xref: /petsc/src/ts/utils/dmplexlandau/plexland.c (revision df4cd43f92eaa320656440c40edb1046daee8f75)
1 #include <../src/mat/impls/aij/seq/aij.h>
2 #include <petsc/private/dmpleximpl.h> /*I "petscdmplex.h" I*/
3 #include <petsclandau.h>              /*I "petsclandau.h"   I*/
4 #include <petscts.h>
5 #include <petscdmforest.h>
6 #include <petscdmcomposite.h>
7 
8 /* Landau collision operator */
9 
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
18 
19 #define PETSC_THREAD_SYNC
20 #include "land_tensors.h"
21 
22 #if defined(PETSC_HAVE_OPENMP)
23   #include <omp.h>
24 #endif
25 
26 static PetscErrorCode LandauGPUMapsDestroy(void *ptr)
27 {
28   P4estVertexMaps *maps = (P4estVertexMaps *)ptr;
29   PetscFunctionBegin;
30   // free device data
31   if (maps[0].deviceType != LANDAU_CPU) {
32 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
33     if (maps[0].deviceType == LANDAU_KOKKOS) {
34       PetscCall(LandauKokkosDestroyMatMaps(maps, maps[0].numgrids)); // implies Kokkos does
35     }                                                                // else could be CUDA
36 #elif defined(PETSC_HAVE_CUDA)
37     if (maps[0].deviceType == LANDAU_CUDA) {
38       PetscCall(LandauCUDADestroyMatMaps(maps, maps[0].numgrids));
39     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps->deviceType %d ?????", maps->deviceType);
40 #endif
41   }
42   // free host data
43   for (PetscInt grid = 0; grid < maps[0].numgrids; grid++) {
44     PetscCall(PetscFree(maps[grid].c_maps));
45     PetscCall(PetscFree(maps[grid].gIdx));
46   }
47   PetscCall(PetscFree(maps));
48 
49   PetscFunctionReturn(PETSC_SUCCESS);
50 }
51 static PetscErrorCode energy_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
52 {
53   PetscReal v2 = 0;
54   PetscFunctionBegin;
55   /* compute v^2 / 2 */
56   for (int i = 0; i < dim; ++i) v2 += x[i] * x[i];
57   /* evaluate the Maxwellian */
58   u[0] = v2 / 2;
59   PetscFunctionReturn(PETSC_SUCCESS);
60 }
61 
62 /* needs double */
63 static PetscErrorCode gamma_m1_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
64 {
65   PetscReal *c2_0_arr = ((PetscReal *)actx);
66   double     u2 = 0, c02 = (double)*c2_0_arr, xx;
67 
68   PetscFunctionBegin;
69   /* compute u^2 / 2 */
70   for (int i = 0; i < dim; ++i) u2 += x[i] * x[i];
71   /* gamma - 1 = g_eps, for conditioning and we only take derivatives */
72   xx = u2 / c02;
73 #if defined(PETSC_USE_DEBUG)
74   u[0] = PetscSqrtReal(1. + xx);
75 #else
76   u[0] = xx / (PetscSqrtReal(1. + xx) + 1.) - 1.; // better conditioned. -1 might help condition and only used for derivative
77 #endif
78   PetscFunctionReturn(PETSC_SUCCESS);
79 }
80 
81 /*
82  LandauFormJacobian_Internal - Evaluates Jacobian matrix.
83 
84  Input Parameters:
85  .  globX - input vector
86  .  actx - optional user-defined context
87  .  dim - dimension
88 
89  Output Parameters:
90  .  J0acP - Jacobian matrix filled, not created
91  */
92 static PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, PetscReal shift, void *a_ctx)
93 {
94   LandauCtx         *ctx = (LandauCtx *)a_ctx;
95   PetscInt           numCells[LANDAU_MAX_GRIDS], Nq, Nb;
96   PetscQuadrature    quad;
97   PetscReal          Eq_m[LANDAU_MAX_SPECIES]; // could be static data w/o quench (ex2)
98   PetscScalar       *cellClosure = NULL;
99   const PetscScalar *xdata       = NULL;
100   PetscDS            prob;
101   PetscContainer     container;
102   P4estVertexMaps   *maps;
103   Mat                subJ[LANDAU_MAX_GRIDS * LANDAU_MAX_BATCH_SZ];
104 
105   PetscFunctionBegin;
106   PetscValidHeaderSpecific(a_X, VEC_CLASSID, 1);
107   PetscValidHeaderSpecific(JacP, MAT_CLASSID, 2);
108   PetscValidPointer(ctx, 5);
109   /* check for matrix container for GPU assembly. Support CPU assembly for debugging */
110   PetscCheck(ctx->plex[0] != NULL, ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
111   PetscCall(PetscLogEventBegin(ctx->events[10], 0, 0, 0, 0));
112   PetscCall(DMGetDS(ctx->plex[0], &prob)); // same DS for all grids
113   PetscCall(PetscObjectQuery((PetscObject)JacP, "assembly_maps", (PetscObject *)&container));
114   if (container) {
115     PetscCheck(ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "maps but no GPU assembly");
116     PetscCall(PetscContainerGetPointer(container, (void **)&maps));
117     PetscCheck(maps, ctx->comm, PETSC_ERR_ARG_WRONG, "empty GPU matrix container");
118     for (PetscInt i = 0; i < ctx->num_grids * ctx->batch_sz; i++) subJ[i] = NULL;
119   } else {
120     PetscCheck(!ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "No maps but GPU assembly");
121     for (PetscInt tid = 0; tid < ctx->batch_sz; tid++) {
122       for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMCreateMatrix(ctx->plex[grid], &subJ[LAND_PACK_IDX(tid, grid)]));
123     }
124     maps = NULL;
125   }
126   // 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)
127   PetscCall(PetscFEGetQuadrature(ctx->fe[0], &quad));
128   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
129   Nb = Nq;
130   PetscCheck(Nq <= LANDAU_MAX_NQ, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nq = %" PetscInt_FMT " > LANDAU_MAX_NQ (%d)", Nq, LANDAU_MAX_NQ);
131   // get metadata for collecting dynamic data
132   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
133     PetscInt cStart, cEnd;
134     PetscCheck(ctx->plex[grid] != NULL, ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
135     PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
136     numCells[grid] = cEnd - cStart; // grids can have different topology
137   }
138   PetscCall(PetscLogEventEnd(ctx->events[10], 0, 0, 0, 0));
139   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 */
140     DM pack;
141     PetscCall(VecGetDM(a_X, &pack));
142     PetscCheck(pack, PETSC_COMM_SELF, PETSC_ERR_PLIB, "pack has no DM");
143     PetscCall(PetscLogEventBegin(ctx->events[1], 0, 0, 0, 0));
144     for (PetscInt fieldA = 0; fieldA < ctx->num_species; fieldA++) {
145       Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
146       if (dim == 2) Eq_m[fieldA] *= 2 * PETSC_PI;                                                  /* add the 2pi term that is not in Landau */
147     }
148     if (!ctx->gpu_assembly) {
149       Vec         *locXArray, *globXArray;
150       PetscScalar *cellClosure_it;
151       PetscInt     cellClosure_sz = 0, nDMs, Nf[LANDAU_MAX_GRIDS];
152       PetscSection section[LANDAU_MAX_GRIDS], globsection[LANDAU_MAX_GRIDS];
153       for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
154         PetscCall(DMGetLocalSection(ctx->plex[grid], &section[grid]));
155         PetscCall(DMGetGlobalSection(ctx->plex[grid], &globsection[grid]));
156         PetscCall(PetscSectionGetNumFields(section[grid], &Nf[grid]));
157       }
158       /* count cellClosure size */
159       PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
160       for (PetscInt grid = 0; grid < ctx->num_grids; grid++) cellClosure_sz += Nb * Nf[grid] * numCells[grid];
161       PetscCall(PetscMalloc1(cellClosure_sz * ctx->batch_sz, &cellClosure));
162       cellClosure_it = cellClosure;
163       PetscCall(PetscMalloc(sizeof(*locXArray) * nDMs, &locXArray));
164       PetscCall(PetscMalloc(sizeof(*globXArray) * nDMs, &globXArray));
165       PetscCall(DMCompositeGetLocalAccessArray(pack, a_X, nDMs, NULL, locXArray));
166       PetscCall(DMCompositeGetAccessArray(pack, a_X, nDMs, NULL, globXArray));
167       for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // OpenMP (once)
168         for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
169           Vec      locX = locXArray[LAND_PACK_IDX(b_id, grid)], globX = globXArray[LAND_PACK_IDX(b_id, grid)], locX2;
170           PetscInt cStart, cEnd, ei;
171           PetscCall(VecDuplicate(locX, &locX2));
172           PetscCall(DMGlobalToLocalBegin(ctx->plex[grid], globX, INSERT_VALUES, locX2));
173           PetscCall(DMGlobalToLocalEnd(ctx->plex[grid], globX, INSERT_VALUES, locX2));
174           PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
175           for (ei = cStart; ei < cEnd; ++ei) {
176             PetscScalar *coef = NULL;
177             PetscCall(DMPlexVecGetClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef));
178             PetscCall(PetscMemcpy(cellClosure_it, coef, Nb * Nf[grid] * sizeof(*cellClosure_it))); /* change if LandauIPReal != PetscScalar */
179             PetscCall(DMPlexVecRestoreClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef));
180             cellClosure_it += Nb * Nf[grid];
181           }
182           PetscCall(VecDestroy(&locX2));
183         }
184       }
185       PetscCheck(cellClosure_it - cellClosure == cellClosure_sz * ctx->batch_sz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "iteration wrong %" PetscCount_FMT " != cellClosure_sz = %" PetscInt_FMT, (PetscCount)(cellClosure_it - cellClosure),
186                  cellClosure_sz * ctx->batch_sz);
