];
    394:  #if LANDAU_DIM==3
    395:               dudz[idx] = u_x[2];
    396: #endif
    397:             }
    398:           } // q
    399:         } // grid
    400:       } // grid*batch
    401:       PetscLogEventEnd(ctx->events[8],0,0,0,0);
    402: #if defined(PETSC_HAVE_THREADSAFETY)
    403:       endtime = MPI_Wtime();
    404:       if (ctx->stage) ctx->times[LANDAU_F_DF] += (endtime - starttime);
    405: #endif
    406:     } // Jacobian setup
    407:     // assemble Jacobian (or mass)
    408:     for (PetscInt tid = 0 ; tid < ctx->batch_sz*elem_offset[num_grids] ; tid++) { // for each element
    409:       const PetscInt b_Nelem      = elem_offset[num_grids];
    410:       const PetscInt glb_elem_idx = tid%b_Nelem, b_id = tid/b_Nelem;
    411:       PetscInt       grid         = 0;
    412: #if defined(PETSC_HAVE_THREADSAFETY)
    413:       double         starttime, endtime;
    414:       starttime                   = MPI_Wtime();
    415: #endif
    416:       while (glb_elem_idx >= elem_offset[grid+1]) grid++;
    417:       {
    418:         const PetscInt     loc_Nf  = ctx->species_offset[grid+1] - ctx->species_offset[grid], loc_elem = glb_elem_idx - elem_offset[grid];
    419:         const PetscInt     moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset), totDim = loc_Nf*Nq, elemMatSize = totDim*totDim;
    420:         PetscScalar        *elemMat;
    421:          const PetscReal   *invJe  = &invJ_a[(ip_offset[grid] + loc_elem*Nq)*dim*dim];
    422:         PetscMalloc1(elemMatSize, &elemMat);
    423:         PetscMemzero(elemMat, elemMatSize*sizeof(*elemMat));
    424:         if (shift==0.0) { // Jacobian
    425:           PetscLogEventBegin(ctx->events[4],0,0,0,0);
    426:         } else {          // mass
    427:           PetscLogEventBegin(ctx->events[16],0,0,0,0);
    428:         }
    429:         for (PetscInt qj = 0; qj < Nq; ++qj) {
    430:           const PetscInt   jpidx_glb = ip_offset[grid] + qj + loc_elem * Nq;
    431:           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
    432:           PetscInt         d,d2,dp,d3,IPf_idx;
    433:           if (shift==0.0) { // Jacobian
    434:             const PetscReal * const invJj = &invJe[qj*dim*dim];
    435:             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];
    436:             const PetscReal         vj[3] = {xx[jpidx_glb], yy[jpidx_glb], zz ? zz[jpidx_glb] : 0}, wj = ww[jpidx_glb];
    437:             // create g2 & g3
    438:             for (d=0;d<LANDAU_DIM;d++) { // clear accumulation data D & K
    439:               gg2_temp[d] = 0;
    440:               for (d2=0;d2<LANDAU_DIM;d2++) gg3_temp[d][d2] = 0;
    441:             }
    442:             /* inner beta reduction */
    443:             IPf_idx = 0;
    444:             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_r*Nfloc_r
    445:               PetscInt  nip_loc_r = numCells[grid_r]*Nq, Nfloc_r = Nf[grid_r];
    446:               for (PetscInt ei_r = 0, loc_fdf_idx = 0; ei_r < numCells[grid_r]; ++ei_r) {
    447:                 for (PetscInt qi = 0; qi < Nq; qi++, ipidx++, loc_fdf_idx++) {
    448:                   const PetscReal wi       = ww[ipidx], x = xx[ipidx], y = yy[ipidx];
    449:                   PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
    450: #if LANDAU_DIM==2
    451:                   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.;
    452:                   LandauTensor2D(vj, x, y, Ud, Uk, mask);
    453: #else
    454:                   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.;
    455:                   if (ctx->use_relativistic_corrections) {
    456:                     LandauTensor3DRelativistic(vj, x, y, z, U, mask, C_0(ctx->v_0));
    457:                   } else {
    458:                     LandauTensor3D(vj, x, y, z, U, mask);
    459:                   }
    460: #endif
    461:                   for (int f = 0; f < Nfloc_r ; ++f) {
    462:                     const PetscInt idx = b_id*IPf_sz_glb + ipf_offset[grid_r] + f*nip_loc_r + ei_r*Nq + qi;  // IPf_idx + f*nip_loc_r + loc_fdf_idx;
    463:                     temp1[0] += dudx[idx]*nu_beta[f+f_off]*invMass[f+f_off];
    464:                     temp1[1] += dudy[idx]*nu_beta[f+f_off]*invMass[f+f_off];
    465: #if LANDAU_DIM==3
    466:                     temp1[2] += dudz[idx]*nu_beta[f+f_off]*invMass[f+f_off];
    467: #endif
    468:                     temp2    += ff[idx]*nu_beta[f+f_off];
    469:                   }
    470:                   temp1[0] *= wi;
    471:                   temp1[1] *= wi;
    472: #if LANDAU_DIM==3
    473:                   temp1[2] *= wi;
    474: #endif
    475:                   temp2    *= wi;
    476: #if LANDAU_DIM==2
    477:                   for (d2 = 0; d2 < 2; d2++) {
    478:                     for (d3 = 0; d3 < 2; ++d3) {
    479:                       /* K = U * grad(f): g2=e: i,A */
    480:                       gg2_temp[d2] += Uk[d2][d3]*temp1[d3];
    481:                       /* D = -U * (I \kron (fx)): g3=f: i,j,A */
    482:                       gg3_temp[d2][d3] += Ud[d2][d3]*temp2;
    483:                     }
    484:                   }
    485: #else
    486:                   for (d2 = 0; d2 < 3; ++d2) {
    487:                     for (d3 = 0; d3 < 3; ++d3) {
    488:                       /* K = U * grad(f): g2 = e: i,A */
    489:                       gg2_temp[d2] += U[d2][d3]*temp1[d3];
    490:                       /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
    491:                       gg3_temp[d2][d3] += U[d2][d3]*temp2;
    492:                     }
    493:                   }
    494: #endif
    495:                 } // qi
    496:               } // ei_r
    497:               IPf_idx += nip_loc_r*Nfloc_r;
    498:             } /* grid_r - IPs */
    500:             // add alpha and put in gg2/3
    501:             for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid]; fieldA < loc_Nf; ++fieldA) {
    502:               for (d2 = 0; d2 < dim; d2++) {
    503:                 gg2[fieldA][d2] = gg2_temp[d2]*nu_alpha[fieldA+f_off];
    504:                 for (d3 = 0; d3 < dim; d3++) {
    505:                   gg3[fieldA][d2][d3] = -gg3_temp[d2][d3]*nu_alpha[fieldA+f_off]*invMass[fieldA+f_off];
    506:                 }
    507:               }
    508:             }
    509:             /* add electric field term once per IP */
    510:             for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid] ; fieldA < loc_Nf; ++fieldA) {
    511:               gg2[fieldA][dim-1] += Eq_m[fieldA+f_off];
    512:             }
    513:             /* Jacobian transform - g2, g3 */
    514:             for (PetscInt fieldA = 0; fieldA < loc_Nf; ++fieldA) {
    515:               for (d = 0; d < dim; ++d) {
    516:                 g2[fieldA][d] = 0.0;
    517:                 for (d2 = 0; d2 < dim; ++d2) {
    518:                   g2[fieldA][d] += invJj[d*dim+d2]*gg2[fieldA][d2];
    519:                   g3[fieldA][d][d2] = 0.0;
    520:                   for (d3 = 0; d3 < dim; ++d3) {
    521:                     for (dp = 0; dp < dim; ++dp) {
    522:                       g3[fieldA][d][d2] += invJj[d*dim + d3]*gg3[fieldA][d3][dp]*invJj[d2*dim + dp];
    523:                     }
    524:                   }
    525:                   g3[fieldA][d][d2] *= wj;
    526:                 }
    527:                 g2[fieldA][d] *= wj;
    528:               }
    529:             }
    530:           } else { // mass
    531:             PetscReal wj = ww[jpidx_glb];
    532:             /* Jacobian transform - g0 */
    533:             for (PetscInt fieldA = 0; fieldA < loc_Nf ; ++fieldA) {
    534:               if (dim==2) {
    535:                 g0[fieldA] = wj * shift * 2. * PETSC_PI; // move this to below and remove g0
    536:               } else {
    537:                 g0[fieldA] = wj * shift; // move this to below and remove g0
    538:               }
    539:             }
    540:           }
    541:           /* FE matrix construction */
    542:           {
    543:             PetscInt  fieldA,d,f,d2,g;
    544:             const PetscReal *BJq = &BB[qj*Nb], *DIq = &DD[qj*Nb*dim];
    545:             /* assemble - on the diagonal (I,I) */
    546:             for (fieldA = 0; fieldA < loc_Nf ; fieldA++) {
    547:               for (f = 0; f < Nb ; f++) {
    548:                 const PetscInt i = fieldA*Nb + f; /* Element matrix row */
    549:                 for (g = 0; g < Nb; ++g) {
    550:                   const PetscInt j    = fieldA*Nb + g; /* Element matrix column */
    551:                   const PetscInt fOff = i*totDim + j;
    552:                   if (shift==0.0) {
    553:                     for (d = 0; d < dim; ++d) {
    554:                       elemMat[fOff] += DIq[f*dim+d]*g2[fieldA][d]*BJq[g];
    555:                       for (d2 = 0; d2 < dim; ++d2) {
    556:                         elemMat[fOff] += DIq[f*dim + d]*g3[fieldA][d][d2]*DIq[g*dim + d2];
    557:                       }
    558:                     }
    559:                   } else { // mass
    560:                     elemMat[fOff] += BJq[f]*g0[fieldA]*BJq[g];
    561:                   }
    562:                 }
    563:               }
    564:             }
    565:           }
    566:         } /* qj loop */
    567:         if (shift==0.0) { // Jacobian
    568:           PetscLogEventEnd(ctx->events[4],0,0,0,0);
    569:         } else {
    570:           PetscLogEventEnd(ctx->events[16],0,0,0,0);
    571:         }
    572: #if defined(PETSC_HAVE_THREADSAFETY)
    573:         endtime = MPI_Wtime();
    574:         if (ctx->stage) ctx->times[LANDAU_KERNEL] += (endtime - starttime);
    575: #endif
    576:         /* assemble matrix */
    577:         if (!container) {
    578:           PetscInt cStart;
    579:           PetscLogEventBegin(ctx->events[6],0,0,0,0);
    580:           DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, NULL);
    581:           DMPlexMatSetClosure(ctx->plex[grid], section[grid], globsection[grid], subJ[ LAND_PACK_IDX(b_id,grid) ], loc_elem + cStart, elemMat, ADD_VALUES);
    582:           PetscLogEventEnd(ctx->events[6],0,0,0,0);
    583:         } else {  // GPU like assembly for debugging
    584:           PetscInt      fieldA,q,f,g,d,nr,nc,rows0[LANDAU_MAX_Q_FACE]={0},cols0[LANDAU_MAX_Q_FACE]={0},rows[LANDAU_MAX_Q_FACE],cols[LANDAU_MAX_Q_FACE];
    585:           PetscScalar   vals[LANDAU_MAX_Q_FACE*LANDAU_MAX_Q_FACE]={0},row_scale[LANDAU_MAX_Q_FACE]={0},col_scale[LANDAU_MAX_Q_FACE]={0};
    586:           LandauIdx     *coo_elem_offsets = (LandauIdx*)ctx->SData_d.coo_elem_offsets, *coo_elem_fullNb = (LandauIdx*)ctx->SData_d.coo_elem_fullNb, (*coo_elem_point_offsets)[LANDAU_MAX_NQ+1] = (LandauIdx (*)[LANDAU_MAX_NQ+1])ctx->SData_d.coo_elem_point_offsets;
    587:           /* assemble - from the diagonal (I,I) in this format for DMPlexMatSetClosure */
    588:           for (fieldA = 0; fieldA < loc_Nf ; fieldA++) {
    589:             LandauIdx *const Idxs = &maps[grid].gIdx[loc_elem][fieldA][0];
    590:             for (f = 0; f < Nb ; f++) {
    591:               PetscInt idx = Idxs[f];
    592:               if (idx >= 0) {
    593:                 nr           = 1;
    594:                 rows0[0]     = idx;
    595:                 row_scale[0] = 1.;
    596:               } else {
    597:                 idx = -idx - 1;
    598:                 for (q = 0, nr = 0; q < maps[grid].num_face; q++, nr++) {
    599:                   if (maps[grid].c_maps[idx][q].gid < 0) break;
    600:                   rows0[q]     = maps[grid].c_maps[idx][q].gid;
    601:                   row_scale[q] = maps[grid].c_maps[idx][q].scale;
    602:                 }
    603:               }
    604:               for (g = 0; g < Nb; ++g) {
    605:                 idx = Idxs[g];
    606:                 if (idx >= 0) {
    607:                   nc = 1;
    608:                   cols0[0]     = idx;
    609:                   col_scale[0] = 1.;
    610:                 } else {
    611:                   idx = -idx - 1;
    612:                   nc = maps[grid].num_face;
    613:                   for (q = 0, nc = 0; q < maps[grid].num_face; q++, nc++) {
    614:                     if (maps[grid].c_maps[idx][q].gid < 0) break;
    615:                     cols0[q]     = maps[grid].c_maps[idx][q].gid;
    616:                     col_scale[q] = maps[grid].c_maps[idx][q].scale;
    617:                   }
    618:                 }
    619:                 const PetscInt    i   = fieldA*Nb + f; /* Element matrix row */
    620:                 const PetscInt    j   = fieldA*Nb + g; /* Element matrix column */
    621:                 const PetscScalar Aij = elemMat[i*totDim + j];
    622:                 if (coo_vals) { // mirror (i,j) in CreateStaticGPUData
    623:                   const int fullNb = coo_elem_fullNb[glb_elem_idx],fullNb2=fullNb*fullNb;
    624:                   const int idx0   = b_id*coo_elem_offsets[elem_offset[num_grids]] + coo_elem_offsets[glb_elem_idx] + fieldA*fullNb2 + fullNb * coo_elem_point_offsets[glb_elem_idx][f] + nr * coo_elem_point_offsets[glb_elem_idx][g];
    625:                   for (int q = 0, idx2 = idx0; q < nr; q++) {
    626:                     for (int d = 0; d < nc; d++, idx2++) {
    627:                       coo_vals[idx2] = row_scale[q]*col_scale[d]*Aij;
    628:                     }
    629:                   }
    630:                 } else {
    631:                   for (q = 0; q < nr; q++) rows[q] = rows0[q] + moffset;
    632:                   for (d = 0; d < nc; d++) cols[d] = cols0[d] + moffset;
    633:                   for (q = 0; q < nr; q++) {
    634:                     for (d = 0; d < nc; d++) {
    635:                       vals[q*nc + d] = row_scale[q]*col_scale[d]*Aij;
    636:                     }
    637:                   }
    638:                   MatSetValues(JacP,nr,rows,nc,cols,vals,ADD_VALUES);
    639:                 }
    640:               }
    641:             }
    642:           }
    643:         }
    644:         if (loc_elem==-1) {
    645:           PetscPrintf(ctx->comm,"CPU Element matrix\n");
    646:           for (int d = 0; d < totDim; ++d) {
    647:             for (int f = 0; f < totDim; ++f) PetscPrintf(ctx->comm," %12.5e",  PetscRealPart(elemMat[d*totDim + f]));
    648:             PetscPrintf(ctx->comm,"\n");
    649:           }
    650:           exit(12);
    651:         }
    652:         PetscFree(elemMat);
    653:       } /* grid */
    654:     } /* outer element & batch loop */
    655:     if (shift==0.0) { // mass
    656:       PetscFree4(ff, dudx, dudy, dudz);
    657:     }
    658:     if (!container) {   // 'CPU' assembly move nest matrix to global JacP
    659:       for (PetscInt b_id = 0 ; b_id < ctx->batch_sz ; b_id++) { // OpenMP
    660:         for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
    661:           const PetscInt    moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset); // b_id*b_N + ctx->mat_offset[grid];
    662:           PetscInt          nloc, nzl, colbuf[1024], row;
    663:           const PetscInt    *cols;
    664:           const PetscScalar *vals;
    665:           Mat               B = subJ[ LAND_PACK_IDX(b_id,grid) ];
    666:           MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
    667:           MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
    668:           MatGetSize(B, &nloc, NULL);
    669:           for (int i=0 ; i<nloc ; i++) {
    670:             MatGetRow(B,i,&nzl,&cols,&vals);
    672:             for (int j=0; j<nzl; j++) colbuf[j] = moffset + cols[j];
    673:             row  = moffset + i;
    674:             MatSetValues(JacP,1,&row,nzl,colbuf,vals,ADD_VALUES);
    675:             MatRestoreRow(B,i,&nzl,&cols,&vals);
    676:           }
    677:           MatDestroy(&B);
    678:         }
    679:       }
    680:     }
    681:     if (coo_vals) {
    682:       MatSetValuesCOO(JacP,coo_vals,ADD_VALUES);
    683:       PetscFree(coo_vals);
    684:     }
    685:   } /* CPU version */
    686:   MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);
    687:   MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);
    688:   /* clean up */
    689:   if (cellClosure) {
    690:     PetscFree(cellClosure);
    691:   }
    692:   if (xdata) {
    693:     VecRestoreArrayReadAndMemType(a_X,&xdata);
    694:   }
    695:   return 0;
    696: }