187       PetscCall(DMCompositeRestoreLocalAccessArray(pack, a_X, nDMs, NULL, locXArray));
188       PetscCall(DMCompositeRestoreAccessArray(pack, a_X, nDMs, NULL, globXArray));
189       PetscCall(PetscFree(locXArray));
190       PetscCall(PetscFree(globXArray));
191       xdata = NULL;
192     } else {
193       PetscMemType mtype;
194       if (ctx->jacobian_field_major_order) { // get data in batch ordering
195         PetscCall(VecScatterBegin(ctx->plex_batch, a_X, ctx->work_vec, INSERT_VALUES, SCATTER_FORWARD));
196         PetscCall(VecScatterEnd(ctx->plex_batch, a_X, ctx->work_vec, INSERT_VALUES, SCATTER_FORWARD));
197         PetscCall(VecGetArrayReadAndMemType(ctx->work_vec, &xdata, &mtype));
198       } else {
199         PetscCall(VecGetArrayReadAndMemType(a_X, &xdata, &mtype));
200       }
201       PetscCheck(mtype == PETSC_MEMTYPE_HOST || ctx->deviceType != LANDAU_CPU, ctx->comm, PETSC_ERR_ARG_WRONG, "CPU run with device data: use -mat_type aij");
202       cellClosure = NULL;
203     }
204     PetscCall(PetscLogEventEnd(ctx->events[1], 0, 0, 0, 0));
205   } else xdata = cellClosure = NULL;
206 
207   /* do it */
208   if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
209     if (ctx->deviceType == LANDAU_CUDA) {
210 #if defined(PETSC_HAVE_CUDA)
211       PetscCall(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));
212 #else
213       SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type %s not built", "cuda");
214 #endif
215     } else if (ctx->deviceType == LANDAU_KOKKOS) {
216 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
217       PetscCall(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));
218 #else
219       SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type %s not built", "kokkos");
220 #endif
221     }
222   } else {               /* CPU version */
223     PetscTabulation *Tf; // used for CPU and print info. Same on all grids and all species
224     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];
225     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;
226     PetscReal        Eq_m[LANDAU_MAX_SPECIES], invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
227     PetscSection     section[LANDAU_MAX_GRIDS], globsection[LANDAU_MAX_GRIDS];
228     PetscScalar     *coo_vals = NULL;
229     for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
230       PetscCall(DMGetLocalSection(ctx->plex[grid], &section[grid]));
231       PetscCall(DMGetGlobalSection(ctx->plex[grid], &globsection[grid]));
232       PetscCall(PetscSectionGetNumFields(section[grid], &Nf[grid]));
233     }
234     /* count IPf size, etc */
235     PetscCall(PetscDSGetTabulation(prob, &Tf)); // Bf, &Df same for all grids
236     const PetscReal *const BB = Tf[0]->T[0], *const DD = Tf[0]->T[1];
237     ip_offset[0] = ipf_offset[0] = elem_offset[0] = 0;
238     for (PetscInt grid = 0; grid < num_grids; grid++) {
239       PetscInt nfloc        = ctx->species_offset[grid + 1] - ctx->species_offset[grid];
240       elem_offset[grid + 1] = elem_offset[grid] + numCells[grid];
241       ip_offset[grid + 1]   = ip_offset[grid] + numCells[grid] * Nq;
242       ipf_offset[grid + 1]  = ipf_offset[grid] + Nq * nfloc * numCells[grid];
243     }
244     IPf_sz_glb = ipf_offset[num_grids];
245     IPf_sz_tot = IPf_sz_glb * ctx->batch_sz;
246     // prep COO
247     if (ctx->coo_assembly) {
248       PetscCall(PetscMalloc1(ctx->SData_d.coo_size, &coo_vals)); // allocate every time?
249       PetscCall(PetscInfo(ctx->plex[0], "COO Allocate %" PetscInt_FMT " values\n", (PetscInt)ctx->SData_d.coo_size));
250     }
251     if (shift == 0.0) { /* compute dynamic data f and df and init data for Jacobian */
252 #if defined(PETSC_HAVE_THREADSAFETY)
253       double starttime, endtime;
254       starttime = MPI_Wtime();
255 #endif
256       PetscCall(PetscLogEventBegin(ctx->events[8], 0, 0, 0, 0));
257       for (PetscInt fieldA = 0; fieldA < ctx->num_species; fieldA++) {
258         invMass[fieldA] = ctx->m_0 / ctx->masses[fieldA];
259         Eq_m[fieldA]    = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
260         if (dim == 2) Eq_m[fieldA] *= 2 * PETSC_PI;                                                     /* add the 2pi term that is not in Landau */
261         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA] / ctx->m_0) * ctx->m_0 / ctx->masses[fieldA];
262         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);
263       }
264       PetscCall(PetscMalloc4(IPf_sz_tot, &ff, IPf_sz_tot, &dudx, IPf_sz_tot, &dudy, dim == 3 ? IPf_sz_tot : 0, &dudz));
265       // F df/dx
266       for (PetscInt tid = 0; tid < ctx->batch_sz * elem_offset[num_grids]; tid++) {                        // for each element
267         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
268         // find my grid:
269         PetscInt grid = 0;
270         while (b_elem_idx >= elem_offset[grid + 1]) grid++; // yuck search for grid
271         {
272           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];
273           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];
274           PetscScalar   *coef, coef_buff[LANDAU_MAX_SPECIES * LANDAU_MAX_NQ];
275           PetscReal     *invJe = &invJ_a[(ip_offset[grid] + loc_elem * Nq) * dim * dim]; // ingJ is static data on batch 0
276           PetscInt       b, f, q;
277           if (cellClosure) {
278             coef = &cellClosure[b_id * IPf_sz_glb + ipf_offset[grid] + loc_elem * Nb * loc_Nf]; // this is const
279           } else {
280             coef = coef_buff;
281             for (f = 0; f < loc_Nf; ++f) {
282               LandauIdx *const Idxs = &maps[grid].gIdx[loc_elem][f][0];
283               for (b = 0; b < Nb; ++b) {
284                 PetscInt idx = Idxs[b];
285                 if (idx >= 0) {
286                   coef[f * Nb + b] = xdata[idx + moffset];
287                 } else {
288                   idx              = -idx - 1;
289                   coef[f * Nb + b] = 0;
290                   for (q = 0; q < maps[grid].num_face; q++) {
291                     PetscInt    id    = maps[grid].c_maps[idx][q].gid;
292                     PetscScalar scale = maps[grid].c_maps[idx][q].scale;
293                     coef[f * Nb + b] += scale * xdata[id + moffset];
294                   }
295                 }
296               }
297             }
298           }
299           /* get f and df */
300           for (PetscInt qi = 0; qi < Nq; qi++) {
301             const PetscReal *invJ = &invJe[qi * dim * dim];
302             const PetscReal *Bq   = &BB[qi * Nb];
303             const PetscReal *Dq   = &DD[qi * Nb * dim];
304             PetscReal        u_x[LANDAU_DIM];
305             /* get f & df */
306             for (f = 0; f < loc_Nf; ++f) {
307               const PetscInt idx = b_id * IPf_sz_glb + ipf_offset[grid] + f * loc_nip + loc_elem * Nq + qi;
308               PetscInt       b, e;
309               PetscReal      refSpaceDer[LANDAU_DIM];
310               ff[idx] = 0.0;
311               for (int d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
312               for (b = 0; b < Nb; ++b) {
313                 const PetscInt cidx = b;
314                 ff[idx] += Bq[cidx] * PetscRealPart(coef[f * Nb + cidx]);
315                 for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[cidx * dim + d] * PetscRealPart(coef[f * Nb + cidx]);
316               }
317               for (int d = 0; d < LANDAU_DIM; ++d) {
318                 for (e = 0, u_x[d] = 0.0; e < LANDAU_DIM; ++e) u_x[d] += invJ[e * dim + d] * refSpaceDer[e];
319               }
320               dudx[idx] = u_x[0];
321               dudy[idx] = u_x[1];
322 #if LANDAU_DIM == 3
323               dudz[idx] = u_x[2];
324 #endif
325             }
326           } // q
327         }   // grid
328       }     // grid*batch
329       PetscCall(PetscLogEventEnd(ctx->events[8], 0, 0, 0, 0));
330 #if defined(PETSC_HAVE_THREADSAFETY)
331       endtime = MPI_Wtime();
332       if (ctx->stage) ctx->times[LANDAU_F_DF] += (endtime - starttime);
333 #endif
334     } // Jacobian setup
335     // assemble Jacobian (or mass)
336     for (PetscInt tid = 0; tid < ctx->batch_sz * elem_offset[num_grids]; tid++) { // for each element
337       const PetscInt b_Nelem      = elem_offset[num_grids];
338       const PetscInt glb_elem_idx = tid % b_Nelem, b_id = tid / b_Nelem;
339       PetscInt       grid = 0;
340 #if defined(PETSC_HAVE_THREADSAFETY)
341       double starttime, endtime;
342       starttime = MPI_Wtime();
343 #endif
344       while (glb_elem_idx >= elem_offset[grid + 1]) grid++;
345       {
346         const PetscInt   loc_Nf = ctx->species_offset[grid + 1] - ctx->species_offset[grid], loc_elem = glb_elem_idx - elem_offset[grid];
347         const PetscInt   moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset), totDim = loc_Nf * Nq, elemMatSize = totDim * totDim;
348         PetscScalar     *elemMat;
349         const PetscReal *invJe = &invJ_a[(ip_offset[grid] + loc_elem * Nq) * dim * dim];
350         PetscCall(PetscMalloc1(elemMatSize, &elemMat));
351         PetscCall(PetscMemzero(elemMat, elemMatSize * sizeof(*elemMat)));
352         if (shift == 0.0) { // Jacobian
353           PetscCall(PetscLogEventBegin(ctx->events[4], 0, 0, 0, 0));
354         } else { // mass
355           PetscCall(PetscLogEventBegin(ctx->events[16], 0, 0, 0, 0));
356         }
357         for (PetscInt qj = 0; qj < Nq; ++qj) {
358           const PetscInt jpidx_glb = ip_offset[grid] + qj + loc_elem * Nq;
359           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
360           PetscInt       d, d2, dp, d3, IPf_idx;
361           if (shift == 0.0) { // Jacobian
362             const PetscReal *const invJj = &invJe[qj * dim * dim];
363             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];
364             const PetscReal        vj[3] = {xx[jpidx_glb], yy[jpidx_glb], zz ? zz[jpidx_glb] : 0}, wj = ww[jpidx_glb];
365             // create g2 & g3
366             for (d = 0; d < LANDAU_DIM; d++) { // clear accumulation data D & K
367               gg2_temp[d] = 0;
368               for (d2 = 0; d2 < LANDAU_DIM; d2++) gg3_temp[d][d2] = 0;
369             }
370             /* inner beta reduction */
371             IPf_idx = 0;
372             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
373               PetscInt nip_loc_r = numCells[grid_r] * Nq, Nfloc_r = Nf[grid_r];
374               for (PetscInt ei_r = 0, loc_fdf_idx = 0; ei_r < numCells[grid_r]; ++ei_r) {
375                 for (PetscInt qi = 0; qi < Nq; qi++, ipidx++, loc_fdf_idx++) {
376                   const PetscReal wi = ww[ipidx], x = xx[ipidx], y = yy[ipidx];
377                   PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
378 #if LANDAU_DIM == 2
379                   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.;
380                   LandauTensor2D(vj, x, y, Ud, Uk, mask);
381 #else
382                   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.;
383                   if (ctx->use_relativistic_corrections) {
384                     LandauTensor3DRelativistic(vj, x, y, z, U, mask, C_0(ctx->v_0));
385                   } else {
386                     LandauTensor3D(vj, x, y, z, U, mask);
387                   }
388 #endif
389                   for (int f = 0; f < Nfloc_r; ++f) {
390                     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;
391                     temp1[0] += dudx[idx] * nu_beta[f + f_off] * invMass[f + f_off];
392                     temp1[1] += dudy[idx] * nu_beta[f + f_off] * invMass[f + f_off];
393 #if LANDAU_DIM == 3
394                     temp1[2] += dudz[idx] * nu_beta[f + f_off] * invMass[f + f_off];
395 #endif
396                     temp2 += ff[idx] * nu_beta[f + f_off];
397                   }
398                   temp1[0] *= wi;
399                   temp1[1] *= wi;
400 #if LANDAU_DIM == 3
401                   temp1[2] *= wi;
402 #endif
403                   temp2 *= wi;
404 #if LANDAU_DIM == 2
405                   for (d2 = 0; d2 < 2; d2++) {
406                     for (d3 = 0; d3 < 2; ++d3) {
407                       /* K = U * grad(f): g2=e: i,A */
408                       gg2_temp[d2] += Uk[d2][d3] * temp1[d3];
409                       /* D = -U * (I \kron (fx)): g3=f: i,j,A */
410                       gg3_temp[d2][d3] += Ud[d2][d3] * temp2;
411                     }
412                   }
413 #else
414                   for (d2 = 0; d2 < 3; ++d2) {
415                     for (d3 = 0; d3 < 3; ++d3) {
416                       /* K = U * grad(f): g2 = e: i,A */
417                       gg2_temp[d2] += U[d2][d3] * temp1[d3];
418                       /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
419                       gg3_temp[d2][d3] += U[d2][d3] * temp2;
420                     }
421                   }
422 #endif
423                 } // qi
424               }   // ei_r
425               IPf_idx += nip_loc_r * Nfloc_r;
426             } /* grid_r - IPs */
427             PetscCheck(IPf_idx == IPf_sz_glb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "IPf_idx != IPf_sz %" PetscInt_FMT " %" PetscInt_FMT, IPf_idx, IPf_sz_glb);
428             // add alpha and put in gg2/3
429             for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid]; fieldA < loc_Nf; ++fieldA) {
430               for (d2 = 0; d2 < LANDAU_DIM; d2++) {
431                 gg2[fieldA][d2] = gg2_temp[d2] * nu_alpha[fieldA + f_off];
432                 for (d3 = 0; d3 < LANDAU_DIM; d3++) gg3[fieldA][d2][d3] = -gg3_temp[d2][d3] * nu_alpha[fieldA + f_off] * invMass[fieldA + f_off];
433               }
434             }
435             /* add electric field term once per IP */
436             for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid]; fieldA < loc_Nf; ++fieldA) gg2[fieldA][LANDAU_DIM - 1] += Eq_m[fieldA + f_off];
437             /* Jacobian transform - g2, g3 */
438             for (PetscInt fieldA = 0; fieldA < loc_Nf; ++fieldA) {
439               for (d = 0; d < dim; ++d) {
440                 g2[fieldA][d] = 0.0;
441                 for (d2 = 0; d2 < dim; ++d2) {
442                   g2[fieldA][d] += invJj[d * dim + d2] * gg2[fieldA][d2];
443                   g3[fieldA][d][d2] = 0.0;
444                   for (d3 = 0; d3 < dim; ++d3) {
445                     for (dp = 0; dp < dim; ++dp) g3[fieldA][d][d2] += invJj[d * dim + d3] * gg3[fieldA][d3][dp] * invJj[d2 * dim + dp];
446                   }
447                   g3[fieldA][d][d2] *= wj;
448                 }
449                 g2[fieldA][d] *= wj;
450               }
451             }
452           } else { // mass
453             PetscReal wj = ww[jpidx_glb];
454             /* Jacobian transform - g0 */
455             for (PetscInt fieldA = 0; fieldA < loc_Nf; ++fieldA) {
456               if (dim == 2) {
457                 g0[fieldA] = wj * shift * 2. * PETSC_PI; // move this to below and remove g0
458               } else {
459                 g0[fieldA] = wj * shift; // move this to below and remove g0
460               }
461             }
462           }
463           /* FE matrix construction */
464           {
465             PetscInt         fieldA, d, f, d2, g;
466             const PetscReal *BJq = &BB[qj * Nb], *DIq = &DD[qj * Nb * dim];
467             /* assemble - on the diagonal (I,I) */
468             for (fieldA = 0; fieldA < loc_Nf; fieldA++) {
469               for (f = 0; f < Nb; f++) {
470                 const PetscInt i = fieldA * Nb + f; /* Element matrix row */
471                 for (g = 0; g < Nb; ++g) {
472                   const PetscInt j    = fieldA * Nb + g; /* Element matrix column */
473                   const PetscInt fOff = i * totDim + j;
474                   if (shift == 0.0) {
475                     for (d = 0; d < dim; ++d) {
476                       elemMat[fOff] += DIq[f * dim + d] * g2[fieldA][d] * BJq[g];
477                       for (d2 = 0; d2 < dim; ++d2) elemMat[fOff] += DIq[f * dim + d] * g3[fieldA][d][d2] * DIq[g * dim + d2];
478                     }
479                   } else { // mass
480                     elemMat[fOff] += BJq[f] * g0[fieldA] * BJq[g];
481                   }
482                 }
483               }
484             }
485           }
486         }                   /* qj loop */
487         if (shift == 0.0) { // Jacobian
488           PetscCall(PetscLogEventEnd(ctx->events[4], 0, 0, 0, 0));
489         } else {
490           PetscCall(PetscLogEventEnd(ctx->events[16], 0, 0, 0, 0));
491         }
492 #if defined(PETSC_HAVE_THREADSAFETY)
493         endtime = MPI_Wtime();
494         if (ctx->stage) ctx->times[LANDAU_KERNEL] += (endtime - starttime);
495 #endif
496         /* assemble matrix */
497         if (!container) {
498           PetscInt cStart;
499           PetscCall(PetscLogEventBegin(ctx->events[6], 0, 0, 0, 0));
500           PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, NULL));
501           PetscCall(DMPlexMatSetClosure(ctx->plex[grid], section[grid], globsection[grid], subJ[LAND_PACK_IDX(b_id, grid)], loc_elem + cStart, elemMat, ADD_VALUES));
502           PetscCall(PetscLogEventEnd(ctx->events[6], 0, 0, 0, 0));
503         } else { // GPU like assembly for debugging
504           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];
505           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};
506           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;
507           /* assemble - from the diagonal (I,I) in this format for DMPlexMatSetClosure */
508           for (fieldA = 0; fieldA < loc_Nf; fieldA++) {
509             LandauIdx *const Idxs = &maps[grid].gIdx[loc_elem][fieldA][0];
510             for (f = 0; f < Nb; f++) {
511               PetscInt idx = Idxs[f];
512               if (idx >= 0) {