    698: #if defined(LANDAU_ADD_BCS)
    699: static void zero_bc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    700:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    701:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    702:                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
    703: {
    704:   uexact[0] = 0;
    705: }
    706: #endif

    708: #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]; }}
    709: static void CircleInflate(PetscReal r1, PetscReal r2, PetscReal r0, PetscInt num_sections, PetscReal x, PetscReal y,
    710:                           PetscReal *outX, PetscReal *outY)
    711: {
    712:   PetscReal rr = PetscSqrtReal(x*x + y*y), outfact, efact;
    713:   if (rr < r1 + PETSC_SQRT_MACHINE_EPSILON) {
    714:     *outX = x; *outY = y;
    715:   } else {
    716:     const PetscReal xy[2] = {x,y}, sinphi=y/rr, cosphi=x/rr;
    717:     PetscReal       cth,sth,xyprime[2],Rth[2][2],rotcos,newrr;
    718:     if (num_sections==2) {
    719:       rotcos  = 0.70710678118654;
    720:       outfact = 1.5; efact = 2.5;
    721:       /* rotate normalized vector into [-pi/4,pi/4) */
    722:       if (sinphi >= 0.) {         /* top cell, -pi/2 */
    723:         cth = 0.707106781186548; sth = -0.707106781186548;
    724:       } else {                    /* bottom cell -pi/8 */
    725:         cth = 0.707106781186548; sth = .707106781186548;
    726:       }
    727:     } else if (num_sections==3) {
    728:       rotcos  = 0.86602540378443;
    729:       outfact = 1.5; efact = 2.5;
    730:       /* rotate normalized vector into [-pi/6,pi/6) */
    731:       if (sinphi >= 0.5) {         /* top cell, -pi/3 */
    732:         cth = 0.5; sth = -0.866025403784439;
    733:       } else if (sinphi >= -.5) {  /* mid cell 0 */
    734:         cth = 1.; sth = .0;
    735:       } else { /* bottom cell +pi/3 */
    736:         cth = 0.5; sth = 0.866025403784439;
    737:       }
    738:     } else if (num_sections==4) {
    739:       rotcos  = 0.9238795325112;
    740:       outfact = 1.5; efact = 3;
    741:       /* rotate normalized vector into [-pi/8,pi/8) */
    742:       if (sinphi >= 0.707106781186548) {         /* top cell, -3pi/8 */
    743:         cth = 0.38268343236509;  sth = -0.923879532511287;
    744:       } else if (sinphi >= 0.) {                 /* mid top cell -pi/8 */
    745:         cth = 0.923879532511287; sth = -.38268343236509;
    746:       } else if (sinphi >= -0.707106781186548) { /* mid bottom cell + pi/8 */
    747:         cth = 0.923879532511287; sth = 0.38268343236509;
    748:       } else {                                   /* bottom cell + 3pi/8 */
    749:         cth = 0.38268343236509;  sth = .923879532511287;
    750:       }
    751:     } else {
    752:       cth = 0.; sth = 0.; rotcos = 0; efact = 0;
    753:     }
    754:     Rth[0][0] = cth; Rth[0][1] =-sth;
    755:     Rth[1][0] = sth; Rth[1][1] = cth;
    756:     MATVEC2(Rth,xy,xyprime);
    757:     if (num_sections==2) {
    758:       newrr = xyprime[0]/rotcos;
    759:     } else {
    760:       PetscReal newcosphi=xyprime[0]/rr, rin = r1, rout = rr - rin;
    761:       PetscReal routmax = r0*rotcos/newcosphi - rin, nroutmax = r0 - rin, routfrac = rout/routmax;
    762:       newrr = rin + routfrac*nroutmax;
    763:     }
    764:     *outX = cosphi*newrr; *outY = sinphi*newrr;
    765:     /* grade */
    766:     PetscReal fact,tt,rs,re, rr = PetscSqrtReal(PetscSqr(*outX) + PetscSqr(*outY));
    767:     if (rr > r2) { rs = r2; re = r0; fact = outfact;} /* outer zone */
    768:     else {         rs = r1; re = r2; fact = efact;} /* electron zone */
    769:     tt = (rs + PetscPowReal((rr - rs)/(re - rs),fact) * (re-rs)) / rr;
    770:     *outX *= tt;
    771:     *outY *= tt;
    772:   }
    773: }

    775: static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
    776: {
    777:   LandauCtx   *ctx = (LandauCtx*)a_ctx;
    778:   PetscReal   r = abc[0], z = abc[1];
    779:   if (ctx->inflate) {
    780:     PetscReal absR, absZ;
    781:     absR = PetscAbs(r);
    782:     absZ = PetscAbs(z);
    783:     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?
    784:     r = (r > 0) ? absR : -absR;
    785:     z = (z > 0) ? absZ : -absZ;
    786:   }
    787:   xyz[0] = r;
    788:   xyz[1] = z;
    789:   if (dim==3) xyz[2] = abc[2];

    791:   return 0;
    792: }

    794: /* create DMComposite of meshes for each species group */
    795: static PetscErrorCode LandauDMCreateVMeshes(MPI_Comm comm_self, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM pack)
    796: {
    797:   { /* p4est, quads */
    798:     /* Create plex mesh of Landau domain */
    799:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    800:       PetscReal radius = ctx->radius[grid];
    801:       if (!ctx->sphere) {
    802:         PetscInt       cells[] = {2,2,2};
    803:         PetscReal      lo[] = {-radius,-radius,-radius}, hi[] = {radius,radius,radius};
    804:         DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim==2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
    805:         if (dim==2) { lo[0] = 0; cells[0] /* = cells[1] */ = 1; }
    806:         DMPlexCreateBoxMesh(comm_self, dim, PETSC_FALSE, cells, lo, hi, periodicity, PETSC_TRUE, &ctx->plex[grid]); // todo: make composite and create dm[grid] here
    807:         DMLocalizeCoordinates(ctx->plex[grid]); /* needed for periodic */
    808:         if (dim==3) PetscObjectSetName((PetscObject) ctx->plex[grid], "cube");
    809:         else PetscObjectSetName((PetscObject) ctx->plex[grid], "half-plane");
    810:       } else if (dim==2) { // sphere is all wrong. should just have one inner radius
    811:         PetscInt       numCells,cells[16][4],i,j;
    812:         PetscInt       numVerts;
    813:         PetscReal      inner_radius1 = ctx->i_radius[grid], inner_radius2 = ctx->e_radius;
    814:         PetscReal      *flatCoords   = NULL;
    815:         PetscInt       *flatCells    = NULL, *pcell;
    816:         if (ctx->num_sections==2) {
    817: #if 1
    818:           numCells = 5;
    819:           numVerts = 10;
    820:           int cells2[][4] = { {0,1,4,3},
    821:                               {1,2,5,4},
    822:                               {3,4,7,6},
    823:                               {4,5,8,7},
    824:                               {6,7,8,9} };
    825:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
    826:           PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
    827:           {
    828:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
    829:             for (j = 0; j < numVerts-1; j++) {
    830:               PetscReal z, r, theta = -PETSC_PI/2 + (j%3) * PETSC_PI/2;
    831:               PetscReal rad = (j >= 6) ? inner_radius1 : (j >= 3) ? inner_radius2 : ctx->radius[grid];
    832:               z = rad * PetscSinReal(theta);
    833:               coords[j][1] = z;
    834:               r = rad * PetscCosReal(theta);
    835:               coords[j][0] = r;
    836:             }
    837:             coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
    838:           }
    839: #else
    840:           numCells = 4;
    841:           numVerts = 8;
    842:           static int     cells2[][4] = {{0,1,2,3},
    843:                                         {4,5,1,0},
    844:                                         {5,6,2,1},
    845:                                         {6,7,3,2}};
    846:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
    847:           loc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
    848:           {
    849:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
    850:             PetscInt j;
    851:             for (j = 0; j < 8; j++) {
    852:               PetscReal z, r;
    853:               PetscReal theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3.;
    854:               PetscReal rad = ctx->radius[grid] * ((j < 4) ? 0.5 : 1.0);
    855:               z = rad * PetscSinReal(theta);
    856:               coords[j][1] = z;
    857:               r = rad * PetscCosReal(theta);
    858:               coords[j][0] = r;
    859:             }
    860:           }
    861: #endif
    862:         } else if (ctx->num_sections==3) {
    863:           numCells = 7;
    864:           numVerts = 12;
    865:           int cells2[][4] = { {0,1,5,4},
    866:                               {1,2,6,5},
    867:                               {2,3,7,6},
    868:                               {4,5,9,8},
    869:                               {5,6,10,9},
    870:                               {6,7,11,10},
    871:                               {8,9,10,11} };
    872:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
    873:           PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
    874:           {
    875:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
    876:             for (j = 0; j < numVerts; j++) {
    877:               PetscReal z, r, theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3;
    878:               PetscReal rad = (j >= 8) ? inner_radius1 : (j >= 4) ? inner_radius2 : ctx->radius[grid];
    879:               z = rad * PetscSinReal(theta);
    880:               coords[j][1] = z;
    881:               r = rad * PetscCosReal(theta);
    882:               coords[j][0] = r;
    883:             }
    884:           }
    885:         } else if (ctx->num_sections==4) {
    886:           numCells = 10;
    887:           numVerts = 16;
    888:           int cells2[][4] = { {0,1,6,5},
    889:                               {1,2,7,6},
    890:                               {2,3,8,7},
    891:                               {3,4,9,8},
    892:                               {5,6,11,10},
    893:                               {6,7,12,11},
    894:                               {7,8,13,12},
    895:                               {8,9,14,13},
    896:                               {10,11,12,15},
    897:                               {12,13,14,15}};
    898:           for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
    899:           PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);
    900:           {
    901:             PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
    902:             for (j = 0; j < numVerts-1; j++) {
    903:               PetscReal z, r, theta = -PETSC_PI/2 + (j%5) * PETSC_PI/4;
    904:               PetscReal rad = (j >= 10) ? inner_radius1 : (j >= 5) ? inner_radius2 : ctx->radius[grid];
    905:               z = rad * PetscSinReal(theta);
    906:               coords[j][1] = z;
    907:               r = rad * PetscCosReal(theta);
    908:               coords[j][0] = r;
    909:             }
    910:             coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
    911:           }
    912:         } else {
    913:           numCells = 0;
    914:           numVerts = 0;
    915:         }
    916:         for (j = 0, pcell = flatCells; j < numCells; j++, pcell += 4) {
    917:           pcell[0] = cells[j][0]; pcell[1] = cells[j][1];
    918:           pcell[2] = cells[j][2]; pcell[3] = cells[j][3];
    919:         }
    920:         DMPlexCreateFromCellListPetsc(comm_self,2,numCells,numVerts,4,ctx->interpolate,flatCells,2,flatCoords,&ctx->plex[grid]);
    921:         PetscFree2(flatCoords,flatCells);
    922:         PetscObjectSetName((PetscObject) ctx->plex[grid], "semi-circle");
    923:       } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Velocity space meshes does not support cubed sphere");

    925:       DMSetFromOptions(ctx->plex[grid]);
    926:     } // grid loop
    927:     PetscObjectSetOptionsPrefix((PetscObject)pack,prefix);
    928:     DMSetFromOptions(pack);

    930:     { /* convert to p4est (or whatever), wait for discretization to create pack */
    931:       char           convType[256];
    932:       PetscBool      flg;

    935:       PetscOptionsBegin(ctx->comm, prefix, "Mesh conversion options", "DMPLEX");
    936:       PetscOptionsFList("-dm_landau_type","Convert DMPlex to another format (p4est)","plexland.c",DMList,DMPLEX,convType,256,&flg);
    937:       PetscOptionsEnd();
    938:       if (flg) {
    939:         ctx->use_p4est = PETSC_TRUE; /* flag for Forest */
    940:         for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    941:           DM dmforest;
    942:           DMConvert(ctx->plex[grid],convType,&dmforest);
    943:           if (dmforest) {
    944:             PetscBool isForest;
    945:             PetscObjectSetOptionsPrefix((PetscObject)dmforest,prefix);
    946:             DMIsForest(dmforest,&isForest);
    947:             if (isForest) {
    948:               if (ctx->sphere && ctx->inflate) {
    949:                 DMForestSetBaseCoordinateMapping(dmforest,GeometryDMLandau,ctx);
    950:               }
    951:               DMDestroy(&ctx->plex[grid]);
    952:               ctx->plex[grid] = dmforest; // Forest for adaptivity
    953:             } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Converted to non Forest?");
    954:           } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Convert failed?");
    955:         }
    956:       } else ctx->use_p4est = PETSC_FALSE; /* flag for Forest */
    957:     }
    958:   } /* non-file */
    959:   DMSetDimension(pack, dim);
    960:   PetscObjectSetName((PetscObject) pack, "Mesh");
    961:   DMSetApplicationContext(pack, ctx);

    963:   return 0;
    964: }

    966: static PetscErrorCode SetupDS(DM pack, PetscInt dim, PetscInt grid, LandauCtx *ctx)
    967: {
    968:   PetscInt        ii,i0;
    969:   char            buf[256];
    970:   PetscSection    section;

    972:   for (ii = ctx->species_offset[grid], i0 = 0 ; ii < ctx->species_offset[grid+1] ; ii++, i0++) {
    973:     if (ii==0) PetscSNPrintf(buf, sizeof(buf), "e");
    974:     else PetscSNPrintf(buf, sizeof(buf), "i%" PetscInt_FMT, ii);
    975:     /* Setup Discretization - FEM */
    976:     PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &ctx->fe[ii]);
    977:     PetscObjectSetName((PetscObject) ctx->fe[ii], buf);
    978:     DMSetField(ctx->plex[grid], i0, NULL, (PetscObject) ctx->fe[ii]);
    979:   }
    980:   DMCreateDS(ctx->plex[grid]);
    981:   DMGetSection(ctx->plex[grid], &section);
    982:   for (PetscInt ii = ctx->species_offset[grid], i0 = 0 ; ii < ctx->species_offset[grid+1] ; ii++, i0++) {
    983:     if (ii==0) PetscSNPrintf(buf, sizeof(buf), "se");
    984:     else PetscSNPrintf(buf, sizeof(buf), "si%" PetscInt_FMT, ii);
    985:     PetscSectionSetComponentName(section, i0, 0, buf);
    986:   }
    987:   return 0;
    988: }

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

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

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

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

    1000: /* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */

    1002: /* Defining $\theta=2T/mc^2$, we thus find that the probability density */
    1003: /* for finding the particle within the interval in a box dx^3 around x is */

    1005: /* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */

    1007: typedef struct {
    1008:   PetscReal v_0;
    1009:   PetscReal kT_m;
    1010:   PetscReal n;
    1011:   PetscReal shift;
    1012: } MaxwellianCtx;

    1014: static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
    1015: {
    1016:   MaxwellianCtx *mctx = (MaxwellianCtx*)actx;
    1017:   PetscInt      i;
    1018:   PetscReal     v2 = 0, theta = 2*mctx->kT_m/(mctx->v_0*mctx->v_0); /* theta = 2kT/mc^2 */
    1019:   /* compute the exponents, v^2 */
    1020:   for (i = 0; i < dim; ++i) v2 += x[i]*x[i];
    1021:   /* evaluate the Maxwellian */
    1022:   u[0] = mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
    1023:   if (mctx->shift!=0.) {
    1024:     v2 = 0;
    1025:     for (i = 0; i < dim-1; ++i) v2 += x[i]*x[i];
    1026:     v2 += (x[dim-1]-mctx->shift)*(x[dim-1]-mctx->shift);
    1027:     /* evaluate the shifted Maxwellian */
    1028:     u[0] += mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
    1029:   }
    1030:   return 0;
    1031: }

    1033: /*@
    1034:  DMPlexLandauAddMaxwellians - Add a Maxwellian distribution to a state

    1036:  Collective on X

    1038:  Input Parameters:
    1039:  .   dm - The mesh (local)
    1040:  +   time - Current time
    1041:  -   temps - Temperatures of each species (global)
    1042:  .   ns - Number density of each species (global)
    1043:  -   grid - index into current grid - just used for offset into temp and ns
    1044:  +   actx - Landau context

    1046:  Output Parameter:
    1047:  .   X  - The state (local to this grid)

    1049:  Level: beginner

    1051:  .keywords: mesh
    1052:  .seealso: DMPlexLandauCreateVelocitySpace()
    1053:  @*/
    1054: PetscErrorCode DMPlexLandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], PetscInt grid, PetscInt b_id, void *actx)
    1055: {
    1056:   LandauCtx      *ctx = (LandauCtx*)actx;
    1057:   PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *);
    1058:   PetscInt       dim;
    1059:   MaxwellianCtx  *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];

    1061:   DMGetDimension(dm, &dim);
    1062:   if (!ctx) DMGetApplicationContext(dm, &ctx);
    1063:   for (PetscInt ii = ctx->species_offset[grid], i0 = 0 ; ii < ctx->species_offset[grid+1] ; ii++, i0++) {
    1064:     mctxs[i0]      = &data[i0];
    1065:     data[i0].v_0   = ctx->v_0; // v_0 same for all grids
    1066:     data[i0].kT_m  = ctx->k*temps[ii]/ctx->masses[ii]; /* kT/m */
    1067:     data[i0].n     = ns[ii] * (1+(double)b_id/100.0); // make solves a little different to mimic application, n[0] use for Conner-Hastie
    1068:     initu[i0]      = maxwellian;
    1069:     data[i0].shift = 0;
    1070:   }
    1071:   data[0].shift = ctx->electronShift;
    1072:   /* need to make ADD_ALL_VALUES work - TODO */
    1073:   DMProjectFunction(dm, time, initu, (void**)mctxs, INSERT_ALL_VALUES, X);
    1074:   return 0;
    1075: }

    1077: /*
    1078:  LandauSetInitialCondition - Addes Maxwellians with context

    1080:  Collective on X

    1082:  Input Parameters:
    1083:  .   dm - The mesh
    1084:  -   grid - index into current grid - just used for offset into temp and ns
    1085:  +   actx - Landau context with T and n

    1087:  Output Parameter:
    1088:  .   X  - The state

    1090:  Level: beginner

    1092:  .keywords: mesh
    1093:  .seealso: DMPlexLandauCreateVelocitySpace(), DMPlexLandauAddMaxwellians()
    1094:  */
    1095: static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, PetscInt grid, PetscInt b_id, void *actx)
    1096: {
    1097:   LandauCtx        *ctx = (LandauCtx*)actx;
    1098:   if (!ctx) DMGetApplicationContext(dm, &ctx);
    1099:   VecZeroEntries(X);
    1100:   DMPlexLandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, grid, b_id, ctx);
    1101:   return 0;
    1102: }

    1104: // adapt a level once. Forest in/out
    1105: static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscInt type, PetscInt grid, LandauCtx *ctx, DM *newForest)
    1106: {
    1107:   DM               forest, plex, adaptedDM = NULL;
    1108:   PetscDS          prob;
    1109:   PetscBool        isForest;
    1110:   PetscQuadrature  quad;
    1111:   PetscInt         Nq, *Nb, cStart, cEnd, c, dim, qj, k;
    1112:   DMLabel          adaptLabel = NULL;

    1114:   forest = ctx->plex[grid];
    1115:   DMCreateDS(forest);
    1116:   DMGetDS(forest, &prob);
    1117:   DMGetDimension(forest, &dim);
    1118:   DMIsForest(forest, &isForest);
    1120:   DMConvert(forest, DMPLEX, &plex);
    1121:   DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
    1122:   DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);
    1123:   PetscFEGetQuadrature(fem, &quad);
    1124:   PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);
    1126:   PetscDSGetDimensions(prob, &Nb);
    1127:   if (type==4) {
    1128:     for (c = cStart; c < cEnd; c++) {
    1129:       DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);
    1130:     }
    1131:     PetscInfo(sol, "Phase:%s: Uniform refinement\n","adaptToleranceFEM");
    1132:   } else if (type==2) {
    1133:     PetscInt  rCellIdx[8], eCellIdx[64], iCellIdx[64], eMaxIdx = -1, iMaxIdx = -1, nr = 0, nrmax = (dim==3) ? 8 : 2;
    1134:     PetscReal minRad = PETSC_INFINITY, r, eMinRad = PETSC_INFINITY, iMinRad = PETSC_INFINITY;
    1135:     for (c = 0; c < 64; c++) { eCellIdx[c] = iCellIdx[c] = -1; }
    1136:     for (c = cStart; c < cEnd; c++) {
    1137:       PetscReal    tt, v0[LANDAU_MAX_NQ*3], detJ[LANDAU_MAX_NQ];
    1138:       DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ);
    1139:       for (qj = 0; qj < Nq; ++qj) {
    1140:         tt = PetscSqr(v0[dim*qj+0]) + PetscSqr(v0[dim*qj+1]) + PetscSqr(((dim==3) ? v0[dim*qj+2] : 0));
    1141:         r  = PetscSqrtReal(tt);
    1142:         if (r < minRad - PETSC_SQRT_MACHINE_EPSILON*10.) {
    1143:           minRad = r;
    1144:           nr     = 0;
    1145:           rCellIdx[nr++]= c;
    1146:           PetscInfo(sol, "\t\tPhase: adaptToleranceFEM Found first inner r=%e, cell %" PetscInt_FMT ", qp %" PetscInt_FMT "/%" PetscInt_FMT "\n", r, c, qj+1, Nq);
    1147:         } else if ((r-minRad) < PETSC_SQRT_MACHINE_EPSILON*100. && nr < nrmax) {
    1148:           for (k=0;k<nr;k++) if (c == rCellIdx[k]) break;
    1149:           if (k==nr) {
    1150:             rCellIdx[nr++]= c;
    1151:             PetscInfo(sol, "\t\t\tPhase: adaptToleranceFEM Found another inner r=%e, cell %" PetscInt_FMT ", qp %" PetscInt_FMT "/%" PetscInt_FMT ", d=%e\n", r, c, qj+1, Nq, r-minRad);
    1152:           }
    1153:         }
    1154:         if (ctx->sphere) {
    1155:           if ((tt=r-ctx->e_radius) > 0) {
    1156:             PetscInfo(sol, "\t\t\t %" PetscInt_FMT " cell r=%g\n",c,tt);
    1157:             if (tt < eMinRad - PETSC_SQRT_MACHINE_EPSILON*100.) {
    1158:               eMinRad = tt;
    1159:               eMaxIdx = 0;
    1160:               eCellIdx[eMaxIdx++] = c;
    1161:             } else if (eMaxIdx > 0 && (tt-eMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != eCellIdx[eMaxIdx-1]) {
    1162:               eCellIdx[eMaxIdx++] = c;
    1163:             }
    1164:           }
    1165:           if ((tt=r-ctx->i_radius[grid]) > 0) {
    1166:             if (tt < iMinRad - 1.e-5) {
    1167:               iMinRad = tt;
    1168:               iMaxIdx = 0;
    1169:               iCellIdx[iMaxIdx++] = c;
    1170:             } else if (iMaxIdx > 0 && (tt-iMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != iCellIdx[iMaxIdx-1]) {
    1171:               iCellIdx[iMaxIdx++] = c;
    1172:             }
    1173:           }
    1174:         }
    1175:       }
    1176:     }
    1177:     for (k=0;k<nr;k++) {
    1178:       DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE);
    1179:     }
    1180:     if (ctx->sphere) {
    1181:       for (c = 0; c < eMaxIdx; c++) {
    1182:         DMLabelSetValue(adaptLabel, eCellIdx[c], DM_ADAPT_REFINE);
    1183:         PetscInfo(sol, "\t\tPhase:%s: refine sphere e cell %" PetscInt_FMT " r=%g\n","adaptToleranceFEM",eCellIdx[c],eMinRad);
    1184:       }
    1185:       for (c = 0; c < iMaxIdx; c++) {
    1186:         DMLabelSetValue(adaptLabel, iCellIdx[c], DM_ADAPT_REFINE);
    1187:         PetscInfo(sol, "\t\tPhase:%s: refine sphere i cell %" PetscInt_FMT " r=%g\n","adaptToleranceFEM",iCellIdx[c],iMinRad);
    1188:       }
    1189:     }
    1190:     PetscInfo(sol, "Phase:%s: Adaptive refine origin cells %" PetscInt_FMT ",%" PetscInt_FMT " r=%g\n","adaptToleranceFEM",rCellIdx[0],rCellIdx[1],minRad);
    1191:   } else if (type==0 || type==1 || type==3) { /* refine along r=0 axis */
    1192:     PetscScalar  *coef = NULL;
    1193:     Vec          coords;
    1194:     PetscInt     csize,Nv,d,nz;
    1195:     DM           cdm;
    1196:     PetscSection cs;
    1197:     DMGetCoordinatesLocal(forest, &coords);
    1198:     DMGetCoordinateDM(forest, &cdm);
    1199:     DMGetLocalSection(cdm, &cs);
    1200:     for (c = cStart; c < cEnd; c++) {
    1201:       PetscInt doit = 0, outside = 0;
    1202:       DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef);
    1203:       Nv = csize/dim;
    1204:       for (nz = d = 0; d < Nv; d++) {
    1205:         PetscReal z = PetscRealPart(coef[d*dim + (dim-1)]), x = PetscSqr(PetscRealPart(coef[d*dim + 0])) + ((dim==3) ? PetscSqr(PetscRealPart(coef[d*dim + 1])) : 0);
    1206:         x = PetscSqrtReal(x);
    1207:         if (x < PETSC_MACHINE_EPSILON*10. && PetscAbs(z)<PETSC_MACHINE_EPSILON*10.) doit = 1;             /* refine origin */
    1208:         else if (type==0 && (z < -PETSC_MACHINE_EPSILON*10. || z > ctx->re_radius+PETSC_MACHINE_EPSILON*10.)) outside++;   /* first pass don't refine bottom */
    1209:         else if (type==1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) outside++; /* don't refine outside electron refine radius */
    1210:         else if (type==3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) outside++; /* don't refine outside ion refine radius */
    1211:         if (x < PETSC_MACHINE_EPSILON*10.) nz++;
    1212:       }
    1213:       DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef);
    1214:       if (doit || (outside<Nv && nz)) {
    1215:         DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);
    1216:       }
    1217:     }
    1218:     PetscInfo(sol, "Phase:%s: RE refinement\n","adaptToleranceFEM");
    1219:   }
    1220:   DMDestroy(&plex);
    1221:   DMAdaptLabel(forest, adaptLabel, &adaptedDM);
    1222:   DMLabelDestroy(&adaptLabel);
    1223:   *newForest = adaptedDM;
    1224:   if (adaptedDM) {
    1225:     if (isForest) {
    1226:       DMForestSetAdaptivityForest(adaptedDM,NULL); // ????
    1227:     } else exit(33); // ???????
    1228:     DMConvert(adaptedDM, DMPLEX, &plex);
    1229:     DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
    1230:     PetscInfo(sol, "\tPhase: adaptToleranceFEM: %" PetscInt_FMT " cells, %" PetscInt_FMT " total quadrature points\n",cEnd-cStart,Nq*(cEnd-cStart));
    1231:     DMDestroy(&plex);
    1232:   } else *newForest = NULL;
    1233:   return 0;
    1234: }

    1236: // forest goes in (ctx->plex[grid]), plex comes out
    1237: static PetscErrorCode adapt(PetscInt grid, LandauCtx *ctx, Vec *uu)
    1238: {
    1239:   PetscInt        adaptIter;

    1241:   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]};
    1242:   for (type=0;type<5;type++) {
    1243:     for (adaptIter = 0; adaptIter<limits[type];adaptIter++) {
    1244:       DM  newForest = NULL;
    1245:       adaptToleranceFEM(ctx->fe[0], *uu, type, grid, ctx, &newForest);
    1246:       if (newForest)  {
    1247:         DMDestroy(&ctx->plex[grid]);
    1248:         VecDestroy(uu);
    1249:         DMCreateGlobalVector(newForest,uu);
    1250:         PetscObjectSetName((PetscObject) *uu, "uAMR");
    1251:         LandauSetInitialCondition(newForest, *uu, grid, 0, ctx);
    1252:         ctx->plex[grid] = newForest;
    1253:       } else {
    1254:         exit(4); // can happen with no AMR and post refinement
    1255:       }
    1256:     }
    1257:   }
    1258:   return 0;
    1259: }

    1261: static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
    1262: {
    1263:   PetscErrorCode    ierr;
    1264:   PetscBool         flg, sph_flg;
    1265:   PetscInt          ii,nt,nm,nc,num_species_grid[LANDAU_MAX_GRIDS];
    1266:   PetscReal         v0_grid[LANDAU_MAX_GRIDS];
    1267:   DM                dummy;

    1269:   DMCreate(ctx->comm,&dummy);
    1270:   /* get options - initialize context */
    1271:   ctx->verbose = 1; // should be 0 for silent compliance
    1272: #if defined(PETSC_HAVE_THREADSAFETY)
    1273:   ctx->batch_sz = PetscNumOMPThreads;
    1274: #else
    1275:   ctx->batch_sz = 1;
    1276: #endif
    1277:   ctx->batch_view_idx = 0;
    1278:   ctx->interpolate    = PETSC_TRUE;
    1279:   ctx->gpu_assembly   = PETSC_TRUE;
    1280:   ctx->aux_bool       = PETSC_FALSE;
    1281:   ctx->electronShift  = 0;
    1282:   ctx->M              = NULL;
    1283:   ctx->J              = NULL;
    1284:   /* geometry and grids */
    1285:   ctx->sphere         = PETSC_FALSE;
    1286:   ctx->inflate        = PETSC_FALSE;
    1287:   ctx->aux_bool       = PETSC_FALSE;
    1288:   ctx->use_p4est      = PETSC_FALSE;
    1289:   ctx->num_sections   = 3; /* 2, 3 or 4 */
    1290:   for (PetscInt grid=0;grid<LANDAU_MAX_GRIDS;grid++) {
    1291:     ctx->radius[grid]           = 5.; /* thermal radius (velocity) */
    1292:     ctx->numAMRRefine[grid]     = 5;
    1293:     ctx->postAMRRefine[grid]    = 0;
    1294:     ctx->species_offset[grid+1] = 1; // one species default
    1295:     num_species_grid[grid]      = 0;
    1296:     ctx->plex[grid] = NULL;     /* cache as expensive to Convert */
    1297:   }
    1298:   ctx->species_offset[0] = 0;
    1299:   ctx->re_radius         = 0.;
    1300:   ctx->vperp0_radius1    = 0;
    1301:   ctx->vperp0_radius2    = 0;
    1302:   ctx->nZRefine1         = 0;
    1303:   ctx->nZRefine2         = 0;
    1304:   ctx->numRERefine       = 0;
    1305:   num_species_grid[0]    = 1; // one species default
    1306:   /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
    1307:   ctx->charges[0]        = -1;  /* electron charge (MKS) */
    1308:   ctx->masses[0]         = 1/1835.469965278441013; /* temporary value in proton mass */
    1309:   ctx->n[0]              = 1;
    1310:   ctx->v_0               = 1; /* thermal velocity, we could start with a scale != 1 */
    1311:   ctx->thermal_temps[0]  = 1;
    1312:   /* constants, etc. */
    1313:   ctx->epsilon0          = 8.8542e-12; /* permittivity of free space (MKS) F/m */
    1314:   ctx->k                 = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
    1315:   ctx->lnLam             = 10;         /* cross section ratio large - small angle collisions */
    1316:   ctx->n_0               = 1.e20;        /* typical plasma n, but could set it to 1 */
    1317:   ctx->Ez                = 0;
    1318:   for (PetscInt grid=0;grid<LANDAU_NUM_TIMERS;grid++) ctx->times[grid] = 0;
    1319:   ctx->use_matrix_mass   =  PETSC_FALSE;
    1320:   ctx->use_relativistic_corrections = PETSC_FALSE;
    1321:   ctx->use_energy_tensor_trick      = PETSC_FALSE; /* Use Eero's trick for energy conservation v --> grad(v^2/2) */
    1322:   ctx->SData_d.w         = NULL;
    1323:   ctx->SData_d.x         = NULL;
    1324:   ctx->SData_d.y         = NULL;
    1325:   ctx->SData_d.z         = NULL;
    1326:   ctx->SData_d.invJ      = NULL;
    1327:   ctx->jacobian_field_major_order     = PETSC_FALSE;
    1328:   ctx->SData_d.coo_elem_offsets       = NULL;
    1329:   ctx->SData_d.coo_elem_point_offsets = NULL;
    1330:   ctx->coo_assembly                   = PETSC_FALSE;
    1331:   ctx->SData_d.coo_elem_fullNb        = NULL;
    1332:   ctx->SData_d.coo_size               = 0;
    1333:   PetscOptionsBegin(ctx->comm, prefix, "Options for Fokker-Plank-Landau collision operator", "none");
    1334:   {
    1335:     char opstring[256];
    1336: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    1337:     ctx->deviceType = LANDAU_KOKKOS;
    1338:     PetscStrcpy(opstring,"kokkos");
    1339: #elif defined(PETSC_HAVE_CUDA)
    1340:     ctx->deviceType = LANDAU_CUDA;
    1341:     PetscStrcpy(opstring,"cuda");
    1342: #else
    1343:     ctx->deviceType = LANDAU_CPU;
    1344:     PetscStrcpy(opstring,"cpu");
    1345: #endif
    1346:     PetscOptionsString("-dm_landau_device_type","Use kernels on 'cpu', 'cuda', or 'kokkos'","plexland.c",opstring,opstring,sizeof(opstring),NULL);
    1347:     PetscStrcmp("cpu",opstring,&flg);
    1348:     if (flg) {
    1349:       ctx->deviceType = LANDAU_CPU;
    1350:     } else {
    1351:       PetscStrcmp("cuda",opstring,&flg);
    1352:       if (flg) {
    1353:         ctx->deviceType = LANDAU_CUDA;
    1354:       } else {
    1355:         PetscStrcmp("kokkos",opstring,&flg);
    1356:         if (flg) ctx->deviceType = LANDAU_KOKKOS;
    1357:         else SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_device_type %s",opstring);
    1358:       }
    1359:     }
    1360:   }
    1361:   PetscOptionsReal("-dm_landau_electron_shift","Shift in thermal velocity of electrons","none",ctx->electronShift,&ctx->electronShift, NULL);
    1362:   PetscOptionsInt("-dm_landau_verbose", "Level of verbosity output", "plexland.c", ctx->verbose, &ctx->verbose, NULL);
    1363:   PetscOptionsInt("-dm_landau_batch_size", "Number of 'vertices' to batch", "ex2.c", ctx->batch_sz, &ctx->batch_sz, NULL);
    1365:   PetscOptionsInt("-dm_landau_batch_view_idx", "Index of batch for diagnostics like plotting", "ex2.c", ctx->batch_view_idx, &ctx->batch_view_idx, NULL);
    1367:   PetscOptionsReal("-dm_landau_Ez","Initial parallel electric field in unites of Conner-Hastie critical field","plexland.c",ctx->Ez,&ctx->Ez, NULL);
    1368:   PetscOptionsReal("-dm_landau_n_0","Normalization constant for number density","plexland.c",ctx->n_0,&ctx->n_0, NULL);
    1369:   PetscOptionsReal("-dm_landau_ln_lambda","Cross section parameter","plexland.c",ctx->lnLam,&ctx->lnLam, NULL);
    1370:   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);
    1371:   PetscOptionsBool("-dm_landau_use_relativistic_corrections", "Use relativistic corrections", "plexland.c", ctx->use_relativistic_corrections, &ctx->use_relativistic_corrections, NULL);
    1372:   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);