513                 nr           = 1;
514                 rows0[0]     = idx;
515                 row_scale[0] = 1.;
516               } else {
517                 idx = -idx - 1;
518                 for (q = 0, nr = 0; q < maps[grid].num_face; q++, nr++) {
519                   if (maps[grid].c_maps[idx][q].gid < 0) break;
520                   rows0[q]     = maps[grid].c_maps[idx][q].gid;
521                   row_scale[q] = maps[grid].c_maps[idx][q].scale;
522                 }
523               }
524               for (g = 0; g < Nb; ++g) {
525                 idx = Idxs[g];
526                 if (idx >= 0) {
527                   nc           = 1;
528                   cols0[0]     = idx;
529                   col_scale[0] = 1.;
530                 } else {
531                   idx = -idx - 1;
532                   nc  = maps[grid].num_face;
533                   for (q = 0, nc = 0; q < maps[grid].num_face; q++, nc++) {
534                     if (maps[grid].c_maps[idx][q].gid < 0) break;
535                     cols0[q]     = maps[grid].c_maps[idx][q].gid;
536                     col_scale[q] = maps[grid].c_maps[idx][q].scale;
537                   }
538                 }
539                 const PetscInt    i   = fieldA * Nb + f; /* Element matrix row */
540                 const PetscInt    j   = fieldA * Nb + g; /* Element matrix column */
541                 const PetscScalar Aij = elemMat[i * totDim + j];
542                 if (coo_vals) { // mirror (i,j) in CreateStaticGPUData
543                   const int fullNb = coo_elem_fullNb[glb_elem_idx], fullNb2 = fullNb * fullNb;
544                   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];
545                   for (int q = 0, idx2 = idx0; q < nr; q++) {
546                     for (int d = 0; d < nc; d++, idx2++) coo_vals[idx2] = row_scale[q] * col_scale[d] * Aij;
547                   }
548                 } else {
549                   for (q = 0; q < nr; q++) rows[q] = rows0[q] + moffset;
550                   for (d = 0; d < nc; d++) cols[d] = cols0[d] + moffset;
551                   for (q = 0; q < nr; q++) {
552                     for (d = 0; d < nc; d++) vals[q * nc + d] = row_scale[q] * col_scale[d] * Aij;
553                   }
554                   PetscCall(MatSetValues(JacP, nr, rows, nc, cols, vals, ADD_VALUES));
555                 }
556               }
557             }
558           }
559         }
560         if (loc_elem == -1) {
561           PetscCall(PetscPrintf(ctx->comm, "CPU Element matrix\n"));
562           for (int d = 0; d < totDim; ++d) {
563             for (int f = 0; f < totDim; ++f) PetscCall(PetscPrintf(ctx->comm, " %12.5e", (double)PetscRealPart(elemMat[d * totDim + f])));
564             PetscCall(PetscPrintf(ctx->comm, "\n"));
565           }
566           exit(12);
567         }
568         PetscCall(PetscFree(elemMat));
569       }                 /* grid */
570     }                   /* outer element & batch loop */
571     if (shift == 0.0) { // mass
572       PetscCall(PetscFree4(ff, dudx, dudy, dudz));
573     }
574     if (!container) {                                         // 'CPU' assembly move nest matrix to global JacP
575       for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // OpenMP
576         for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
577           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];
578           PetscInt           nloc, nzl, colbuf[1024], row;
579           const PetscInt    *cols;
580           const PetscScalar *vals;
581           Mat                B = subJ[LAND_PACK_IDX(b_id, grid)];
582           PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
583           PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
584           PetscCall(MatGetSize(B, &nloc, NULL));
585           for (int i = 0; i < nloc; i++) {
586             PetscCall(MatGetRow(B, i, &nzl, &cols, &vals));
587             PetscCheck(nzl <= 1024, PetscObjectComm((PetscObject)B), PETSC_ERR_PLIB, "Row too big: %" PetscInt_FMT, nzl);
588             for (int j = 0; j < nzl; j++) colbuf[j] = moffset + cols[j];
589             row = moffset + i;
590             PetscCall(MatSetValues(JacP, 1, &row, nzl, colbuf, vals, ADD_VALUES));
591             PetscCall(MatRestoreRow(B, i, &nzl, &cols, &vals));
592           }
593           PetscCall(MatDestroy(&B));
594         }
595       }
596     }
597     if (coo_vals) {
598       PetscCall(MatSetValuesCOO(JacP, coo_vals, ADD_VALUES));
599       PetscCall(PetscFree(coo_vals));
600     }
601   } /* CPU version */
602   PetscCall(MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY));
603   PetscCall(MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY));
604   /* clean up */
605   if (cellClosure) PetscCall(PetscFree(cellClosure));
606   if (xdata) PetscCall(VecRestoreArrayReadAndMemType(a_X, &xdata));
607   PetscFunctionReturn(PETSC_SUCCESS);
608 }
609 
610 #if defined(LANDAU_ADD_BCS)
611 static void zero_bc(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
612 {
613   uexact[0] = 0;
614 }
615 #endif
616 
617 #define MATVEC2(__a, __x, __p) \
618   { \
619     int i, j; \
620     for (i = 0.; i < 2; i++) { \
621       __p[i] = 0; \
622       for (j = 0.; j < 2; j++) __p[i] += __a[i][j] * __x[j]; \
623     } \
624   }
625 static void CircleInflate(PetscReal r1, PetscReal r2, PetscReal r0, PetscInt num_sections, PetscReal x, PetscReal y, PetscReal *outX, PetscReal *outY)
626 {
627   PetscReal rr = PetscSqrtReal(x * x + y * y), outfact, efact;
628   if (rr < r1 + PETSC_SQRT_MACHINE_EPSILON) {
629     *outX = x;
630     *outY = y;
631   } else {
632     const PetscReal xy[2] = {x, y}, sinphi = y / rr, cosphi = x / rr;
633     PetscReal       cth, sth, xyprime[2], Rth[2][2], rotcos, newrr;
634     if (num_sections == 2) {
635       rotcos  = 0.70710678118654;
636       outfact = 1.5;
637       efact   = 2.5;
638       /* rotate normalized vector into [-pi/4,pi/4) */
639       if (sinphi >= 0.) { /* top cell, -pi/2 */
640         cth = 0.707106781186548;
641         sth = -0.707106781186548;
642       } else { /* bottom cell -pi/8 */
643         cth = 0.707106781186548;
644         sth = .707106781186548;
645       }
646     } else if (num_sections == 3) {
647       rotcos  = 0.86602540378443;
648       outfact = 1.5;
649       efact   = 2.5;
650       /* rotate normalized vector into [-pi/6,pi/6) */
651       if (sinphi >= 0.5) { /* top cell, -pi/3 */
652         cth = 0.5;
653         sth = -0.866025403784439;
654       } else if (sinphi >= -.5) { /* mid cell 0 */
655         cth = 1.;
656         sth = .0;
657       } else { /* bottom cell +pi/3 */
658         cth = 0.5;
659         sth = 0.866025403784439;
660       }
661     } else if (num_sections == 4) {
662       rotcos  = 0.9238795325112;
663       outfact = 1.5;
664       efact   = 3;
665       /* rotate normalized vector into [-pi/8,pi/8) */
666       if (sinphi >= 0.707106781186548) { /* top cell, -3pi/8 */
667         cth = 0.38268343236509;
668         sth = -0.923879532511287;
669       } else if (sinphi >= 0.) { /* mid top cell -pi/8 */
670         cth = 0.923879532511287;
671         sth = -.38268343236509;
672       } else if (sinphi >= -0.707106781186548) { /* mid bottom cell + pi/8 */
673         cth = 0.923879532511287;
674         sth = 0.38268343236509;
675       } else { /* bottom cell + 3pi/8 */
676         cth = 0.38268343236509;
677         sth = .923879532511287;
678       }
679     } else {
680       cth    = 0.;
681       sth    = 0.;
682       rotcos = 0;
683       efact  = 0;
684     }
685     Rth[0][0] = cth;
686     Rth[0][1] = -sth;
687     Rth[1][0] = sth;
688     Rth[1][1] = cth;
689     MATVEC2(Rth, xy, xyprime);
690     if (num_sections == 2) {
691       newrr = xyprime[0] / rotcos;
692     } else {
693       PetscReal newcosphi = xyprime[0] / rr, rin = r1, rout = rr - rin;
694       PetscReal routmax = r0 * rotcos / newcosphi - rin, nroutmax = r0 - rin, routfrac = rout / routmax;
695       newrr = rin + routfrac * nroutmax;
696     }
697     *outX = cosphi * newrr;
698     *outY = sinphi * newrr;
699     /* grade */
700     PetscReal fact, tt, rs, re, rr = PetscSqrtReal(PetscSqr(*outX) + PetscSqr(*outY));
701     if (rr > r2) {
702       rs   = r2;
703       re   = r0;
704       fact = outfact;
705     } /* outer zone */
706     else {
707       rs   = r1;
708       re   = r2;
709       fact = efact;
710     } /* electron zone */
711     tt = (rs + PetscPowReal((rr - rs) / (re - rs), fact) * (re - rs)) / rr;
712     *outX *= tt;
713     *outY *= tt;
714   }
715 }
716 
717 static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
718 {
719   LandauCtx *ctx = (LandauCtx *)a_ctx;
720   PetscReal  r = abc[0], z = abc[1];
721   if (ctx->inflate) {
722     PetscReal absR, absZ;
723     absR = PetscAbs(r);
724     absZ = PetscAbs(z);
725     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?