    1374:   /* get num species with temperature, set defaults */
    1375:   for (ii=1;ii<LANDAU_MAX_SPECIES;ii++) {
    1376:     ctx->thermal_temps[ii] = 1;
    1377:     ctx->charges[ii]       = 1;
    1378:     ctx->masses[ii]        = 1;
    1379:     ctx->n[ii]             = 1;
    1380:   }
    1381:   nt = LANDAU_MAX_SPECIES;
    1382:   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);
    1383:   if (flg) {
    1384:     PetscInfo(dummy, "num_species set to number of thermal temps provided (%" PetscInt_FMT ")\n",nt);
    1385:     ctx->num_species = nt;
    1386:   } else SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
    1387:   for (ii=0;ii<ctx->num_species;ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
    1388:   nm = LANDAU_MAX_SPECIES-1;
    1389:   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);
    1390:   if (flg && nm != ctx->num_species-1) {
    1391:     SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"num ion masses %" PetscInt_FMT " != num species %" PetscInt_FMT "",nm,ctx->num_species-1);
    1392:   }
    1393:   nm = LANDAU_MAX_SPECIES;
    1394:   PetscOptionsRealArray("-dm_landau_n", "Number density of each species = n_s * n_0", "plexland.c", ctx->n, &nm, &flg);
    1396:   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
    1397:   ctx->masses[0] = 9.10938356e-31; /* electron mass kg (should be about right already) */
    1398:   ctx->m_0 = ctx->masses[0]; /* arbitrary reference mass, electrons */
    1399:   nc = LANDAU_MAX_SPECIES-1;
    1400:   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);
    1402:   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
    1403:   /* geometry and grids */
    1404:   nt = LANDAU_MAX_GRIDS;
    1405:   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);
    1406:   if (flg) {
    1407:     ctx->num_grids = nt;
    1408:     for (ii=nt=0;ii<ctx->num_grids;ii++) nt += num_species_grid[ii];
    1410:   } else {
    1411:     ctx->num_grids = 1; // go back to a single grid run
    1412:     num_species_grid[0] = ctx->num_species;
    1413:   }
    1414:   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];
    1416:   for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
    1417:     int iii = ctx->species_offset[grid]; // normalize with first (arbitrary) species on grid
    1418:     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 */
    1419:   }
    1420:   ii = 0;
    1421:   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);
    1422:   ctx->v_0 = v0_grid[ii]; /* arbitrary units for non dimensionalization: global mean velocity in 1D of electrons */
    1423:   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 */
    1424:   /* domain */
    1425:   nt = LANDAU_MAX_GRIDS;
    1426:   PetscOptionsRealArray("-dm_landau_domain_radius","Phase space size in units of thermal velocity of grid","plexland.c",ctx->radius,&nt, &flg);
    1428:   for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
    1429:     if (flg && ctx->radius[grid] <= 0) { /* negative is ratio of c */
    1430:       if (ctx->radius[grid] == 0) ctx->radius[grid] = 0.75;
    1431:       else ctx->radius[grid] = -ctx->radius[grid];
    1432:       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)
    1433:       PetscInfo(dummy, "Change domain radius to %g for grid %" PetscInt_FMT "\n",ctx->radius[grid],grid);
    1434:     }
    1435:     ctx->radius[grid] *= v0_grid[grid]/ctx->v_0; // scale domain by thermal radius relative to v_0
    1436:   }
    1437:   /* amr parametres */
    1438:   nt = LANDAU_MAX_GRIDS;
    1439:   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);
    1441:   nt = LANDAU_MAX_GRIDS;
    1442:   PetscOptionsIntArray("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &nt, &flg);
    1443:   for (ii=1;ii<ctx->num_grids;ii++)  ctx->postAMRRefine[ii] = ctx->postAMRRefine[0]; // all grids the same now
    1444:   PetscOptionsInt("-dm_landau_amr_re_levels", "Number of levels to refine along v_perp=0, z>0", "plexland.c", ctx->numRERefine, &ctx->numRERefine, &flg);
    1445:   PetscOptionsInt("-dm_landau_amr_z_refine1",  "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine1, &ctx->nZRefine1, &flg);
    1446:   PetscOptionsInt("-dm_landau_amr_z_refine2",  "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine2, &ctx->nZRefine2, &flg);
    1447:   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);
    1448:   PetscOptionsReal("-dm_landau_z_radius1","velocity range to refine r=0 axis (for electrons)","plexland.c",ctx->vperp0_radius1,&ctx->vperp0_radius1, &flg);
    1449:   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);
    1450:   /* spherical domain (not used) */
    1451:   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);
    1452:   PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, &sph_flg);
    1453:   PetscOptionsBool("-dm_landau_inflate", "With sphere, inflate for curved edges", "plexland.c", ctx->inflate, &ctx->inflate, &flg);
    1454:   PetscOptionsReal("-dm_landau_e_radius","Electron thermal velocity, used for circular meshes","plexland.c",ctx->e_radius, &ctx->e_radius, &flg);
    1455:   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an e radius but did not set sphere, user error really */
    1456:   if (!flg) {
    1457:     ctx->e_radius = 1.5*PetscSqrtReal(8*ctx->k*ctx->thermal_temps[0]/ctx->masses[0]/PETSC_PI)/ctx->v_0;
    1458:   }
    1459:   nt = LANDAU_MAX_GRIDS;
    1460:   PetscOptionsRealArray("-dm_landau_i_radius","Ion thermal velocity, used for circular meshes","plexland.c",ctx->i_radius, &nt, &flg);
    1461:   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE;
    1462:   if (!flg) {
    1463:     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
    1464:   }
    1467:   /* processing options */
    1468:   PetscOptionsBool("-dm_landau_gpu_assembly", "Assemble Jacobian on GPU", "plexland.c", ctx->gpu_assembly, &ctx->gpu_assembly, NULL);
    1469:   if (ctx->deviceType == LANDAU_CPU || ctx->deviceType == LANDAU_KOKKOS) { // make Kokkos
    1470:     PetscOptionsBool("-dm_landau_coo_assembly", "Assemble Jacobian with Kokkos on 'device'", "plexland.c", ctx->coo_assembly, &ctx->coo_assembly, NULL);
    1472:   }
    1473:   PetscOptionsBool("-dm_landau_jacobian_field_major_order", "Reorder Jacobian for GPU assembly with field major, or block diagonal, ordering", "plexland.c", ctx->jacobian_field_major_order, &ctx->jacobian_field_major_order, NULL);
    1475:   PetscOptionsEnd();

    1477:   for (ii=ctx->num_species;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] = ctx->thermal_temps[ii]  = ctx->charges[ii] = 0;
    1478:   if (ctx->verbose > 0) {
    1479:     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);
    1480:     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);
    1481:     PetscPrintf(ctx->comm, "n:             e: %10.3e                           i: %10.3e %10.3e\n", ctx->n[0],ctx->n[1],ctx->num_species>2 ? ctx->n[2] : 0);
    1482:     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, %" PetscInt_FMT " batched\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",ctx->batch_sz);
    1483:     PetscPrintf(ctx->comm, "Domain radius (AMR levels) grid %" PetscInt_FMT ": %10.3e (%" PetscInt_FMT ") ",0,ctx->radius[0],ctx->numAMRRefine[0]);
    1484:     for (ii=1;ii<ctx->num_grids;ii++) PetscPrintf(ctx->comm, ", %" PetscInt_FMT ": %10.3e (%" PetscInt_FMT ") ",ii,ctx->radius[ii],ctx->numAMRRefine[ii]);
    1485:     PetscPrintf(ctx->comm,"\n");
    1486:     if (ctx->jacobian_field_major_order) {
    1487:       PetscPrintf(ctx->comm,"Using field major order for GPU Jacobian\n");
    1488:     } else {
    1489:       PetscPrintf(ctx->comm,"Using default Plex order for all matrices\n");
    1490:     }
    1491:   }
    1492:   DMDestroy(&dummy);
    1493:   {
    1494:     PetscMPIInt    rank;
    1495:     MPI_Comm_rank(ctx->comm, &rank);
    1496:     ctx->stage = 0;
    1497:     PetscLogEventRegister("Landau Create", DM_CLASSID, &ctx->events[13]); /* 13 */
    1498:     PetscLogEventRegister(" GPU ass. setup", DM_CLASSID, &ctx->events[2]); /* 2 */
    1499:     PetscLogEventRegister(" Build matrix", DM_CLASSID, &ctx->events[12]); /* 12 */
    1500:     PetscLogEventRegister(" Assembly maps", DM_CLASSID, &ctx->events[15]); /* 15 */
    1501:     PetscLogEventRegister("Landau Mass mat", DM_CLASSID, &ctx->events[14]); /* 14 */
    1502:     PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[11]); /* 11 */
    1503:     PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[0]); /* 0 */
    1504:     PetscLogEventRegister("Landau Mass", DM_CLASSID, &ctx->events[9]); /* 9 */
    1505:     PetscLogEventRegister(" Preamble", DM_CLASSID, &ctx->events[10]); /* 10 */
    1506:     PetscLogEventRegister(" static IP Data", DM_CLASSID, &ctx->events[7]); /* 7 */
    1507:     PetscLogEventRegister(" dynamic IP-Jac", DM_CLASSID, &ctx->events[1]); /* 1 */
    1508:     PetscLogEventRegister(" Kernel-init", DM_CLASSID, &ctx->events[3]); /* 3 */
    1509:     PetscLogEventRegister(" Jac-f-df (GPU)", DM_CLASSID, &ctx->events[8]); /* 8 */
    1510:     PetscLogEventRegister(" J Kernel (GPU)", DM_CLASSID, &ctx->events[4]); /* 4 */
    1511:     PetscLogEventRegister(" M Kernel (GPU)", DM_CLASSID, &ctx->events[16]); /* 16 */
    1512:     PetscLogEventRegister(" Copy to CPU", DM_CLASSID, &ctx->events[5]); /* 5 */
    1513:     PetscLogEventRegister(" CPU assemble", DM_CLASSID, &ctx->events[6]); /* 6 */

    1515:     if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
    1516:       PetscOptionsClearValue(NULL,"-snes_converged_reason");
    1517:       PetscOptionsClearValue(NULL,"-ksp_converged_reason");
    1518:       PetscOptionsClearValue(NULL,"-snes_monitor");
    1519:       PetscOptionsClearValue(NULL,"-ksp_monitor");
    1520:       PetscOptionsClearValue(NULL,"-ts_monitor");
    1521:       PetscOptionsClearValue(NULL,"-ts_view");
    1522:       PetscOptionsClearValue(NULL,"-ts_adapt_monitor");
    1523:       PetscOptionsClearValue(NULL,"-dm_landau_amr_dm_view");
    1524:       PetscOptionsClearValue(NULL,"-dm_landau_amr_vec_view");
    1525:       PetscOptionsClearValue(NULL,"-dm_landau_mass_dm_view");
    1526:       PetscOptionsClearValue(NULL,"-dm_landau_mass_view");
    1527:       PetscOptionsClearValue(NULL,"-dm_landau_jacobian_view");
    1528:       PetscOptionsClearValue(NULL,"-dm_landau_mat_view");
    1529:       PetscOptionsClearValue(NULL,"-pc_bjkokkos_ksp_converged_reason");
    1530:       PetscOptionsClearValue(NULL,"-pc_bjkokkos_ksp_monitor");
    1531:       PetscOptionsClearValue(NULL,"-");
    1532:       PetscOptionsClearValue(NULL,"-info");
    1533:     }
    1534:   }
    1535:   return 0;
    1536: }

    1538: static PetscErrorCode CreateStaticGPUData(PetscInt dim, IS grid_batch_is_inv[], LandauCtx *ctx)
    1539: {
    1540:   PetscSection      section[LANDAU_MAX_GRIDS],globsection[LANDAU_MAX_GRIDS];
    1541:   PetscQuadrature   quad;
    1542:   const PetscReal   *quadWeights;
    1543:   PetscInt          numCells[LANDAU_MAX_GRIDS],Nq,Nf[LANDAU_MAX_GRIDS], ncellsTot=0;
    1544:   PetscTabulation   *Tf;
    1545:   PetscDS           prob;

    1547:   DMGetDS(ctx->plex[0], &prob); // same DS for all grids
    1548:   PetscDSGetTabulation(prob, &Tf); // Bf, &Df same for all grids
    1549:   /* DS, Tab and quad is same on all grids */
    1551:   PetscFEGetQuadrature(ctx->fe[0], &quad);
    1552:   PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL,  &quadWeights);
    1554:   /* setup each grid */
    1555:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    1556:     PetscInt cStart, cEnd;
    1558:     DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
    1559:     numCells[grid] = cEnd - cStart; // grids can have different topology
    1560:     DMGetLocalSection(ctx->plex[grid], &section[grid]);
    1561:     DMGetGlobalSection(ctx->plex[grid], &globsection[grid]);
    1562:     PetscSectionGetNumFields(section[grid], &Nf[grid]);
    1563:     ncellsTot += numCells[grid];
    1564:   }
    1565: #define MAP_BF_SIZE (64*LANDAU_DIM*LANDAU_DIM*LANDAU_MAX_Q_FACE*LANDAU_MAX_SPECIES)
    1566:   /* create GPU assembly data */
    1567:   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
    1568:     PetscContainer          container;
    1569:     PetscScalar             elemMatrix[LANDAU_MAX_NQ*LANDAU_MAX_NQ*LANDAU_MAX_SPECIES*LANDAU_MAX_SPECIES], *elMat;
    1570:     pointInterpolationP4est pointMaps[MAP_BF_SIZE][LANDAU_MAX_Q_FACE];
    1571:     P4estVertexMaps         *maps;
    1572:     const PetscInt          *plex_batch=NULL,Nb=Nq; // tensor elements;
    1573:     LandauIdx               *coo_elem_offsets=NULL, *coo_elem_fullNb=NULL, (*coo_elem_point_offsets)[LANDAU_MAX_NQ+1] = NULL;
    1574:     /* create GPU asssembly data */
    1575:     PetscInfo(ctx->plex[0], "Make GPU maps %d\n",1);
    1576:     PetscLogEventBegin(ctx->events[2],0,0,0,0);
    1577:     PetscMalloc(sizeof(*maps)*ctx->num_grids, &maps);

    1579:     if (ctx->coo_assembly) { // setup COO assembly -- put COO metadata directly in ctx->SData_d
    1580:       PetscMalloc3(ncellsTot+1,&coo_elem_offsets,ncellsTot,&coo_elem_fullNb,ncellsTot, &coo_elem_point_offsets); // array of integer pointers
    1581:       coo_elem_offsets[0] = 0; // finish later
    1582:       PetscInfo(ctx->plex[0], "COO initialization, %" PetscInt_FMT " cells\n",ncellsTot);
    1583:       ctx->SData_d.coo_n_cellsTot         = ncellsTot;
    1584:       ctx->SData_d.coo_elem_offsets       = (void*)coo_elem_offsets;
    1585:       ctx->SData_d.coo_elem_fullNb        = (void*)coo_elem_fullNb;
    1586:       ctx->SData_d.coo_elem_point_offsets = (void*)coo_elem_point_offsets;
    1587:     } else {
    1588:       ctx->SData_d.coo_elem_offsets       = ctx->SData_d.coo_elem_fullNb = NULL;
    1589:       ctx->SData_d.coo_elem_point_offsets = NULL;
    1590:       ctx->SData_d.coo_n_cellsTot         = 0;
    1591:     }