726     r = (r > 0) ? absR : -absR;
727     z = (z > 0) ? absZ : -absZ;
728   }
729   xyz[0] = r;
730   xyz[1] = z;
731   if (dim == 3) xyz[2] = abc[2];
732 
733   PetscFunctionReturn(PETSC_SUCCESS);
734 }
735 
736 /* create DMComposite of meshes for each species group */
737 static PetscErrorCode LandauDMCreateVMeshes(MPI_Comm comm_self, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM pack)
738 {
739   PetscFunctionBegin;
740   { /* p4est, quads */
741     /* Create plex mesh of Landau domain */
742     for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
743       PetscReal par_radius = ctx->radius_par[grid], perp_radius = ctx->radius_perp[grid];
744       if (!ctx->sphere) {
745         PetscReal      lo[] = {-perp_radius, -par_radius, -par_radius}, hi[] = {perp_radius, par_radius, par_radius};
746         DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim == 2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
747         if (dim == 2) lo[0] = 0;
748         else {
749           lo[1] = -perp_radius;
750           hi[1] = perp_radius; // 3D y is a perp
751         }
752         PetscCall(DMPlexCreateBoxMesh(comm_self, dim, PETSC_FALSE, ctx->cells0, lo, hi, periodicity, PETSC_TRUE, &ctx->plex[grid])); // todo: make composite and create dm[grid] here
753         PetscCall(DMLocalizeCoordinates(ctx->plex[grid]));                                                                           /* needed for periodic */
754         if (dim == 3) PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], "cube"));
755         else PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], "half-plane"));
756       } else if (dim == 2) { // sphere is all wrong. should just have one inner radius
757         PetscInt   numCells, cells[16][4], i, j;
758         PetscInt   numVerts;
759         PetscReal  inner_radius1 = ctx->i_radius[grid], inner_radius2 = ctx->e_radius;
760         PetscReal *flatCoords = NULL;
761         PetscInt  *flatCells  = NULL, *pcell;
762         if (ctx->num_sections == 2) {
763 #if 1
764           numCells        = 5;
765           numVerts        = 10;
766           int cells2[][4] = {
767             {0, 1, 4, 3},
768             {1, 2, 5, 4},
769             {3, 4, 7, 6},
770             {4, 5, 8, 7},
771             {6, 7, 8, 9}
772           };
773           for (i = 0; i < numCells; i++)
774             for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
775           PetscCall(PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells));
776           {
777             PetscReal(*coords)[2] = (PetscReal(*)[2])flatCoords;
778             for (j = 0; j < numVerts - 1; j++) {
779               PetscReal z, r, theta = -PETSC_PI / 2 + (j % 3) * PETSC_PI / 2;
780               PetscReal rad = (j >= 6) ? inner_radius1 : (j >= 3) ? inner_radius2 : ctx->radius[grid];
781               z             = rad * PetscSinReal(theta);
782               coords[j][1]  = z;
783               r             = rad * PetscCosReal(theta);
784               coords[j][0]  = r;
785             }
786             coords[numVerts - 1][0] = coords[numVerts - 1][1] = 0;
787           }
788 #else
789           numCells = 4;
790           numVerts = 8;
791           static int cells2[][4] = {
792             {0, 1, 2, 3},
793             {4, 5, 1, 0},
794             {5, 6, 2, 1},
795             {6, 7, 3, 2}
796           };
797           for (i = 0; i < numCells; i++)
798             for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
799           PetscCall(loc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells));
800           {
801             PetscReal(*coords)[2] = (PetscReal(*)[2])flatCoords;
802             PetscInt j;
803             for (j = 0; j < 8; j++) {
804               PetscReal z, r;
805               PetscReal theta = -PETSC_PI / 2 + (j % 4) * PETSC_PI / 3.;
806               PetscReal rad = ctx->radius[grid] * ((j < 4) ? 0.5 : 1.0);
807               z = rad * PetscSinReal(theta);
808               coords[j][1] = z;
809               r = rad * PetscCosReal(theta);
810               coords[j][0] = r;
811             }
812           }
813 #endif
814         } else if (ctx->num_sections == 3) {
815           numCells        = 7;
816           numVerts        = 12;
817           int cells2[][4] = {
818             {0, 1, 5,  4 },
819             {1, 2, 6,  5 },
820             {2, 3, 7,  6 },
821             {4, 5, 9,  8 },
822             {5, 6, 10, 9 },
823             {6, 7, 11, 10},
824             {8, 9, 10, 11}
825           };
826           for (i = 0; i < numCells; i++)
827             for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
828           PetscCall(PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells));
829           {
830             PetscReal(*coords)[2] = (PetscReal(*)[2])flatCoords;
831             for (j = 0; j < numVerts; j++) {
832               PetscReal z, r, theta = -PETSC_PI / 2 + (j % 4) * PETSC_PI / 3;
833               PetscReal rad = (j >= 8) ? inner_radius1 : (j >= 4) ? inner_radius2 : ctx->radius[grid];
834               z             = rad * PetscSinReal(theta);
835               coords[j][1]  = z;
836               r             = rad * PetscCosReal(theta);
837               coords[j][0]  = r;
838             }
839           }
840         } else if (ctx->num_sections == 4) {
841           numCells        = 10;
842           numVerts        = 16;
843           int cells2[][4] = {
844             {0,  1,  6,  5 },
845             {1,  2,  7,  6 },
846             {2,  3,  8,  7 },
847             {3,  4,  9,  8 },
848             {5,  6,  11, 10},
849             {6,  7,  12, 11},
850             {7,  8,  13, 12},
851             {8,  9,  14, 13},
852             {10, 11, 12, 15},
853             {12, 13, 14, 15}
854           };
855           for (i = 0; i < numCells; i++)
856             for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
857           PetscCall(PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells));
858           {
859             PetscReal(*coords)[2] = (PetscReal(*)[2])flatCoords;
860             for (j = 0; j < numVerts - 1; j++) {
861               PetscReal z, r, theta = -PETSC_PI / 2 + (j % 5) * PETSC_PI / 4;
862               PetscReal rad = (j >= 10) ? inner_radius1 : (j >= 5) ? inner_radius2 : ctx->radius[grid];
863               z             = rad * PetscSinReal(theta);
864               coords[j][1]  = z;
865               r             = rad * PetscCosReal(theta);
866               coords[j][0]  = r;
867             }
868             coords[numVerts - 1][0] = coords[numVerts - 1][1] = 0;
869           }
870         } else {
871           numCells = 0;
872           numVerts = 0;
873         }
874         for (j = 0, pcell = flatCells; j < numCells; j++, pcell += 4) {
875           pcell[0] = cells[j][0];
876           pcell[1] = cells[j][1];
877           pcell[2] = cells[j][2];
878           pcell[3] = cells[j][3];
879         }
880         PetscCall(DMPlexCreateFromCellListPetsc(comm_self, 2, numCells, numVerts, 4, ctx->interpolate, flatCells, 2, flatCoords, &ctx->plex[grid]));
881         PetscCall(PetscFree2(flatCoords, flatCells));
882         PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], "semi-circle"));
883       } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Velocity space meshes does not support cubed sphere");
884 
885       PetscCall(DMSetFromOptions(ctx->plex[grid]));
886     } // grid loop
887     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)pack, prefix));
888 
889     { /* convert to p4est (or whatever), wait for discretization to create pack */
890       char      convType[256];
891       PetscBool flg;
892 
893       PetscOptionsBegin(ctx->comm, prefix, "Mesh conversion options", "DMPLEX");
894       PetscCall(PetscOptionsFList("-dm_landau_type", "Convert DMPlex to another format (p4est)", "plexland.c", DMList, DMPLEX, convType, 256, &flg));
895       PetscOptionsEnd();
896       if (flg) {
897         ctx->use_p4est = PETSC_TRUE; /* flag for Forest */
898         for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
899           DM dmforest;
900           PetscCall(DMConvert(ctx->plex[grid], convType, &dmforest));
901           if (dmforest) {
902             PetscBool isForest;
903             PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dmforest, prefix));
904             PetscCall(DMIsForest(dmforest, &isForest));
905             if (isForest) {
906               if (ctx->sphere && ctx->inflate) PetscCall(DMForestSetBaseCoordinateMapping(dmforest, GeometryDMLandau, ctx));
907               PetscCall(DMDestroy(&ctx->plex[grid]));
908               ctx->plex[grid] = dmforest; // Forest for adaptivity
909             } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Converted to non Forest?");
910           } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Convert failed?");
911         }
912       } else ctx->use_p4est = PETSC_FALSE; /* flag for Forest */
913     }
914   } /* non-file */
915   PetscCall(DMSetDimension(pack, dim));
916   PetscCall(PetscObjectSetName((PetscObject)pack, "Mesh"));
917   PetscCall(DMSetApplicationContext(pack, ctx));
918 
919   PetscFunctionReturn(PETSC_SUCCESS);
920 }
921 
922 static PetscErrorCode SetupDS(DM pack, PetscInt dim, PetscInt grid, LandauCtx *ctx)
923 {
924   PetscInt     ii, i0;
925   char         buf[256];
926   PetscSection section;
927 
928   PetscFunctionBegin;
929   for (ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
930     if (ii == 0) PetscCall(PetscSNPrintf(buf, sizeof(buf), "e"));
931     else PetscCall(PetscSNPrintf(buf, sizeof(buf), "i%" PetscInt_FMT, ii));
932     /* Setup Discretization - FEM */
933     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &ctx->fe[ii]));
934     PetscCall(PetscObjectSetName((PetscObject)ctx->fe[ii], buf));
935     PetscCall(DMSetField(ctx->plex[grid], i0, NULL, (PetscObject)ctx->fe[ii]));
936   }
937   PetscCall(DMCreateDS(ctx->plex[grid]));
938   PetscCall(DMGetSection(ctx->plex[grid], &section));
939   for (PetscInt ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
940     if (ii == 0) PetscCall(PetscSNPrintf(buf, sizeof(buf), "se"));
941     else PetscCall(PetscSNPrintf(buf, sizeof(buf), "si%" PetscInt_FMT, ii));
942     PetscCall(PetscSectionSetComponentName(section, i0, 0, buf));
943   }
944   PetscFunctionReturn(PETSC_SUCCESS);
945 }
946 
947 /* Define a Maxwellian function for testing out the operator. */
948 
949 /* Using cartesian velocity space coordinates, the particle */
950 /* density, [1/m^3], is defined according to */
951 
952 /* $$ n=\int_{R^3} dv^3 \left(\frac{m}{2\pi T}\right)^{3/2}\exp [- mv^2/(2T)] $$ */
953 
954 /* Using some constant, c, we normalize the velocity vector into a */
955 /* dimensionless variable according to v=c*x. Thus the density, $n$, becomes */
956 
957 /* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */
958 
959 /* Defining $\theta=2T/mc^2$, we thus find that the probability density */
960 /* for finding the particle within the interval in a box dx^3 around x is */
961 
962 /* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */
963 
964 typedef struct {
965   PetscReal v_0;
966   PetscReal kT_m;
967   PetscReal n;
968   PetscReal shift;
969 } MaxwellianCtx;
970 
971 static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
972 {
973   MaxwellianCtx *mctx = (MaxwellianCtx *)actx;
974   PetscInt       i;
975   PetscReal      v2 = 0, theta = 2 * mctx->kT_m / (mctx->v_0 * mctx->v_0); /* theta = 2kT/mc^2 */
976   PetscFunctionBegin;
977   /* compute the exponents, v^2 */
978   for (i = 0; i < dim; ++i) v2 += x[i] * x[i];
979   /* evaluate the Maxwellian */
980   u[0] = mctx->n * PetscPowReal(PETSC_PI * theta, -1.5) * (PetscExpReal(-v2 / theta));
981   if (mctx->shift != 0.) {
982     v2 = 0;
983     for (i = 0; i < dim - 1; ++i) v2 += x[i] * x[i];
984     v2 += (x[dim - 1] - mctx->shift) * (x[dim - 1] - mctx->shift);
985     /* evaluate the shifted Maxwellian */
986     u[0] += mctx->n * PetscPowReal(PETSC_PI * theta, -1.5) * (PetscExpReal(-v2 / theta));
987   }
988   PetscFunctionReturn(PETSC_SUCCESS);
989 }
990 
991 /*@
992  DMPlexLandauAddMaxwellians - Add a Maxwellian distribution to a state
993 
994  Collective
995 
996  Input Parameters:
997  .   dm - The mesh (local)
998  +   time - Current time
999  -   temps - Temperatures of each species (global)
1000  .   ns - Number density of each species (global)
1001  -   grid - index into current grid - just used for offset into temp and ns
1002  .   b_id - batch index
1003  -   n_batch - number of batches
1004  +   actx - Landau context
1005 
1006  Output Parameter:
1007  .   X  - The state (local to this grid)
1008 
1009  Level: beginner
1010 
1011  .keywords: mesh
1012  .seealso: `DMPlexLandauCreateVelocitySpace()`
1013  @*/
1014 PetscErrorCode DMPlexLandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], PetscInt grid, PetscInt b_id, PetscInt n_batch, void *actx)
1015 {
1016   LandauCtx *ctx = (LandauCtx *)actx;
1017   PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
1018   PetscInt       dim;
1019   MaxwellianCtx *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];
1020 
1021   PetscFunctionBegin;
1022   PetscCall(DMGetDimension(dm, &dim));
1023   if (!ctx) PetscCall(DMGetApplicationContext(dm, &ctx));
1024   for (PetscInt ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
1025     mctxs[i0]      = &data[i0];
1026     data[i0].v_0   = ctx->v_0;                                            // v_0 same for all grids
1027     data[i0].kT_m  = ctx->k * temps[ii] / ctx->masses[ii];                /* kT/m */
1028     data[i0].n     = ns[ii] * (1 + 0.1 * (double)b_id / (double)n_batch); // ramp density up 10% to mimic application, n[0] use for Conner-Hastie
1029     initu[i0]      = maxwellian;
1030     data[i0].shift = 0;
1031   }
1032   data[0].shift = ctx->electronShift;
1033   /* need to make ADD_ALL_VALUES work - TODO */
1034   PetscCall(DMProjectFunction(dm, time, initu, (void **)mctxs, INSERT_ALL_VALUES, X));
1035   PetscFunctionReturn(PETSC_SUCCESS);
1036 }
1037 
1038 /*
1039  LandauSetInitialCondition - Addes Maxwellians with context
1040 
1041  Collective
1042 
1043  Input Parameters:
1044  .   dm - The mesh
1045  -   grid - index into current grid - just used for offset into temp and ns
1046  .   b_id - batch index
1047  -   n_batch - number of batches
1048  +   actx - Landau context with T and n
1049 
1050  Output Parameter:
1051  .   X  - The state
1052 
1053  Level: beginner
1054 
1055  .keywords: mesh
1056  .seealso: `DMPlexLandauCreateVelocitySpace()`, `DMPlexLandauAddMaxwellians()`
1057  */
1058 static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, PetscInt grid, PetscInt b_id, PetscInt n_batch, void *actx)
1059 {
1060   LandauCtx *ctx = (LandauCtx *)actx;
1061   PetscFunctionBegin;
1062   if (!ctx) PetscCall(DMGetApplicationContext(dm, &ctx));
1063   PetscCall(VecZeroEntries(X));
1064   PetscCall(DMPlexLandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, grid, b_id, n_batch, ctx));
1065   PetscFunctionReturn(PETSC_SUCCESS);
1066 }
1067 
1068 // adapt a level once. Forest in/out
1069 static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscInt type, PetscInt grid, LandauCtx *ctx, DM *newForest)
1070 {
1071   DM              forest, plex, adaptedDM = NULL;
1072   PetscDS         prob;
1073   PetscBool       isForest;
1074   PetscQuadrature quad;
1075   PetscInt        Nq, *Nb, cStart, cEnd, c, dim, qj, k;
1076   DMLabel         adaptLabel = NULL;
1077 
1078   PetscFunctionBegin;
1079   forest = ctx->plex[grid];
1080   PetscCall(DMCreateDS(forest));
1081   PetscCall(DMGetDS(forest, &prob));
1082   PetscCall(DMGetDimension(forest, &dim));
1083   PetscCall(DMIsForest(forest, &isForest));
1084   PetscCheck(isForest, ctx->comm, PETSC_ERR_ARG_WRONG, "! Forest");
1085   PetscCall(DMConvert(forest, DMPLEX, &plex));
1086   PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
1087   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "adapt", &adaptLabel));
1088   PetscCall(PetscFEGetQuadrature(fem, &quad));
1089   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
1090   PetscCheck(Nq <= LANDAU_MAX_NQ, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nq = %" PetscInt_FMT " > LANDAU_MAX_NQ (%d)", Nq, LANDAU_MAX_NQ);
1091   PetscCall(PetscDSGetDimensions(prob, &Nb));
1092   if (type == 4) {
1093     for (c = cStart; c < cEnd; c++) PetscCall(DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE));
1094     PetscCall(PetscInfo(sol, "Phase:%s: Uniform refinement\n", "adaptToleranceFEM"));
1095   } else if (type == 2) {
1096     PetscInt  rCellIdx[8], eCellIdx[64], iCellIdx[64], eMaxIdx = -1, iMaxIdx = -1, nr = 0, nrmax = (dim == 3) ? 8 : 2;
1097     PetscReal minRad = PETSC_INFINITY, r, eMinRad = PETSC_INFINITY, iMinRad = PETSC_INFINITY;
1098     for (c = 0; c < 64; c++) eCellIdx[c] = iCellIdx[c] = -1;
1099     for (c = cStart; c < cEnd; c++) {
1100       PetscReal tt, v0[LANDAU_MAX_NQ * 3], detJ[LANDAU_MAX_NQ];
1101       PetscCall(DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ));
1102       for (qj = 0; qj < Nq; ++qj) {
1103         tt = PetscSqr(v0[dim * qj + 0]) + PetscSqr(v0[dim * qj + 1]) + PetscSqr(((dim == 3) ? v0[dim * qj + 2] : 0));
1104         r  = PetscSqrtReal(tt);
1105         if (r < minRad - PETSC_SQRT_MACHINE_EPSILON * 10.) {
1106           minRad         = r;
1107           nr             = 0;
1108           rCellIdx[nr++] = c;
1109           PetscCall(PetscInfo(sol, "\t\tPhase: adaptToleranceFEM Found first inner r=%e, cell %" PetscInt_FMT ", qp %" PetscInt_FMT "/%" PetscInt_FMT "\n", (double)r, c, qj + 1, Nq));
1110         } else if ((r - minRad) < PETSC_SQRT_MACHINE_EPSILON * 100. && nr < nrmax) {
1111           for (k = 0; k < nr; k++)
1112             if (c == rCellIdx[k]) break;
1113           if (k == nr) {
1114             rCellIdx[nr++] = c;
1115             PetscCall(PetscInfo(sol, "\t\t\tPhase: adaptToleranceFEM Found another inner r=%e, cell %" PetscInt_FMT ", qp %" PetscInt_FMT "/%" PetscInt_FMT ", d=%e\n", (double)r, c, qj + 1, Nq, (double)(r - minRad)));
1116           }
1117         }
1118         if (ctx->sphere) {
1119           if ((tt = r - ctx->e_radius) > 0) {
1120             PetscCall(PetscInfo(sol, "\t\t\t %" PetscInt_FMT " cell r=%g\n", c, (double)tt));
1121             if (tt < eMinRad - PETSC_SQRT_MACHINE_EPSILON * 100.) {
1122               eMinRad             = tt;
1123               eMaxIdx             = 0;
1124               eCellIdx[eMaxIdx++] = c;
1125             } else if (eMaxIdx > 0 && (tt - eMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != eCellIdx[eMaxIdx - 1]) {
1126               eCellIdx[eMaxIdx++] = c;
1127             }
1128           }
1129           if ((tt = r - ctx->i_radius[grid]) > 0) {
1130             if (tt < iMinRad - 1.e-5) {
1131               iMinRad             = tt;
1132               iMaxIdx             = 0;
1133               iCellIdx[iMaxIdx++] = c;
1134             } else if (iMaxIdx > 0 && (tt - iMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != iCellIdx[iMaxIdx - 1]) {
1135               iCellIdx[iMaxIdx++] = c;
1136             }
1137           }
1138         }
1139       }
1140     }
1141     for (k = 0; k < nr; k++) PetscCall(DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE));
1142     if (ctx->sphere) {
1143       for (c = 0; c < eMaxIdx; c++) {
1144         PetscCall(DMLabelSetValue(adaptLabel, eCellIdx[c], DM_ADAPT_REFINE));
1145         PetscCall(PetscInfo(sol, "\t\tPhase:%s: refine sphere e cell %" PetscInt_FMT " r=%g\n", "adaptToleranceFEM", eCellIdx[c], (double)eMinRad));
1146       }
1147       for (c = 0; c < iMaxIdx; c++) {
1148         PetscCall(DMLabelSetValue(adaptLabel, iCellIdx[c], DM_ADAPT_REFINE));
1149         PetscCall(PetscInfo(sol, "\t\tPhase:%s: refine sphere i cell %" PetscInt_FMT " r=%g\n", "adaptToleranceFEM", iCellIdx[c], (double)iMinRad));
1150       }
1151     }
1152     PetscCall(PetscInfo(sol, "Phase:%s: Adaptive refine origin cells %" PetscInt_FMT ",%" PetscInt_FMT " r=%g\n", "adaptToleranceFEM", rCellIdx[0], rCellIdx[1], (double)minRad));
1153   } else if (type == 0 || type == 1 || type == 3) { /* refine along r=0 axis */
1154     PetscScalar *coef = NULL;
1155     Vec          coords;
1156     PetscInt     csize, Nv, d, nz;
1157     DM           cdm;
1158     PetscSection cs;
1159     PetscCall(DMGetCoordinatesLocal(forest, &coords));
1160     PetscCall(DMGetCoordinateDM(forest, &cdm));
1161     PetscCall(DMGetLocalSection(cdm, &cs));
1162     for (c = cStart; c < cEnd; c++) {
1163       PetscInt doit = 0, outside = 0;
1164       PetscCall(DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef));
1165       Nv = csize / dim;
1166       for (nz = d = 0; d < Nv; d++) {
1167         PetscReal z = PetscRealPart(coef[d * dim + (dim - 1)]), x = PetscSqr(PetscRealPart(coef[d * dim + 0])) + ((dim == 3) ? PetscSqr(PetscRealPart(coef[d * dim + 1])) : 0);
1168         x = PetscSqrtReal(x);
1169         if (x < PETSC_MACHINE_EPSILON * 10. && PetscAbs(z) < PETSC_MACHINE_EPSILON * 10.) doit = 1;                              /* refine origin */
1170         else if (type == 0 && (z < -PETSC_MACHINE_EPSILON * 10. || z > ctx->re_radius + PETSC_MACHINE_EPSILON * 10.)) outside++; /* first pass don't refine bottom */
1171         else if (type == 1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) outside++;                                  /* don't refine outside electron refine radius */
1172         else if (type == 3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) outside++;                                  /* don't refine outside ion refine radius */
1173         if (x < PETSC_MACHINE_EPSILON * 10.) nz++;
1174       }
1175       PetscCall(DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef));
1176       if (doit || (outside < Nv && nz)) PetscCall(DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE));
1177     }
1178     PetscCall(PetscInfo(sol, "Phase:%s: RE refinement\n", "adaptToleranceFEM"));
1179   }
1180   PetscCall(DMDestroy(&plex));
1181   PetscCall(DMAdaptLabel(forest, adaptLabel, &adaptedDM));
1182   PetscCall(DMLabelDestroy(&adaptLabel));
1183   *newForest = adaptedDM;