    1593:     ctx->SData_d.coo_max_fullnb = 0;
    1594:     for (PetscInt grid=0,glb_elem_idx=0;grid<ctx->num_grids;grid++) {
    1595:       PetscInt cStart, cEnd, Nfloc = Nf[grid], totDim = Nfloc*Nq;
    1596:       if (grid_batch_is_inv[grid]) {
    1597:         ISGetIndices(grid_batch_is_inv[grid], &plex_batch);
    1598:       }
    1599:       DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
    1600:       // make maps
    1601:       maps[grid].d_self       = NULL;
    1602:       maps[grid].num_elements = numCells[grid];
    1603:       maps[grid].num_face = (PetscInt)(pow(Nq,1./((double)dim))+.001); // Q
    1604:       maps[grid].num_face = (PetscInt)(pow(maps[grid].num_face,(double)(dim-1))+.001); // Q^2
    1605:       maps[grid].num_reduced  = 0;
    1606:       maps[grid].deviceType   = ctx->deviceType;
    1607:       maps[grid].numgrids     = ctx->num_grids;
    1608:       // count reduced and get
    1609:       PetscMalloc(maps[grid].num_elements * sizeof(*maps[grid].gIdx), &maps[grid].gIdx);
    1610:       for (int ej = cStart, eidx = 0 ; ej < cEnd; ++ej, ++eidx, glb_elem_idx++) {
    1611:         if (coo_elem_offsets) coo_elem_offsets[glb_elem_idx+1] = coo_elem_offsets[glb_elem_idx]; // start with last one, then add
    1612:         for (int fieldA=0;fieldA<Nf[grid];fieldA++) {
    1613:           int fullNb = 0;
    1614:           for (int q = 0; q < Nb; ++q) {
    1615:             PetscInt    numindices,*indices;
    1616:             PetscScalar *valuesOrig = elMat = elemMatrix;
    1617:             PetscArrayzero(elMat, totDim*totDim);
    1618:             elMat[ (fieldA*Nb + q)*totDim + fieldA*Nb + q] = 1;
    1619:             DMPlexGetClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);
    1620:             for (PetscInt f = 0 ; f < numindices ; ++f) { // look for a non-zero on the diagonal
    1621:               if (PetscAbs(PetscRealPart(elMat[f*numindices + f])) > PETSC_MACHINE_EPSILON) {
    1622:                 // found it
    1623:                 if (PetscAbs(PetscRealPart(elMat[f*numindices + f] - 1.)) < PETSC_MACHINE_EPSILON) { // normal vertex 1.0
    1624:                   if (plex_batch) {
    1625:                     maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx) plex_batch[indices[f]];
    1626:                   } else {
    1627:                     maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)indices[f];
    1628:                   }
    1629:                   fullNb++;
    1630:                 } else { //found a constraint
    1631:                   int       jj      = 0;
    1632:                   PetscReal sum     = 0;
    1633:                   const PetscInt ff = f;
    1634:                   maps[grid].gIdx[eidx][fieldA][q] = -maps[grid].num_reduced - 1; // store (-)index: id = -(idx+1): idx = -id - 1

    1636:                   do {  // constraints are continuous in Plex - exploit that here
    1637:                     int ii; // get 'scale'
    1638:                     for (ii = 0, pointMaps[maps[grid].num_reduced][jj].scale = 0; ii < maps[grid].num_face; ii++) { // sum row of outer product to recover vector value
    1639:                       if (ff + ii < numindices) { // 3D has Q and Q^2 interps so might run off end. We could test that elMat[f*numindices + ff + ii] > 0, and break if not
    1640:                         pointMaps[maps[grid].num_reduced][jj].scale += PetscRealPart(elMat[f*numindices + ff + ii]);
    1641:                       }
    1642:                     }
    1643:                     sum += pointMaps[maps[grid].num_reduced][jj].scale; // diagnostic
    1644:                     // get 'gid'
    1645:                     if (pointMaps[maps[grid].num_reduced][jj].scale == 0) pointMaps[maps[grid].num_reduced][jj].gid = -1; // 3D has Q and Q^2 interps
    1646:                     else {
    1647:                       if (plex_batch) {
    1648:                         pointMaps[maps[grid].num_reduced][jj].gid = plex_batch[indices[f]];
    1649:                       } else {
    1650:                         pointMaps[maps[grid].num_reduced][jj].gid = indices[f];
    1651:                       }
    1652:                       fullNb++;
    1653:                     }
    1654:                   } while (++jj < maps[grid].num_face && ++f < numindices); // jj is incremented if we hit the end
    1655:                   while (jj < maps[grid].num_face) {
    1656:                     pointMaps[maps[grid].num_reduced][jj].scale = 0;
    1657:                     pointMaps[maps[grid].num_reduced][jj].gid = -1;
    1658:                     jj++;
    1659:                   }
    1660:                   if (PetscAbs(sum-1.0) > 10*PETSC_MACHINE_EPSILON) { // debug
    1661:                     int       d,f;
    1662:                     PetscReal tmp = 0;
    1663:                     PetscPrintf(PETSC_COMM_SELF,"\t\t%" PetscInt_FMT ".%" PetscInt_FMT ".%" PetscInt_FMT ") ERROR total I = %22.16e (LANDAU_MAX_Q_FACE=%d, #face=%" PetscInt_FMT ")\n",eidx,q,fieldA,sum,LANDAU_MAX_Q_FACE,maps[grid].num_face);
    1664:                     for (d = 0, tmp = 0; d < numindices; ++d) {
    1665:                       if (tmp!=0 && PetscAbs(tmp-1.0) > 10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"%3" PetscInt_FMT ") %3" PetscInt_FMT ": ",d,indices[d]);
    1666:                       for (f = 0; f < numindices; ++f) {
    1667:                         tmp += PetscRealPart(elMat[d*numindices + f]);
    1668:                       }
    1669:                       if (tmp!=0) PetscPrintf(ctx->comm," | %22.16e\n",tmp);
    1670:                     }
    1671:                   }
    1672:                   maps[grid].num_reduced++;
    1674:                 }
    1675:                 break;
    1676:               }
    1677:             }
    1678:             // cleanup
    1679:             DMPlexRestoreClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);
    1680:             if (elMat != valuesOrig) DMRestoreWorkArray(ctx->plex[grid], numindices*numindices, MPIU_SCALAR, &elMat);
    1681:           }
    1682:           if (ctx->coo_assembly) { // setup COO assembly
    1683:             coo_elem_offsets[glb_elem_idx+1] += fullNb*fullNb; // one species block, adds a block for each species, on this element in this grid
    1684:             if (fieldA==0) { // cache full Nb for this element, on this grid per species
    1685:               coo_elem_fullNb[glb_elem_idx] = fullNb;
    1686:               if (fullNb>ctx->SData_d.coo_max_fullnb) ctx->SData_d.coo_max_fullnb = fullNb;
    1688:           }
    1689:         } // field
    1690:       } // cell
    1691:       // allocate and copy point data maps[grid].gIdx[eidx][field][q]
    1692:       PetscMalloc(maps[grid].num_reduced * sizeof(*maps[grid].c_maps), &maps[grid].c_maps);
    1693:       for (int ej = 0; ej < maps[grid].num_reduced; ++ej) {
    1694:         for (int q = 0; q < maps[grid].num_face; ++q) {
    1695:           maps[grid].c_maps[ej][q].scale = pointMaps[ej][q].scale;
    1696:           maps[grid].c_maps[ej][q].gid   = pointMaps[ej][q].gid;
    1697:         }
    1698:       }
    1699: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    1700:       if (ctx->deviceType == LANDAU_KOKKOS) {
    1701:         LandauKokkosCreateMatMaps(maps, pointMaps, Nf, Nq, grid); // imples Kokkos does
    1702:       } // else could be CUDA
    1703: #endif
    1704: #if defined(PETSC_HAVE_CUDA)
    1705:       if (ctx->deviceType == LANDAU_CUDA) {
    1706:         LandauCUDACreateMatMaps(maps, pointMaps, Nf, Nq, grid);
    1707:       }
    1708: #endif
    1709:       if (plex_batch) {
    1710:         ISRestoreIndices(grid_batch_is_inv[grid], &plex_batch);
    1711:         ISDestroy(&grid_batch_is_inv[grid]); // we are done with this
    1712:       }
    1713:     } /* grids */
    1714:     // finish COO
    1715:     if (ctx->coo_assembly) { // setup COO assembly
    1716:       PetscInt *oor, *ooc;
    1717:       ctx->SData_d.coo_size = coo_elem_offsets[ncellsTot]*ctx->batch_sz;
    1718:       PetscMalloc2(ctx->SData_d.coo_size,&oor,ctx->SData_d.coo_size,&ooc);
    1719:       for (int i=0;i<ctx->SData_d.coo_size;i++) oor[i] = ooc[i] = -1;
    1720:       // get
    1721:       for (int grid=0,glb_elem_idx=0;grid<ctx->num_grids;grid++) {
    1722:         for (int ej = 0 ; ej < numCells[grid] ; ++ej, glb_elem_idx++) {
    1723:           const int              fullNb = coo_elem_fullNb[glb_elem_idx];
    1724:           const LandauIdx *const Idxs = &maps[grid].gIdx[ej][0][0]; // just use field-0 maps, They should be the same but this is just for COO storage
    1725:           coo_elem_point_offsets[glb_elem_idx][0] = 0;
    1726:           for (int f=0, cnt2=0;f<Nb;f++) {
    1727:             int idx = Idxs[f];
    1728:             coo_elem_point_offsets[glb_elem_idx][f+1] = coo_elem_point_offsets[glb_elem_idx][f]; // start at last
    1729:             if (idx >= 0) {
    1730:               cnt2++;
    1731:               coo_elem_point_offsets[glb_elem_idx][f+1]++; // inc
    1732:             } else {
    1733:               idx = -idx - 1;
    1734:               for (int q = 0 ; q < maps[grid].num_face; q++) {
    1735:                 if (maps[grid].c_maps[idx][q].gid < 0) break;
    1736:                 cnt2++;
    1737:                 coo_elem_point_offsets[glb_elem_idx][f+1]++; // inc
    1738:               }
    1739:             }
    1741:           }
    1743:         }
    1744:       }
    1745:       // set
    1746:       for (PetscInt b_id = 0 ; b_id < ctx->batch_sz ; b_id++) {
    1747:         for (int grid=0,glb_elem_idx=0;grid<ctx->num_grids;grid++) {
    1748:           const PetscInt moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset);
    1749:           for (int ej = 0 ; ej < numCells[grid] ; ++ej, glb_elem_idx++) {
    1750:             const int  fullNb = coo_elem_fullNb[glb_elem_idx],fullNb2=fullNb*fullNb;
    1751:             // set (i,j)
    1752:             for (int fieldA=0;fieldA<Nf[grid];fieldA++) {
    1753:               const LandauIdx *const Idxs = &maps[grid].gIdx[ej][fieldA][0];
    1754:               int                    rows[LANDAU_MAX_Q_FACE],cols[LANDAU_MAX_Q_FACE];
    1755:               for (int f = 0; f < Nb; ++f) {
    1756:                 const int nr =  coo_elem_point_offsets[glb_elem_idx][f+1] - coo_elem_point_offsets[glb_elem_idx][f];
    1757:                 if (nr==1) rows[0] = Idxs[f];
    1758:                 else {
    1759:                   const int idx = -Idxs[f] - 1;
    1760:                   for (int q = 0; q < nr; q++) {
    1761:                     rows[q] = maps[grid].c_maps[idx][q].gid;
    1762:                   }
    1763:                 }
    1764:                 for (int g = 0; g < Nb; ++g) {
    1765:                   const int nc =  coo_elem_point_offsets[glb_elem_idx][g+1] - coo_elem_point_offsets[glb_elem_idx][g];
    1766:                   if (nc==1) cols[0] = Idxs[g];
    1767:                   else {
    1768:                     const int idx = -Idxs[g] - 1;
    1769:                     for (int q = 0; q < nc; q++) {
    1770:                       cols[q] = maps[grid].c_maps[idx][q].gid;
    1771:                     }
    1772:                   }
    1773:                   const int idx0 = b_id*coo_elem_offsets[ncellsTot] + coo_elem_offsets[glb_elem_idx] + fieldA*fullNb2 + fullNb * coo_elem_point_offsets[glb_elem_idx][f] + nr * coo_elem_point_offsets[glb_elem_idx][g];
    1774:                   for (int q = 0, idx = idx0; q < nr; q++) {
    1775:                     for (int d = 0; d < nc; d++, idx++) {
    1776:                       oor[idx] = rows[q] + moffset;
    1777:                       ooc[idx] = cols[d] + moffset;
    1778:                     }
    1779:                   }
    1780:                 }
    1781:               }
    1782:             }
    1783:           } // cell
    1784:         } // grid
    1785:       } // batch
    1786:       MatSetPreallocationCOO(ctx->J,ctx->SData_d.coo_size,oor,ooc);
    1787:       PetscFree2(oor,ooc);
    1788:     }
    1789:     PetscContainerCreate(PETSC_COMM_SELF, &container);
    1790:     PetscContainerSetPointer(container, (void *)maps);
    1791:     PetscContainerSetUserDestroy(container, LandauGPUMapsDestroy);
    1792:     PetscObjectCompose((PetscObject) ctx->J, "assembly_maps", (PetscObject) container);
    1793:     PetscContainerDestroy(&container);
    1794:     PetscLogEventEnd(ctx->events[2],0,0,0,0);
    1795:   } // end GPU assembly
    1796:   { /* create static point data, Jacobian called first, only one vertex copy */
    1797:     PetscReal      *invJe,*ww,*xx,*yy,*zz=NULL,*invJ_a;
    1798:     PetscInt       outer_ipidx, outer_ej,grid, nip_glb = 0;
    1799:     PetscFE        fe;
    1800:     const PetscInt Nb = Nq;
    1801:     PetscLogEventBegin(ctx->events[7],0,0,0,0);
    1802:     PetscInfo(ctx->plex[0], "Initialize static data\n");
    1803:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) nip_glb += Nq*numCells[grid];
    1804:     /* collect f data, first time is for Jacobian, but make mass now */
    1805:     if (ctx->verbose > 0) {
    1806:       PetscInt ncells = 0, N;
    1807:       MatGetSize(ctx->J,&N,NULL);
    1808:       for (PetscInt grid=0;grid<ctx->num_grids;grid++) ncells += numCells[grid];
    1809:       PetscPrintf(ctx->comm,"%" PetscInt_FMT ") %s %" PetscInt_FMT " IPs, %" PetscInt_FMT " cells total, Nb=%" PetscInt_FMT ", Nq=%" PetscInt_FMT ", dim=%" PetscInt_FMT ", Tab: Nb=%" PetscInt_FMT " Nf=%" PetscInt_FMT " Np=%" PetscInt_FMT " cdim=%" PetscInt_FMT " N=%" PetscInt_FMT "\n",0,"FormLandau",nip_glb,ncells, Nb, Nq, dim, Nb, ctx->num_species, Nb, dim, N);
    1810:     }
    1811:     PetscMalloc4(nip_glb,&ww,nip_glb,&xx,nip_glb,&yy,nip_glb*dim*dim,&invJ_a);
    1812:     if (dim==3) {
    1813:       PetscMalloc1(nip_glb,&zz);
    1814:     }
    1815:     if (ctx->use_energy_tensor_trick) {
    1816:       PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &fe);
    1817:       PetscObjectSetName((PetscObject) fe, "energy");
    1818:     }
    1819:     /* init each grids static data - no batch */
    1820:     for (grid=0, outer_ipidx=0, outer_ej=0 ; grid < ctx->num_grids ; grid++) { // OpenMP (once)
    1821:       Vec             v2_2 = NULL; // projected function: v^2/2 for non-relativistic, gamma... for relativistic
    1822:       PetscSection    e_section;
    1823:       DM              dmEnergy;
    1824:       PetscInt        cStart, cEnd, ej;

    1826:       DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd);
    1827:       // prep energy trick, get v^2 / 2 vector
    1828:       if (ctx->use_energy_tensor_trick) {
    1829:         PetscErrorCode (*energyf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {ctx->use_relativistic_corrections ? gamma_m1_f : energy_f};
    1830:         Vec            glob_v2;
    1831:         PetscReal      *c2_0[1], data[1] = {PetscSqr(C_0(ctx->v_0))};