1184   if (adaptedDM) {
1185     if (isForest) {
1186       PetscCall(DMForestSetAdaptivityForest(adaptedDM, NULL)); // ????
1187     } else exit(33);                                           // ???????
1188     PetscCall(DMConvert(adaptedDM, DMPLEX, &plex));
1189     PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
1190     PetscCall(PetscInfo(sol, "\tPhase: adaptToleranceFEM: %" PetscInt_FMT " cells, %" PetscInt_FMT " total quadrature points\n", cEnd - cStart, Nq * (cEnd - cStart)));
1191     PetscCall(DMDestroy(&plex));
1192   } else *newForest = NULL;
1193   PetscFunctionReturn(PETSC_SUCCESS);
1194 }
1195 
1196 // forest goes in (ctx->plex[grid]), plex comes out
1197 static PetscErrorCode adapt(PetscInt grid, LandauCtx *ctx, Vec *uu)
1198 {
1199   PetscInt adaptIter;
1200 
1201   PetscFunctionBegin;
1202   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]};
1203   for (type = 0; type < 5; type++) {
1204     for (adaptIter = 0; adaptIter < limits[type]; adaptIter++) {
1205       DM newForest = NULL;
1206       PetscCall(adaptToleranceFEM(ctx->fe[0], *uu, type, grid, ctx, &newForest));
1207       if (newForest) {
1208         PetscCall(DMDestroy(&ctx->plex[grid]));
1209         PetscCall(VecDestroy(uu));
1210         PetscCall(DMCreateGlobalVector(newForest, uu));
1211         PetscCall(PetscObjectSetName((PetscObject)*uu, "uAMR"));
1212         PetscCall(LandauSetInitialCondition(newForest, *uu, grid, 0, 1, ctx));
1213         ctx->plex[grid] = newForest;
1214       } else {
1215         exit(4); // can happen with no AMR and post refinement
1216       }
1217     }
1218   }
1219   PetscFunctionReturn(PETSC_SUCCESS);
1220 }
1221 
1222 static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
1223 {
1224   PetscBool flg, sph_flg;
1225   PetscInt  ii, nt, nm, nc, num_species_grid[LANDAU_MAX_GRIDS];
1226   PetscReal v0_grid[LANDAU_MAX_GRIDS];
1227   DM        dummy;
1228 
1229   PetscFunctionBegin;
1230   PetscCall(DMCreate(ctx->comm, &dummy));
1231   /* get options - initialize context */
1232   ctx->verbose = 1; // should be 0 for silent compliance
1233 #if defined(PETSC_HAVE_THREADSAFETY) && defined(PETSC_HAVE_OPENMP)
1234   ctx->batch_sz = PetscNumOMPThreads;
1235 #else
1236   ctx->batch_sz = 1;
1237 #endif
1238   ctx->batch_view_idx = 0;
1239   ctx->interpolate    = PETSC_TRUE;
1240   ctx->gpu_assembly   = PETSC_TRUE;
1241   ctx->norm_state     = 0;
1242   ctx->electronShift  = 0;
1243   ctx->M              = NULL;
1244   ctx->J              = NULL;
1245   /* geometry and grids */
1246   ctx->sphere       = PETSC_FALSE;
1247   ctx->inflate      = PETSC_FALSE;
1248   ctx->use_p4est    = PETSC_FALSE;
1249   ctx->num_sections = 3; /* 2, 3 or 4 */
1250   for (PetscInt grid = 0; grid < LANDAU_MAX_GRIDS; grid++) {
1251     ctx->radius[grid]             = 5.; /* thermal radius (velocity) */
1252     ctx->radius_perp[grid]        = 5.; /* thermal radius (velocity) */
1253     ctx->radius_par[grid]         = 5.; /* thermal radius (velocity) */
1254     ctx->numAMRRefine[grid]       = 5;
1255     ctx->postAMRRefine[grid]      = 0;
1256     ctx->species_offset[grid + 1] = 1; // one species default
1257     num_species_grid[grid]        = 0;
1258     ctx->plex[grid]               = NULL; /* cache as expensive to Convert */
1259   }
1260   ctx->species_offset[0] = 0;
1261   ctx->re_radius         = 0.;
1262   ctx->vperp0_radius1    = 0;
1263   ctx->vperp0_radius2    = 0;
1264   ctx->nZRefine1         = 0;
1265   ctx->nZRefine2         = 0;
1266   ctx->numRERefine       = 0;
1267   num_species_grid[0]    = 1; // one species default
1268   /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
1269   ctx->charges[0]       = -1;                       /* electron charge (MKS) */
1270   ctx->masses[0]        = 1 / 1835.469965278441013; /* temporary value in proton mass */
1271   ctx->n[0]             = 1;
1272   ctx->v_0              = 1; /* thermal velocity, we could start with a scale != 1 */
1273   ctx->thermal_temps[0] = 1;
1274   /* constants, etc. */
1275   ctx->epsilon0 = 8.8542e-12;     /* permittivity of free space (MKS) F/m */
1276   ctx->k        = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
1277   ctx->lnLam    = 10;             /* cross section ratio large - small angle collisions */
1278   ctx->n_0      = 1.e20;          /* typical plasma n, but could set it to 1 */
1279   ctx->Ez       = 0;
1280   for (PetscInt grid = 0; grid < LANDAU_NUM_TIMERS; grid++) ctx->times[grid] = 0;
1281   for (PetscInt ii = 0; ii < LANDAU_DIM; ii++) ctx->cells0[ii] = 2;
1282   if (LANDAU_DIM == 2) ctx->cells0[0] = 1;
1283   ctx->use_matrix_mass                = PETSC_FALSE;
1284   ctx->use_relativistic_corrections   = PETSC_FALSE;
1285   ctx->use_energy_tensor_trick        = PETSC_FALSE; /* Use Eero's trick for energy conservation v --> grad(v^2/2) */
1286   ctx->SData_d.w                      = NULL;
1287   ctx->SData_d.x                      = NULL;
1288   ctx->SData_d.y                      = NULL;
1289   ctx->SData_d.z                      = NULL;
1290   ctx->SData_d.invJ                   = NULL;
1291   ctx->jacobian_field_major_order     = PETSC_FALSE;
1292   ctx->SData_d.coo_elem_offsets       = NULL;
1293   ctx->SData_d.coo_elem_point_offsets = NULL;
1294   ctx->coo_assembly                   = PETSC_FALSE;
1295   ctx->SData_d.coo_elem_fullNb        = NULL;
1296   ctx->SData_d.coo_size               = 0;
1297   PetscOptionsBegin(ctx->comm, prefix, "Options for Fokker-Plank-Landau collision operator", "none");
1298   {
1299     char opstring[256];
1300 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1301     ctx->deviceType = LANDAU_KOKKOS;
1302     PetscCall(PetscStrcpy(opstring, "kokkos"));
1303 #elif defined(PETSC_HAVE_CUDA)
1304     ctx->deviceType = LANDAU_CUDA;
1305     PetscCall(PetscStrcpy(opstring, "cuda"));
1306 #else
1307     ctx->deviceType = LANDAU_CPU;
1308     PetscCall(PetscStrcpy(opstring, "cpu"));
1309 #endif
1310     PetscCall(PetscOptionsString("-dm_landau_device_type", "Use kernels on 'cpu', 'cuda', or 'kokkos'", "plexland.c", opstring, opstring, sizeof(opstring), NULL));
1311     PetscCall(PetscStrcmp("cpu", opstring, &flg));
1312     if (flg) {
1313       ctx->deviceType = LANDAU_CPU;
1314     } else {
1315       PetscCall(PetscStrcmp("cuda", opstring, &flg));
1316       if (flg) {
1317         ctx->deviceType = LANDAU_CUDA;
1318       } else {
1319         PetscCall(PetscStrcmp("kokkos", opstring, &flg));
1320         if (flg) ctx->deviceType = LANDAU_KOKKOS;
1321         else SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_device_type %s", opstring);
1322       }
1323     }
1324   }
1325   PetscCall(PetscOptionsReal("-dm_landau_electron_shift", "Shift in thermal velocity of electrons", "none", ctx->electronShift, &ctx->electronShift, NULL));
1326   PetscCall(PetscOptionsInt("-dm_landau_verbose", "Level of verbosity output", "plexland.c", ctx->verbose, &ctx->verbose, NULL));
1327   PetscCall(PetscOptionsInt("-dm_landau_batch_size", "Number of 'vertices' to batch", "ex2.c", ctx->batch_sz, &ctx->batch_sz, NULL));
1328   PetscCheck(LANDAU_MAX_BATCH_SZ >= ctx->batch_sz, ctx->comm, PETSC_ERR_ARG_WRONG, "LANDAU_MAX_BATCH_SZ %" PetscInt_FMT " < ctx->batch_sz %" PetscInt_FMT, (PetscInt)LANDAU_MAX_BATCH_SZ, ctx->batch_sz);
1329   PetscCall(PetscOptionsInt("-dm_landau_batch_view_idx", "Index of batch for diagnostics like plotting", "ex2.c", ctx->batch_view_idx, &ctx->batch_view_idx, NULL));
1330   PetscCheck(ctx->batch_view_idx < ctx->batch_sz, ctx->comm, PETSC_ERR_ARG_WRONG, "-ctx->batch_view_idx %" PetscInt_FMT " > ctx->batch_sz %" PetscInt_FMT, ctx->batch_view_idx, ctx->batch_sz);
1331   PetscCall(PetscOptionsReal("-dm_landau_Ez", "Initial parallel electric field in unites of Conner-Hastie critical field", "plexland.c", ctx->Ez, &ctx->Ez, NULL));
1332   PetscCall(PetscOptionsReal("-dm_landau_n_0", "Normalization constant for number density", "plexland.c", ctx->n_0, &ctx->n_0, NULL));