    1833:         DMClone(ctx->plex[grid], &dmEnergy);
    1834:         PetscObjectSetName((PetscObject) dmEnergy, "energy");
    1835:         DMSetField(dmEnergy, 0, NULL, (PetscObject)fe);
    1836:         DMCreateDS(dmEnergy);
    1837:         DMGetSection(dmEnergy, &e_section);
    1838:         DMGetGlobalVector(dmEnergy,&glob_v2);
    1839:         PetscObjectSetName((PetscObject) glob_v2, "trick");
    1840:         c2_0[0] = &data[0];
    1841:         DMProjectFunction(dmEnergy, 0., energyf, (void**)c2_0, INSERT_ALL_VALUES, glob_v2);
    1842:         DMGetLocalVector(dmEnergy, &v2_2);
    1843:         VecZeroEntries(v2_2); /* zero BCs so don't set */
    1844:         DMGlobalToLocalBegin(dmEnergy, glob_v2, INSERT_VALUES, v2_2);
    1845:         DMGlobalToLocalEnd  (dmEnergy, glob_v2, INSERT_VALUES, v2_2);
    1846:         DMViewFromOptions(dmEnergy,NULL, "-energy_dm_view");
    1847:         VecViewFromOptions(glob_v2,NULL, "-energy_vec_view");
    1848:         DMRestoreGlobalVector(dmEnergy, &glob_v2);
    1849:       }
    1850:       /* append part of the IP data for each grid */
    1851:       for (ej = 0 ; ej < numCells[grid]; ++ej, ++outer_ej) {
    1852:         PetscScalar *coefs = NULL;
    1853:         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);
    1854:         invJe = invJ_a + outer_ej*Nq*dim*dim;
    1855:         DMPlexComputeCellGeometryFEM(ctx->plex[grid], ej+cStart, quad, vj, Jdummy, invJe, detJj);
    1856:         if (ctx->use_energy_tensor_trick) {
    1857:           DMPlexVecGetClosure(dmEnergy, e_section, v2_2, ej+cStart, NULL, &coefs);
    1858:         }
    1859:         /* create static point data */
    1860:         for (PetscInt qj = 0; qj < Nq; qj++, outer_ipidx++) {
    1861:           const PetscInt  gidx = outer_ipidx;
    1862:           const PetscReal *invJ = &invJe[qj*dim*dim];
    1863:           ww    [gidx] = detJj[qj] * quadWeights[qj];
    1864:           if (dim==2) ww    [gidx] *=              vj[qj * dim + 0];  /* cylindrical coordinate, w/o 2pi */
    1865:           // get xx, yy, zz
    1866:           if (ctx->use_energy_tensor_trick) {
    1867:             double                  refSpaceDer[3],eGradPhi[3];
    1868:             const PetscReal * const DD = Tf[0]->T[1];
    1869:             const PetscReal         *Dq = &DD[qj*Nb*dim];
    1870:             for (int d = 0; d < 3; ++d) refSpaceDer[d] = eGradPhi[d] = 0.0;
    1871:             for (int b = 0; b < Nb; ++b) {
    1872:               for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[b*dim+d]*PetscRealPart(coefs[b]);
    1873:             }
    1874:             xx[gidx] = 1e10;
    1875:             if (ctx->use_relativistic_corrections) {
    1876:               double dg2_c2 = 0;
    1877:               //for (int d = 0; d < dim; ++d) refSpaceDer[d] *= c02;
    1878:               for (int d = 0; d < dim; ++d) dg2_c2 += PetscSqr(refSpaceDer[d]);
    1879:               dg2_c2 *= (double)c02;
    1880:               if (dg2_c2 >= .999) {
    1881:                 xx[gidx] = vj[qj * dim + 0]; /* coordinate */
    1882:                 yy[gidx] = vj[qj * dim + 1];
    1883:                 if (dim==3) zz[gidx] = vj[qj * dim + 2];
    1884:                 PetscPrintf(ctx->comm,"Error: %12.5e %" PetscInt_FMT ".%" PetscInt_FMT ") 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]);
    1885:               } else {
    1886:                 PetscReal fact = c02/PetscSqrtReal(1. - dg2_c2);
    1887:                 for (int d = 0; d < dim; ++d) refSpaceDer[d] *= fact;
    1888:                 // could test with other point u' that (grad - grad') * U (refSpaceDer, refSpaceDer') == 0
    1889:               }
    1890:             }
    1891:             if (xx[gidx] == 1e10) {
    1892:               for (int d = 0; d < dim; ++d) {
    1893:                 for (int e = 0 ; e < dim; ++e) {
    1894:                   eGradPhi[d] += invJ[e*dim+d]*refSpaceDer[e];
    1895:                 }
    1896:               }
    1897:               xx[gidx] = eGradPhi[0];
    1898:               yy[gidx] = eGradPhi[1];
    1899:               if (dim==3) zz[gidx] = eGradPhi[2];
    1900:             }
    1901:           } else {
    1902:             xx[gidx] = vj[qj * dim + 0]; /* coordinate */
    1903:             yy[gidx] = vj[qj * dim + 1];
    1904:             if (dim==3) zz[gidx] = vj[qj * dim + 2];
    1905:           }
    1906:         } /* q */
    1907:         if (ctx->use_energy_tensor_trick) {
    1908:           DMPlexVecRestoreClosure(dmEnergy, e_section, v2_2, ej+cStart, NULL, &coefs);
    1909:         }
    1910:       } /* ej */
    1911:       if (ctx->use_energy_tensor_trick) {
    1912:         DMRestoreLocalVector(dmEnergy, &v2_2);
    1913:         DMDestroy(&dmEnergy);
    1914:       }
    1915:     } /* grid */
    1916:     if (ctx->use_energy_tensor_trick) {
    1917:       PetscFEDestroy(&fe);
    1918:     }
    1919:     /* cache static data */
    1920:     if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
    1921: #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_KOKKOS_KERNELS)
    1922:       PetscReal invMass[LANDAU_MAX_SPECIES],nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
    1923:       for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
    1924:         for (PetscInt ii=ctx->species_offset[grid];ii<ctx->species_offset[grid+1];ii++) {
    1925:           invMass[ii]  = ctx->m_0/ctx->masses[ii];
    1926:           nu_alpha[ii] = PetscSqr(ctx->charges[ii]/ctx->m_0)*ctx->m_0/ctx->masses[ii];
    1927:           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);
    1928:         }
    1929:       }
    1930:       if (ctx->deviceType == LANDAU_CUDA) {
    1931: #if defined(PETSC_HAVE_CUDA)
    1932:         PetscCall(LandauCUDAStaticDataSet(ctx->plex[0], Nq, ctx->batch_sz, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset,
    1933:                                         nu_alpha, nu_beta, invMass, invJ_a, xx, yy, zz, ww, &ctx->SData_d));
    1934: #else
    1935:         SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type cuda not built");
    1936: #endif
    1937:       } else if (ctx->deviceType == LANDAU_KOKKOS) {
    1938: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    1939:         PetscCall(LandauKokkosStaticDataSet(ctx->plex[0], Nq, ctx->batch_sz, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset,
    1940:                                           nu_alpha, nu_beta, invMass,invJ_a,xx,yy,zz,ww,&ctx->SData_d));
    1941: #else
    1942:         SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type kokkos not built");
    1943: #endif
    1944:       }
    1945: #endif
    1946:       /* free */
    1947:       PetscFree4(ww,xx,yy,invJ_a);
    1948:       if (dim==3) {
    1949:         PetscFree(zz);
    1950:       }
    1951:     } else { /* CPU version, just copy in, only use part */
    1952:       ctx->SData_d.w = (void*)ww;
    1953:       ctx->SData_d.x = (void*)xx;
    1954:       ctx->SData_d.y = (void*)yy;
    1955:       ctx->SData_d.z = (void*)zz;
    1956:       ctx->SData_d.invJ = (void*)invJ_a;
    1957:     }
    1958:     PetscLogEventEnd(ctx->events[7],0,0,0,0);
    1959:   } // initialize
    1960:   return 0;
    1961: }

    1963: /* < v, u > */
    1964: static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    1965:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    1966:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    1967:                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
    1968: {
    1969:   g0[0] = 1.;
    1970: }

    1972: /* < v, u > */
    1973: static void g0_fake(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    1974:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    1975:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    1976:                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
    1977: {
    1978:   static double ttt = 1;
    1979:   g0[0] = ttt++;
    1980: }

    1982: /* < v, u > */
    1983: static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    1984:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    1985:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    1986:                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
    1987: {
    1988:   g0[0] = 2.*PETSC_PI*x[0];
    1989: }

    1991: static PetscErrorCode MatrixNfDestroy(void *ptr)
    1992: {
    1993:   PetscInt *nf = (PetscInt *)ptr;
    1994:   PetscFree(nf);
    1995:   return 0;
    1996: }

    1998: static PetscErrorCode LandauCreateMatrix(MPI_Comm comm, Vec X, IS grid_batch_is_inv[LANDAU_MAX_GRIDS], LandauCtx *ctx)
    1999: {
    2000:   PetscInt       *idxs=NULL;
    2001:   Mat            subM[LANDAU_MAX_GRIDS];

    2003:   if (!ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
    2004:     return 0;
    2005:   }
    2006:   // get the RCM for this grid to separate out species into blocks -- create 'idxs' & 'ctx->batch_is'
    2007:   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    2008:     PetscMalloc1(ctx->mat_offset[ctx->num_grids]*ctx->batch_sz, &idxs);
    2009:   }
    2010:   for (PetscInt grid=0 ; grid < ctx->num_grids ; grid++) {
    2011:     const PetscInt *values, n = ctx->mat_offset[grid+1] - ctx->mat_offset[grid];
    2012:     Mat             gMat;
    2013:     DM              massDM;
    2014:     PetscDS         prob;
    2015:     Vec             tvec;
    2016:     // get "mass" matrix for reordering
    2017:     DMClone(ctx->plex[grid], &massDM);
    2018:     DMCopyFields(ctx->plex[grid], massDM);
    2019:     DMCreateDS(massDM);
    2020:     DMGetDS(massDM, &prob);
    2021:     for (int ix=0, ii=ctx->species_offset[grid];ii<ctx->species_offset[grid+1];ii++,ix++) {
    2022:       PetscDSSetJacobian(prob, ix, ix, g0_fake, NULL, NULL, NULL);
    2023:     }
    2024:     PetscOptionsInsertString(NULL,"-dm_preallocate_only");
    2025:     DMSetFromOptions(massDM);
    2026:     DMCreateMatrix(massDM, &gMat);
    2027:     PetscOptionsInsertString(NULL,"-dm_preallocate_only false");
    2028:     MatSetOption(gMat,MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);
    2029:     MatSetOption(gMat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);
    2030:     DMCreateLocalVector(ctx->plex[grid],&tvec);
    2031:     DMPlexSNESComputeJacobianFEM(massDM, tvec, gMat, gMat, ctx);
    2032:     MatViewFromOptions(gMat, NULL, "-dm_landau_reorder_mat_view");
    2033:     DMDestroy(&massDM);
    2034:     VecDestroy(&tvec);
    2035:     subM[grid] = gMat;
    2036:     if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    2037:       MatOrderingType rtype = MATORDERINGRCM;
    2038:       IS              isrow,isicol;
    2039:       MatGetOrdering(gMat,rtype,&isrow,&isicol);
    2040:       ISInvertPermutation(isrow,PETSC_DECIDE,&grid_batch_is_inv[grid]);
    2041:       ISGetIndices(isrow, &values);
    2042:       for (PetscInt b_id=0 ; b_id < ctx->batch_sz ; b_id++) { // add batch size DMs for this species grid
    2043: #if !defined(LANDAU_SPECIES_MAJOR)
    2044:         PetscInt N = ctx->mat_offset[ctx->num_grids], n0 = ctx->mat_offset[grid] + b_id*N;
    2045:         for (int ii = 0; ii < n; ++ii) idxs[n0+ii] = values[ii] + n0;
    2046: #else
    2047:         PetscInt n0 = ctx->mat_offset[grid]*ctx->batch_sz + b_id*n;
    2048:         for (int ii = 0; ii < n; ++ii) idxs[n0+ii] = values[ii] + n0;
    2049: #endif
    2050:       }
    2051:       ISRestoreIndices(isrow, &values);
    2052:       ISDestroy(&isrow);
    2053:       ISDestroy(&isicol);
    2054:     }
    2055:   }
    2056:   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    2057:     ISCreateGeneral(comm,ctx->mat_offset[ctx->num_grids]*ctx->batch_sz,idxs,PETSC_OWN_POINTER,&ctx->batch_is);
    2058:   }
    2059:   // get a block matrix
    2060:   for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
    2061:     Mat               B = subM[grid];
    2062:     PetscInt          nloc, nzl, colbuf[1024], row;
    2063:     MatGetSize(B, &nloc, NULL);
    2064:     for (PetscInt b_id = 0 ; b_id < ctx->batch_sz ; b_id++) {
    2065:       const PetscInt    moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset);
    2066:       const PetscInt    *cols;
    2067:       const PetscScalar *vals;
    2068:       for (int i=0 ; i<nloc ; i++) {
    2069:         MatGetRow(B,i,&nzl,&cols,&vals);
    2071:         for (int j=0; j<nzl; j++) colbuf[j] = cols[j] + moffset;
    2072:         row = i + moffset;
    2073:         MatSetValues(ctx->J,1,&row,nzl,colbuf,vals,INSERT_VALUES);
    2074:         MatRestoreRow(B,i,&nzl,&cols,&vals);
    2075:       }
    2076:     }
    2077:   }
    2078:   for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
    2079:     MatDestroy(&subM[grid]);
    2080:   }
    2081:   MatAssemblyBegin(ctx->J,MAT_FINAL_ASSEMBLY);
    2082:   MatAssemblyEnd(ctx->J,MAT_FINAL_ASSEMBLY);

    2084:   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    2085:     Mat            mat_block_order;
    2086:     MatCreateSubMatrix(ctx->J,ctx->batch_is,ctx->batch_is,MAT_INITIAL_MATRIX,&mat_block_order); // use MatPermute
    2087:     MatViewFromOptions(mat_block_order, NULL, "-dm_landau_field_major_mat_view");
    2088:     MatDestroy(&ctx->J);
    2089:     ctx->J = mat_block_order;
    2090:     // override ops to make KSP work in field major space
    2091:     ctx->seqaij_mult                  = mat_block_order->ops->mult;
    2092:     mat_block_order->ops->mult        = LandauMatMult;
    2093:     mat_block_order->ops->multadd     = LandauMatMultAdd;
    2094:     ctx->seqaij_solve                 = NULL;
    2095:     ctx->seqaij_getdiagonal           = mat_block_order->ops->getdiagonal;
    2096:     mat_block_order->ops->getdiagonal = LandauMatGetDiagonal;
    2097:     ctx->seqaij_multtranspose         = mat_block_order->ops->multtranspose;
    2098:     mat_block_order->ops->multtranspose = LandauMatMultTranspose;
    2099:     VecDuplicate(X,&ctx->work_vec);
    2100:     VecScatterCreate(X, ctx->batch_is, ctx->work_vec, NULL, &ctx->plex_batch);
    2101:   }

    2103:   return 0;
    2104: }

    2106: PetscErrorCode DMPlexLandauCreateMassMatrix(DM pack, Mat *Amat);
    2107: /*@C
    2108:  DMPlexLandauCreateVelocitySpace - Create a DMPlex velocity space mesh

    2110:  Collective on comm

    2112:  Input Parameters:
    2113:  +   comm  - The MPI communicator
    2114:  .   dim - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
    2115:  -   prefix - prefix for options (not tested)

    2117:  Output Parameter:
    2118:  .   pack  - The DM object representing the mesh
    2119:  +   X - A vector (user destroys)
    2120:  -   J - Optional matrix (object destroys)

    2122:  Level: beginner

    2124:  .keywords: mesh
    2125:  .seealso: DMPlexCreate(), DMPlexLandauDestroyVelocitySpace()
    2126:  @*/
    2127: PetscErrorCode DMPlexLandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *pack)
    2128: {
    2129:   LandauCtx      *ctx;
    2130:   Vec            Xsub[LANDAU_MAX_GRIDS];
    2131:   IS             grid_batch_is_inv[LANDAU_MAX_GRIDS];

    2135:   PetscNew(&ctx);
    2136:   ctx->comm = comm; /* used for diagnostics and global errors */
    2137:   /* process options */
    2138:   ProcessOptions(ctx,prefix);
    2139:   if (dim==2) ctx->use_relativistic_corrections = PETSC_FALSE;
    2140:   /* Create Mesh */
    2141:   DMCompositeCreate(PETSC_COMM_SELF,pack);
    2142:   PetscLogEventBegin(ctx->events[13],0,0,0,0);
    2143:   PetscLogEventBegin(ctx->events[15],0,0,0,0);
    2144:   LandauDMCreateVMeshes(PETSC_COMM_SELF, dim, prefix, ctx, *pack); // creates grids (Forest of AMR)
    2145:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    2146:     /* create FEM */
    2147:     SetupDS(ctx->plex[grid],dim,grid,ctx);
    2148:     /* set initial state */
    2149:     DMCreateGlobalVector(ctx->plex[grid],&Xsub[grid]);
    2150:     PetscObjectSetName((PetscObject) Xsub[grid], "u_orig");
    2151:     /* initial static refinement, no solve */
    2152:     LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, 0, ctx);
    2153:     /* forest refinement - forest goes in (if forest), plex comes out */
    2154:     if (ctx->use_p4est) {
    2155:       DM plex;
    2156:       adapt(grid,ctx,&Xsub[grid]); // forest goes in, plex comes out
    2157:       DMViewFromOptions(ctx->plex[grid],NULL,"-dm_landau_amr_dm_view"); // need to differentiate - todo
    2158:       VecViewFromOptions(Xsub[grid], NULL, "-dm_landau_amr_vec_view");
    2159:       // convert to plex, all done with this level
    2160:       DMConvert(ctx->plex[grid], DMPLEX, &plex);
    2161:       DMDestroy(&ctx->plex[grid]);
    2162:       ctx->plex[grid] = plex;
    2163:     }
    2164: #if !defined(LANDAU_SPECIES_MAJOR)
    2165:     DMCompositeAddDM(*pack,ctx->plex[grid]);
    2166: #else
    2167:     for (PetscInt b_id=0;b_id<ctx->batch_sz;b_id++) { // add batch size DMs for this species grid
    2168:       DMCompositeAddDM(*pack,ctx->plex[grid]);
    2169:     }
    2170: #endif
    2171:     DMSetApplicationContext(ctx->plex[grid], ctx);
    2172:   }
    2173: #if !defined(LANDAU_SPECIES_MAJOR)
    2174:   // stack the batched DMs, could do it all here!!! b_id=0
    2175:   for (PetscInt b_id=1;b_id<ctx->batch_sz;b_id++) {
    2176:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    2177:       DMCompositeAddDM(*pack,ctx->plex[grid]);
    2178:     }
    2179:   }
    2180: #endif
    2181:   // create ctx->mat_offset
    2182:   ctx->mat_offset[0] = 0;
    2183:   for (PetscInt grid=0 ; grid < ctx->num_grids ; grid++) {
    2184:     PetscInt    n;
    2185:     VecGetLocalSize(Xsub[grid],&n);
    2186:     ctx->mat_offset[grid+1] = ctx->mat_offset[grid] + n;
    2187:   }
    2188:   // creat DM & Jac
    2189:   DMSetApplicationContext(*pack, ctx);
    2190:   PetscOptionsInsertString(NULL,"-dm_preallocate_only");
    2191:   DMSetFromOptions(*pack);
    2192:   DMCreateMatrix(*pack, &ctx->J);
    2193:   PetscOptionsInsertString(NULL,"-dm_preallocate_only false");
    2194:   MatSetOption(ctx->J,MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);
    2195:   MatSetOption(ctx->J,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);
    2196:   PetscObjectSetName((PetscObject)ctx->J, "Jac");
    2197:   // construct initial conditions in X
    2198:   DMCreateGlobalVector(*pack,X);
    2199:   for (PetscInt grid=0 ; grid < ctx->num_grids ; grid++) {
    2200:     PetscInt n;
    2201:     VecGetLocalSize(Xsub[grid],&n);
    2202:     for (PetscInt b_id = 0 ; b_id < ctx->batch_sz ; b_id++) {
    2203:       PetscScalar const *values;
    2204:       const PetscInt    moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset);
    2205:       LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, b_id, ctx);
    2206:       VecGetArrayRead(Xsub[grid],&values);
    2207:       for (int i=0, idx = moffset; i<n; i++, idx++) {
    2208:         VecSetValue(*X,idx,values[i],INSERT_VALUES);
    2209:       }
    2210:       VecRestoreArrayRead(Xsub[grid],&values);
    2211:     }
    2212:   }
    2213:   // cleanup
    2214:   for (PetscInt grid=0 ; grid < ctx->num_grids ; grid++) {
    2215:     VecDestroy(&Xsub[grid]);
    2216:   }
    2217:   /* check for correct matrix type */
    2218:   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
    2219:     PetscBool flg;
    2220:     if (ctx->deviceType == LANDAU_CUDA) {
    2221:       PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");
    2223:     } else if (ctx->deviceType == LANDAU_KOKKOS) {
    2224:       PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,MATAIJKOKKOS,"");
    2225: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    2227: #else
    2229: #endif
    2230:     }
    2231:   }
    2232:   PetscLogEventEnd(ctx->events[15],0,0,0,0);
    2233:   // create field major ordering

    2235:   ctx->work_vec   = NULL;
    2236:   ctx->plex_batch = NULL;
    2237:   ctx->batch_is   = NULL;
    2238:   for (int i=0;i<LANDAU_MAX_GRIDS;i++) grid_batch_is_inv[i] = NULL;
    2239:   PetscLogEventBegin(ctx->events[12],0,0,0,0);
    2240:   LandauCreateMatrix(comm, *X, grid_batch_is_inv, ctx);
    2241:   PetscLogEventEnd(ctx->events[12],0,0,0,0);

    2243:   // create AMR GPU assembly maps and static GPU data
    2244:   CreateStaticGPUData(dim,grid_batch_is_inv,ctx);

    2246:   PetscLogEventEnd(ctx->events[13],0,0,0,0);

    2248:   // create mass matrix
    2249:   DMPlexLandauCreateMassMatrix(*pack, NULL);

    2251:   if (J) *J = ctx->J;

    2253:   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    2254:     PetscContainer container;
    2255:     // cache ctx for KSP with batch/field major Jacobian ordering -ksp_type gmres/etc -dm_landau_jacobian_field_major_order
    2256:     PetscContainerCreate(PETSC_COMM_SELF, &container);
    2257:     PetscContainerSetPointer(container, (void *)ctx);
    2258:     PetscObjectCompose((PetscObject) ctx->J, "LandauCtx", (PetscObject) container);
    2259:     PetscContainerDestroy(&container);
    2260:     // batch solvers need to map -- can batch solvers work
    2261:     PetscContainerCreate(PETSC_COMM_SELF, &container);
    2262:     PetscContainerSetPointer(container, (void *)ctx->plex_batch);
    2263:     PetscObjectCompose((PetscObject) ctx->J, "plex_batch_is", (PetscObject) container);
    2264:     PetscContainerDestroy(&container);
    2265:   }
    2266:   // for batch solvers
    2267:   {
    2268:     PetscContainer  container;
    2269:     PetscInt        *pNf;
    2270:     PetscContainerCreate(PETSC_COMM_SELF, &container);
    2271:     PetscMalloc1(sizeof(*pNf), &pNf);
    2272:     *pNf = ctx->batch_sz;
    2273:     PetscContainerSetPointer(container, (void *)pNf);
    2274:     PetscContainerSetUserDestroy(container, MatrixNfDestroy);
    2275:     PetscObjectCompose((PetscObject)ctx->J, "batch size", (PetscObject) container);
    2276:     PetscContainerDestroy(&container);
    2277:   }

    2279:   return 0;
    2280: }

    2282: /*@
    2283:  DMPlexLandauDestroyVelocitySpace - Destroy a DMPlex velocity space mesh

    2285:  Collective on dm

    2287:  Input/Output Parameters:
    2288:  .   dm - the dm to destroy

    2290:  Level: beginner

    2292:  .keywords: mesh
    2293:  .seealso: DMPlexLandauCreateVelocitySpace()
    2294:  @*/
    2295: PetscErrorCode DMPlexLandauDestroyVelocitySpace(DM *dm)
    2296: {
    2297:   LandauCtx      *ctx;
    2298:   DMGetApplicationContext(*dm, &ctx);
    2299:   MatDestroy(&ctx->M);
    2300:   MatDestroy(&ctx->J);
    2301:   for (PetscInt ii=0;ii<ctx->num_species;ii++) PetscFEDestroy(&ctx->fe[ii]);
    2302:   ISDestroy(&ctx->batch_is);
    2303:   VecDestroy(&ctx->work_vec);
    2304:   VecScatterDestroy(&ctx->plex_batch);
    2305:   if (ctx->deviceType == LANDAU_CUDA) {
    2306: #if defined(PETSC_HAVE_CUDA)
    2307:     LandauCUDAStaticDataClear(&ctx->SData_d);
    2308: #else
    2309:     SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
    2310: #endif
    2311:   } else if (ctx->deviceType == LANDAU_KOKKOS) {
    2312: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    2313:     LandauKokkosStaticDataClear(&ctx->SData_d);
    2314: #else
    2315:     SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
    2316: #endif
    2317:   } else {
    2318:     if (ctx->SData_d.x) { /* in a CPU run */
    2319:       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;
    2320:       LandauIdx *coo_elem_offsets = (LandauIdx*)ctx->SData_d.coo_elem_offsets, *coo_elem_fullNb = (LandauIdx*)ctx->SData_d.coo_elem_fullNb, (*coo_elem_point_offsets)[LANDAU_MAX_NQ+1] = (LandauIdx (*)[LANDAU_MAX_NQ+1])ctx->SData_d.coo_elem_point_offsets;
    2321:       PetscFree4(ww,xx,yy,invJ);
    2322:       if (zz) {
    2323:         PetscFree(zz);
    2324:       }
    2325:       if (coo_elem_offsets) {
    2326:         PetscFree3(coo_elem_offsets,coo_elem_fullNb,coo_elem_point_offsets); // could be NULL
    2327:       }
    2328:     }
    2329:   }

    2331:   if (ctx->times[LANDAU_MATRIX_TOTAL] > 0) { // OMP timings
    2332:     PetscPrintf(ctx->comm, "TSStep               N  1.0 %10.3e\n",ctx->times[LANDAU_EX2_TSSOLVE]);
    2333:     PetscPrintf(ctx->comm, "2:           Solve:  %10.3e with %" PetscInt_FMT " threads\n",ctx->times[LANDAU_EX2_TSSOLVE] - ctx->times[LANDAU_MATRIX_TOTAL],ctx->batch_sz);
    2334:     PetscPrintf(ctx->comm, "3:          Landau:  %10.3e\n",ctx->times[LANDAU_MATRIX_TOTAL]);
    2335:     PetscPrintf(ctx->comm, "Landau Jacobian       %" PetscInt_FMT " 1.0 %10.3e\n",(PetscInt)ctx->times[LANDAU_JACOBIAN_COUNT],ctx->times[LANDAU_JACOBIAN]);
    2336:     PetscPrintf(ctx->comm, "Landau Operator       N 1.0  %10.3e\n",ctx->times[LANDAU_OPERATOR]);
    2337:     PetscPrintf(ctx->comm, "Landau Mass           N 1.0  %10.3e\n",ctx->times[LANDAU_MASS]);
    2338:     PetscPrintf(ctx->comm, " Jac-f-df (GPU)       N 1.0  %10.3e\n",ctx->times[LANDAU_F_DF]);
    2339:     PetscPrintf(ctx->comm, " Kernel (GPU)         N 1.0  %10.3e\n",ctx->times[LANDAU_KERNEL]);
    2340:     PetscPrintf(ctx->comm, "MatLUFactorNum        X 1.0 %10.3e\n",ctx->times[KSP_FACTOR]);
    2341:     PetscPrintf(ctx->comm, "MatSolve              X 1.0 %10.3e\n",ctx->times[KSP_SOLVE]);
    2342:   }
    2343:   for (PetscInt grid=0 ; grid < ctx->num_grids ; grid++) {
    2344:     DMDestroy(&ctx->plex[grid]);
    2345:   }
    2346:   PetscFree(ctx);
    2347:   DMDestroy(dm);
    2348:   return 0;
    2349: }

    2351: /* < v, ru > */
    2352: static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    2353:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    2354:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    2355:                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
    2356: {
    2357:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
    2358:   f0[0] = u[ii];
    2359: }

    2361: /* < v, ru > */
    2362: static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    2363:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    2364:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    2365:                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
    2366: {
    2367:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
    2368:   f0[0] = x[jj]*u[ii]; /* x momentum */
    2369: }

    2371: static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    2372:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    2373:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    2374:                     PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
    2375: {
    2376:   PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
    2377:   double tmp1 = 0.;
    2378:   for (i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
    2379:   f0[0] = tmp1*u[ii];
    2380: }

    2382: static PetscErrorCode gamma_n_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *actx)
    2383: {
    2384:   const PetscReal *c2_0_arr = ((PetscReal*)actx);
    2385:   const PetscReal c02 = c2_0_arr[0];

    2387:   for (int s = 0 ; s < Nf ; s++) {
    2388:     PetscReal tmp1 = 0.;
    2389:     for (int i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
    2390: #if defined(PETSC_USE_DEBUG)
    2391:     u[s] = PetscSqrtReal(1. + tmp1/c02);//  u[0] = PetscSqrtReal(1. + xx);
    2392: #else
    2393:     {
    2394:       PetscReal xx = tmp1/c02;
    2395:       u[s] = xx/(PetscSqrtReal(1. + xx) + 1.); // better conditioned = xx/(PetscSqrtReal(1. + xx) + 1.)
    2396:     }
    2397: #endif
    2398:   }
    2399:   return 0;
    2400: }

    2402: /* < v, ru > */
    2403: static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    2404:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    2405:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    2406:                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
    2407: {
    2408:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
    2409:   f0[0] = 2.*PETSC_PI*x[0]*u[ii];
    2410: }

    2412: /* < v, ru > */
    2413: static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    2414:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    2415:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    2416:                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
    2417: {
    2418:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
    2419:   f0[0] = 2.*PETSC_PI*x[0]*x[1]*u[ii];
    2420: }

    2422: static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    2423:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    2424:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    2425:                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
    2426: {
    2427:   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
    2428:   f0[0] =  2.*PETSC_PI*x[0]*(x[0]*x[0] + x[1]*x[1])*u[ii];
    2429: }

    2431: /*@
    2432:  DMPlexLandauPrintNorms - collects moments and prints them

    2434:  Collective on dm

    2436:  Input Parameters:
    2437:  +   X  - the state
    2438:  -   stepi - current step to print

    2440:  Level: beginner

    2442:  .keywords: mesh
    2443:  .seealso: DMPlexLandauCreateVelocitySpace()
    2444:  @*/
    2445: PetscErrorCode DMPlexLandauPrintNorms(Vec X, PetscInt stepi)
    2446: {
    2447:   LandauCtx      *ctx;
    2448:   PetscDS        prob;
    2449:   DM             pack;
    2450:   PetscInt       cStart, cEnd, dim, ii, i0, nDMs;
    2451:   PetscScalar    xmomentumtot=0, ymomentumtot=0, zmomentumtot=0, energytot=0, densitytot=0, tt[LANDAU_MAX_SPECIES];
    2452:   PetscScalar    xmomentum[LANDAU_MAX_SPECIES],  ymomentum[LANDAU_MAX_SPECIES],  zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
    2453:   Vec            *globXArray;

    2455:   VecGetDM(X, &pack);
    2457:   DMGetDimension(pack, &dim);
    2459:   DMGetApplicationContext(pack, &ctx);
    2461:   /* print momentum and energy */
    2462:   DMCompositeGetNumberDM(pack,&nDMs);
    2464:   PetscMalloc(sizeof(*globXArray)*nDMs, &globXArray);
    2465:   DMCompositeGetAccessArray(pack, X, nDMs, NULL, globXArray);
    2466:   for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) {
    2467:     Vec Xloc = globXArray[ LAND_PACK_IDX(ctx->batch_view_idx,grid) ];
    2468:     DMGetDS(ctx->plex[grid], &prob);
    2469:     for (ii=ctx->species_offset[grid],i0=0;ii<ctx->species_offset[grid+1];ii++,i0++) {
    2470:       PetscScalar user[2] = { (PetscScalar)i0, (PetscScalar)ctx->charges[ii]};
    2471:       PetscDSSetConstants(prob, 2, user);
    2472:       if (dim==2) { /* 2/3X + 3V (cylindrical coordinates) */
    2473:         PetscDSSetObjective(prob, 0, &f0_s_rden);
    2474:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2475:         density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
    2476:         PetscDSSetObjective(prob, 0, &f0_s_rmom);
    2477:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2478:         zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
    2479:         PetscDSSetObjective(prob, 0, &f0_s_rv2);
    2480:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2481:         energy[ii] = tt[0]*0.5*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
    2482:         zmomentumtot += zmomentum[ii];
    2483:         energytot  += energy[ii];
    2484:         densitytot += density[ii];
    2485:         PetscPrintf(ctx->comm, "%3D) species-%" PetscInt_FMT ": charge density= %20.13e z-momentum= %20.13e energy= %20.13e",stepi,ii,PetscRealPart(density[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));
    2486:       } else { /* 2/3Xloc + 3V */
    2487:         PetscDSSetObjective(prob, 0, &f0_s_den);
    2488:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2489:         density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
    2490:         PetscDSSetObjective(prob, 0, &f0_s_mom);
    2491:         user[1] = 0;
    2492:         PetscDSSetConstants(prob, 2, user);
    2493:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2494:         xmomentum[ii]  = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
    2495:         user[1] = 1;
    2496:         PetscDSSetConstants(prob, 2, user);
    2497:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2498:         ymomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
    2499:         user[1] = 2;
    2500:         PetscDSSetConstants(prob, 2, user);
    2501:         DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2502:         zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
    2503:         if (ctx->use_relativistic_corrections) {
    2504:           /* gamma * M * f */
    2505:           if (ii==0 && grid==0) { // do all at once
    2506:             Vec            Mf, globGamma, *globMfArray, *globGammaArray;
    2507:             PetscErrorCode (*gammaf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {gamma_n_f};
    2508:             PetscReal      *c2_0[1], data[1];

    2510:             VecDuplicate(X,&globGamma);
    2511:             VecDuplicate(X,&Mf);
    2512:             PetscMalloc(sizeof(*globMfArray)*nDMs, &globMfArray);
    2513:             PetscMalloc(sizeof(*globMfArray)*nDMs, &globGammaArray);
    2514:             /* M * f */
    2515:             MatMult(ctx->M,X,Mf);
    2516:             /* gamma */
    2517:             DMCompositeGetAccessArray(pack, globGamma, nDMs, NULL, globGammaArray);
    2518:             for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) { // yes a grid loop in a grid loop to print nice, need to fix for batching
    2519:               Vec v1 = globGammaArray[ LAND_PACK_IDX(ctx->batch_view_idx,grid) ];
    2520:               data[0] = PetscSqr(C_0(ctx->v_0));
    2521:               c2_0[0] = &data[0];
    2522:               DMProjectFunction(ctx->plex[grid], 0., gammaf, (void**)c2_0, INSERT_ALL_VALUES, v1);
    2523:             }
    2524:             DMCompositeRestoreAccessArray(pack, globGamma, nDMs, NULL, globGammaArray);
    2525:             /* gamma * Mf */
    2526:             DMCompositeGetAccessArray(pack, globGamma, nDMs, NULL, globGammaArray);
    2527:             DMCompositeGetAccessArray(pack, Mf, nDMs, NULL, globMfArray);
    2528:             for (PetscInt grid = 0; grid < ctx->num_grids ; grid++) { // yes a grid loop in a grid loop to print nice
    2529:               PetscInt Nf = ctx->species_offset[grid+1] - ctx->species_offset[grid], N, bs;
    2530:               Vec      Mfsub = globMfArray[ LAND_PACK_IDX(ctx->batch_view_idx,grid) ], Gsub = globGammaArray[ LAND_PACK_IDX(ctx->batch_view_idx,grid) ], v1, v2;
    2531:               // get each component
    2532:               VecGetSize(Mfsub,&N);
    2533:               VecCreate(ctx->comm,&v1);
    2534:               VecSetSizes(v1,PETSC_DECIDE,N/Nf);
    2535:               VecCreate(ctx->comm,&v2);
    2536:               VecSetSizes(v2,PETSC_DECIDE,N/Nf);
    2537:               VecSetFromOptions(v1); // ???
    2538:               VecSetFromOptions(v2);
    2539:               // get each component
    2540:               VecGetBlockSize(Gsub,&bs);
    2542:               VecGetBlockSize(Mfsub,&bs);
    2544:               for (int i=0, ix=ctx->species_offset[grid] ; i<Nf ; i++, ix++) {
    2545:                 PetscScalar val;
    2546:                 VecStrideGather(Gsub,i,v1,INSERT_VALUES);
    2547:                 VecStrideGather(Mfsub,i,v2,INSERT_VALUES);
    2548:                 VecDot(v1,v2,&val);
    2549:                 energy[ix] = PetscRealPart(val)*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ix];
    2550:               }
    2551:               VecDestroy(&v1);
    2552:               VecDestroy(&v2);
    2553:             } /* grids */
    2554:             DMCompositeRestoreAccessArray(pack, globGamma, nDMs, NULL, globGammaArray);
    2555:             DMCompositeRestoreAccessArray(pack, Mf, nDMs, NULL, globMfArray);
    2556:             PetscFree(globGammaArray);
    2557:             PetscFree(globMfArray);
    2558:             VecDestroy(&globGamma);
    2559:             VecDestroy(&Mf);
    2560:           }
    2561:         } else {
    2562:           PetscDSSetObjective(prob, 0, &f0_s_v2);
    2563:           DMPlexComputeIntegralFEM(ctx->plex[grid],Xloc,tt,ctx);
    2564:           energy[ii]    = 0.5*tt[0]*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
    2565:         }
    2566:         PetscPrintf(ctx->comm, "%3" PetscInt_FMT ") species %" PetscInt_FMT ": density=%20.13e, x-momentum=%20.13e, y-momentum=%20.13e, z-momentum=%20.13e, energy=%21.13e",stepi,ii,PetscRealPart(density[ii]),PetscRealPart(xmomentum[ii]),PetscRealPart(ymomentum[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));
    2567:         xmomentumtot += xmomentum[ii];
    2568:         ymomentumtot += ymomentum[ii];
    2569:         zmomentumtot += zmomentum[ii];
    2570:         energytot    += energy[ii];
    2571:         densitytot   += density[ii];
    2572:       }
    2573:       if (ctx->num_species>1) PetscPrintf(ctx->comm, "\n");
    2574:     }
    2575:   }
    2576:   DMCompositeRestoreAccessArray(pack, X, nDMs, NULL, globXArray);
    2577:   PetscFree(globXArray);
    2578:   /* totals */
    2579:   DMPlexGetHeightStratum(ctx->plex[0],0,&cStart,&cEnd);
    2580:   if (ctx->num_species>1) {
    2581:     if (dim==2) {
    2582:       PetscPrintf(ctx->comm, "\t%3" PetscInt_FMT ") Total: charge density=%21.13e, momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %" PetscInt_FMT " cells on electron grid)",stepi,(double)PetscRealPart(densitytot),(double)PetscRealPart(zmomentumtot),(double)PetscRealPart(energytot),(double)(ctx->masses[1]/ctx->masses[0]),cEnd-cStart);
    2583:     } else {
    2584:       PetscPrintf(ctx->comm, "\t%3" PetscInt_FMT ") 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, %" PetscInt_FMT " cells)",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);
    2585:     }
    2586:   } else PetscPrintf(ctx->comm, " -- %" PetscInt_FMT " cells",cEnd-cStart);
    2587:   PetscPrintf(ctx->comm,"\n");
    2588:   return 0;
    2589: }

    2591: /*@
    2592:  DMPlexLandauCreateMassMatrix - Create mass matrix for Landau in Plex space (not field major order of Jacobian)

    2594:  Collective on pack

    2596:  Input Parameters:
    2597:  . pack     - the DM object

    2599:  Output Parameters:
    2600:  . Amat - The mass matrix (optional), mass matrix is added to the DM context

    2602:  Level: beginner

    2604:  .keywords: mesh
    2605:  .seealso: DMPlexLandauCreateVelocitySpace()
    2606:  @*/
    2607: PetscErrorCode DMPlexLandauCreateMassMatrix(DM pack, Mat *Amat)
    2608: {
    2609:   DM             mass_pack,massDM[LANDAU_MAX_GRIDS];
    2610:   PetscDS        prob;
    2611:   PetscInt       ii,dim,N1=1,N2;
    2612:   LandauCtx      *ctx;
    2613:   Mat            packM,subM[LANDAU_MAX_GRIDS];

    2617:   DMGetApplicationContext(pack, &ctx);
    2619:   PetscLogEventBegin(ctx->events[14],0,0,0,0);
    2620:   DMGetDimension(pack, &dim);
    2621:   DMCompositeCreate(PetscObjectComm((PetscObject) pack),&mass_pack);
    2622:   /* create pack mass matrix */
    2623:   for (PetscInt grid=0, ix=0 ; grid<ctx->num_grids ; grid++) {
    2624:     DMClone(ctx->plex[grid], &massDM[grid]);
    2625:     DMCopyFields(ctx->plex[grid], massDM[grid]);
    2626:     DMCreateDS(massDM[grid]);
    2627:     DMGetDS(massDM[grid], &prob);
    2628:     for (ix=0, ii=ctx->species_offset[grid];ii<ctx->species_offset[grid+1];ii++,ix++) {
    2629:       if (dim==3) PetscDSSetJacobian(prob, ix, ix, g0_1, NULL, NULL, NULL);
    2630:       else        PetscDSSetJacobian(prob, ix, ix, g0_r, NULL, NULL, NULL);
    2631:     }
    2632: #if !defined(LANDAU_SPECIES_MAJOR)
    2633:     DMCompositeAddDM(mass_pack,massDM[grid]);
    2634: #else
    2635:     for (PetscInt b_id=0;b_id<ctx->batch_sz;b_id++) { // add batch size DMs for this species grid
    2636:       DMCompositeAddDM(mass_pack,massDM[grid]);
    2637:     }
    2638: #endif
    2639:     DMCreateMatrix(massDM[grid], &subM[grid]);
    2640:   }
    2641: #if !defined(LANDAU_SPECIES_MAJOR)
    2642:   // stack the batched DMs
    2643:   for (PetscInt b_id=1;b_id<ctx->batch_sz;b_id++) {
    2644:     for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    2645:       DMCompositeAddDM(mass_pack, massDM[grid]);
    2646:     }
    2647:   }
    2648: #endif
    2649:   PetscOptionsInsertString(NULL,"-dm_preallocate_only");
    2650:   DMSetFromOptions(mass_pack);
    2651:   DMCreateMatrix(mass_pack, &packM);
    2652:   PetscOptionsInsertString(NULL,"-dm_preallocate_only false");
    2653:   MatSetOption(packM,MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);
    2654:   MatSetOption(packM,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);
    2655:   DMDestroy(&mass_pack);
    2656:   /* make mass matrix for each block */
    2657:   for (PetscInt grid=0;grid<ctx->num_grids;grid++) {
    2658:     Vec locX;
    2659:     DM  plex = massDM[grid];
    2660:     DMGetLocalVector(plex, &locX);
    2661:     /* Mass matrix is independent of the input, so no need to fill locX */
    2662:     DMPlexSNESComputeJacobianFEM(plex, locX, subM[grid], subM[grid], ctx);
    2663:     DMRestoreLocalVector(plex, &locX);
    2664:     DMDestroy(&massDM[grid]);
    2665:   }
    2666:   MatGetSize(ctx->J, &N1, NULL);
    2667:   MatGetSize(packM, &N2, NULL);
    2669:   /* assemble block diagonals */
    2670:   for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
    2671:     Mat               B = subM[grid];
    2672:     PetscInt          nloc, nzl, colbuf[1024], row;
    2673:     MatGetSize(B, &nloc, NULL);
    2674:     for (PetscInt b_id = 0 ; b_id < ctx->batch_sz ; b_id++) {
    2675:       const PetscInt    moffset = LAND_MOFFSET(b_id,grid,ctx->batch_sz,ctx->num_grids,ctx->mat_offset);
    2676:       const PetscInt    *cols;
    2677:       const PetscScalar *vals;
    2678:       for (int i=0 ; i<nloc ; i++) {
    2679:         MatGetRow(B,i,&nzl,&cols,&vals);
    2681:         for (int j=0; j<nzl; j++) colbuf[j] = cols[j] + moffset;
    2682:         row = i + moffset;
    2683:         MatSetValues(packM,1,&row,nzl,colbuf,vals,INSERT_VALUES);
    2684:         MatRestoreRow(B,i,&nzl,&cols,&vals);
    2685:       }
    2686:     }
    2687:   }
    2688:   // cleanup
    2689:   for (PetscInt grid=0 ; grid<ctx->num_grids ; grid++) {
    2690:     MatDestroy(&subM[grid]);
    2691:   }
    2692:   MatAssemblyBegin(packM,MAT_FINAL_ASSEMBLY);
    2693:   MatAssemblyEnd(packM,MAT_FINAL_ASSEMBLY);
    2694:   PetscObjectSetName((PetscObject)packM, "mass");
    2695:   MatViewFromOptions(packM,NULL,"-dm_landau_mass_view");
    2696:   ctx->M = packM;
    2697:   if (Amat) *Amat = packM;
    2698:   PetscLogEventEnd(ctx->events[14],0,0,0,0);
    2699:   return 0;
    2700: }

    2702: /*@
    2703:  DMPlexLandauIFunction - TS residual calculation

    2705:  Collective on ts

    2707:  Input Parameters:
    2708:  +   TS  - The time stepping context
    2709:  .   time_dummy - current time (not used)
    2710:  -   X - Current state
    2711:  +   X_t - Time derivative of current state
    2712:  .   actx - Landau context

    2714:  Output Parameter:
    2715:  .   F  - The residual

    2717:  Level: beginner

    2719:  .keywords: mesh
    2720:  .seealso: DMPlexLandauCreateVelocitySpace(), DMPlexLandauIJacobian()
    2721:  @*/
    2722: PetscErrorCode DMPlexLandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
    2723: {
    2724:   LandauCtx      *ctx=(LandauCtx*)actx;
    2725:   PetscInt       dim;
    2726:   DM             pack;
    2727: #if defined(PETSC_HAVE_THREADSAFETY)
    2728:   double         starttime, endtime;
    2729: #endif

    2731:   TSGetDM(ts,&pack);
    2732:   DMGetApplicationContext(pack, &ctx);
    2734:   if (ctx->stage) {
    2735:     PetscLogStagePush(ctx->stage);
    2736:   }
    2737:   PetscLogEventBegin(ctx->events[11],0,0,0,0);
    2738:   PetscLogEventBegin(ctx->events[0],0,0,0,0);
    2739: #if defined(PETSC_HAVE_THREADSAFETY)
    2740:   starttime = MPI_Wtime();
    2741: #endif
    2742:   DMGetDimension(pack, &dim);
    2743:   if (!ctx->aux_bool) {
    2744:     PetscInfo(ts, "Create Landau Jacobian t=%g X=%p %s\n",time_dummy,X_t,ctx->aux_bool ? " -- seems to be in line search" : "");
    2745:     LandauFormJacobian_Internal(X,ctx->J,dim,0.0,(void*)ctx);
    2746:     MatViewFromOptions(ctx->J, NULL, "-dm_landau_jacobian_view");
    2747:     ctx->aux_bool = PETSC_TRUE;
    2748:   } else {
    2749:     PetscInfo(ts, "Skip forming Jacobian, has not changed (should check norm)\n");
    2750:   }
    2751:   /* mat vec for op */
    2752:   MatMult(ctx->J,X,F); /* C*f */
    2753:   /* add time term */
    2754:   if (X_t) {
    2755:     MatMultAdd(ctx->M,X_t,F,F);
    2756:   }
    2757: #if defined(PETSC_HAVE_THREADSAFETY)
    2758:   if (ctx->stage) {
    2759:     endtime = MPI_Wtime();
    2760:     ctx->times[LANDAU_OPERATOR] += (endtime - starttime);
    2761:     ctx->times[LANDAU_JACOBIAN] += (endtime - starttime);
    2762:     ctx->times[LANDAU_JACOBIAN_COUNT] += 1;
    2763:   }
    2764: #endif
    2765:   PetscLogEventEnd(ctx->events[0],0,0,0,0);
    2766:   PetscLogEventEnd(ctx->events[11],0,0,0,0);
    2767:   if (ctx->stage) {
    2768:     PetscLogStagePop();
    2769: #if defined(PETSC_HAVE_THREADSAFETY)
    2770:     ctx->times[LANDAU_MATRIX_TOTAL] += (endtime - starttime);
    2771: #endif
    2772:   }
    2773:   return 0;
    2774: }

    2776: /*@
    2777:  DMPlexLandauIJacobian - TS Jacobian construction

    2779:  Collective on ts

    2781:  Input Parameters:
    2782:  +   TS  - The time stepping context
    2783:  .   time_dummy - current time (not used)
    2784:  -   X - Current state
    2785:  +   U_tdummy - Time derivative of current state (not used)
    2786:  .   shift - shift for du/dt term
    2787:  -   actx - Landau context

    2789:  Output Parameter:
    2790:  .   Amat  - Jacobian
    2791:  +   Pmat  - same as Amat

    2793:  Level: beginner

    2795:  .keywords: mesh
    2796:  .seealso: DMPlexLandauCreateVelocitySpace(), DMPlexLandauIFunction()
    2797:  @*/
    2798: PetscErrorCode DMPlexLandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
    2799: {
    2800:   LandauCtx      *ctx=NULL;
    2801:   PetscInt       dim;
    2802:   DM             pack;
    2803: #if defined(PETSC_HAVE_THREADSAFETY)
    2804:   double         starttime, endtime;
    2805: #endif
    2806:   TSGetDM(ts,&pack);
    2807:   DMGetApplicationContext(pack, &ctx);
    2810:   DMGetDimension(pack, &dim);
    2811:   /* get collision Jacobian into A */
    2812:   if (ctx->stage) {
    2813:     PetscLogStagePush(ctx->stage);
    2814:   }
    2815:   PetscLogEventBegin(ctx->events[11],0,0,0,0);
    2816:   PetscLogEventBegin(ctx->events[9],0,0,0,0);
    2817: #if defined(PETSC_HAVE_THREADSAFETY)
    2818:   starttime = MPI_Wtime();
    2819: #endif
    2820:   PetscInfo(ts, "Adding just mass to Jacobian t=%g, shift=%g\n",(double)time_dummy,(double)shift);
    2823:   if (!ctx->use_matrix_mass) {
    2824:     LandauFormJacobian_Internal(X,ctx->J,dim,shift,(void*)ctx);
    2825:     MatViewFromOptions(ctx->J, NULL, "-dm_landau_mat_view");
    2826:   } else { /* add mass */
    2827:     MatAXPY(Pmat,shift,ctx->M,SAME_NONZERO_PATTERN);
    2828:   }
    2829:   ctx->aux_bool = PETSC_FALSE;
    2830: #if defined(PETSC_HAVE_THREADSAFETY)
    2831:   if (ctx->stage) {
    2832:     endtime = MPI_Wtime();
    2833:     ctx->times[LANDAU_OPERATOR] += (endtime - starttime);
    2834:     ctx->times[LANDAU_MASS] += (endtime - starttime);
    2835:   }
    2836: #endif
    2837:   PetscLogEventEnd(ctx->events[9],0,0,0,0);
    2838:   PetscLogEventEnd(ctx->events[11],0,0,0,0);
    2839:   if (ctx->stage) {
    2840:     PetscLogStagePop();
    2841: #if defined(PETSC_HAVE_THREADSAFETY)
    2842:     ctx->times[LANDAU_MATRIX_TOTAL] += (endtime - starttime);
    2843: #endif
    2844:   }
    2845:   return 0;
    2846: }