1333   PetscCall(PetscOptionsReal("-dm_landau_ln_lambda", "Cross section parameter", "plexland.c", ctx->lnLam, &ctx->lnLam, NULL));
1334   PetscCall(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));
1335   PetscCall(PetscOptionsBool("-dm_landau_use_relativistic_corrections", "Use relativistic corrections", "plexland.c", ctx->use_relativistic_corrections, &ctx->use_relativistic_corrections, NULL));
1336   PetscCall(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,
1337                              &ctx->use_energy_tensor_trick, NULL));
1338 
1339   /* get num species with temperature, set defaults */
1340   for (ii = 1; ii < LANDAU_MAX_SPECIES; ii++) {
1341     ctx->thermal_temps[ii] = 1;
1342     ctx->charges[ii]       = 1;
1343     ctx->masses[ii]        = 1;
1344     ctx->n[ii]             = 1;
1345   }
1346   nt = LANDAU_MAX_SPECIES;
1347   PetscCall(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));
1348   if (flg) {
1349     PetscCall(PetscInfo(dummy, "num_species set to number of thermal temps provided (%" PetscInt_FMT ")\n", nt));
1350     ctx->num_species = nt;
1351   } else SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
1352   for (ii = 0; ii < ctx->num_species; ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
1353   nm = LANDAU_MAX_SPECIES - 1;
1354   PetscCall(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));
1355   PetscCheck(!flg || nm == ctx->num_species - 1, ctx->comm, PETSC_ERR_ARG_WRONG, "num ion masses %" PetscInt_FMT " != num species %" PetscInt_FMT, nm, ctx->num_species - 1);
1356   nm = LANDAU_MAX_SPECIES;
1357   PetscCall(PetscOptionsRealArray("-dm_landau_n", "Number density of each species = n_s * n_0", "plexland.c", ctx->n, &nm, &flg));
1358   PetscCheck(!flg || nm == ctx->num_species, ctx->comm, PETSC_ERR_ARG_WRONG, "wrong num n: %" PetscInt_FMT " != num species %" PetscInt_FMT, nm, ctx->num_species);
1359   for (ii = 0; ii < LANDAU_MAX_SPECIES; ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
1360   ctx->masses[0] = 9.10938356e-31;                                           /* electron mass kg (should be about right already) */
1361   ctx->m_0       = ctx->masses[0];                                           /* arbitrary reference mass, electrons */
1362   nc             = LANDAU_MAX_SPECIES - 1;
1363   PetscCall(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));
1364   if (flg) PetscCheck(nc == ctx->num_species - 1, ctx->comm, PETSC_ERR_ARG_WRONG, "num charges %" PetscInt_FMT " != num species %" PetscInt_FMT, nc, ctx->num_species - 1);
1365   for (ii = 0; ii < LANDAU_MAX_SPECIES; ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
1366   /* geometry and grids */
1367   nt = LANDAU_MAX_GRIDS;
1368   PetscCall(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));
1369   if (flg) {
1370     ctx->num_grids = nt;
1371     for (ii = nt = 0; ii < ctx->num_grids; ii++) nt += num_species_grid[ii];
1372     PetscCheck(ctx->num_species == nt, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_num_species_grid: sum %" PetscInt_FMT " != num_species = %" PetscInt_FMT ". %" PetscInt_FMT " grids (check that number of grids <= LANDAU_MAX_GRIDS = %d)", nt, ctx->num_species,
1373                ctx->num_grids, LANDAU_MAX_GRIDS);
1374   } else {
1375     ctx->num_grids      = 1; // go back to a single grid run
1376     num_species_grid[0] = ctx->num_species;
1377   }
1378   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];
1379   PetscCheck(ctx->species_offset[ctx->num_grids] == ctx->num_species, ctx->comm, PETSC_ERR_ARG_WRONG, "ctx->species_offset[ctx->num_grids] %" PetscInt_FMT " != ctx->num_species = %" PetscInt_FMT " ???????????", ctx->species_offset[ctx->num_grids],
1380              ctx->num_species);
1381   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
1382     int iii       = ctx->species_offset[grid];                                          // normalize with first (arbitrary) species on grid
1383     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 */
1384   }
1385   ii = 0;
1386   PetscCall(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));
1387   ctx->v_0 = v0_grid[ii];                                                                                                                       /* arbitrary units for non dimensionalization: global mean velocity in 1D of electrons */
1388   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 */
1389   /* domain */
1390   nt = LANDAU_MAX_GRIDS;
1391   PetscCall(PetscOptionsRealArray("-dm_landau_domain_radius", "Phase space size in units of thermal velocity of grid", "plexland.c", ctx->radius, &nt, &flg));
1392   if (flg) {
1393     PetscCheck(nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_domain_radius: given %" PetscInt_FMT " radius != number grids %" PetscInt_FMT, nt, ctx->num_grids);
1394     while (nt--) ctx->radius_par[nt] = ctx->radius_perp[nt] = ctx->radius[nt];
1395   } else {
1396     nt = LANDAU_MAX_GRIDS;
1397     PetscCall(PetscOptionsRealArray("-dm_landau_domain_max_par", "Parallel velocity domain size in units of thermal velocity of grid", "plexland.c", ctx->radius_par, &nt, &flg));
1398     if (flg) PetscCheck(nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_domain_max_par: given %" PetscInt_FMT " radius != number grids %" PetscInt_FMT, nt, ctx->num_grids);
1399     PetscCall(PetscOptionsRealArray("-dm_landau_domain_max_perp", "Perpendicular velocity domain size in units of thermal velocity of grid", "plexland.c", ctx->radius_perp, &nt, &flg));
1400     if (flg) PetscCheck(nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_domain_max_perp: given %" PetscInt_FMT " radius != number grids %" PetscInt_FMT, nt, ctx->num_grids);
1401   }
1402   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
1403     if (flg && ctx->radius[grid] <= 0) { /* negative is ratio of c - need to set par and perp with this -- todo */
1404       if (ctx->radius[grid] == 0) ctx->radius[grid] = 0.75;
1405       else ctx->radius[grid] = -ctx->radius[grid];
1406       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)
1407       PetscCall(PetscInfo(dummy, "Change domain radius to %g for grid %" PetscInt_FMT "\n", (double)ctx->radius[grid], grid));
1408     }
1409     ctx->radius[grid] *= v0_grid[grid] / ctx->v_0;      // scale domain by thermal radius relative to v_0
1410     ctx->radius_perp[grid] *= v0_grid[grid] / ctx->v_0; // scale domain by thermal radius relative to v_0
1411     ctx->radius_par[grid] *= v0_grid[grid] / ctx->v_0;  // scale domain by thermal radius relative to v_0
1412   }
1413   /* amr parameters */
1414   nt = LANDAU_DIM;
1415   PetscCall(PetscOptionsIntArray("-dm_landau_num_cells", "Number of cells in each dimension of base grid", "plexland.c", ctx->cells0, &nt, &flg));
1416   nt = LANDAU_MAX_GRIDS;
1417   PetscCall(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));
1418   PetscCheck(!flg || nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_amr_levels_max: given %" PetscInt_FMT " != number grids %" PetscInt_FMT, nt, ctx->num_grids);
1419   nt = LANDAU_MAX_GRIDS;
1420   PetscCall(PetscOptionsIntArray("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &nt, &flg));
1421   for (ii = 1; ii < ctx->num_grids; ii++) ctx->postAMRRefine[ii] = ctx->postAMRRefine[0]; // all grids the same now
1422   PetscCall(PetscOptionsInt("-dm_landau_amr_re_levels", "Number of levels to refine along v_perp=0, z>0", "plexland.c", ctx->numRERefine, &ctx->numRERefine, &flg));
1423   PetscCall(PetscOptionsInt("-dm_landau_amr_z_refine1", "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine1, &ctx->nZRefine1, &flg));
1424   PetscCall(PetscOptionsInt("-dm_landau_amr_z_refine2", "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine2, &ctx->nZRefine2, &flg));
1425   PetscCall(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));
1426   PetscCall(PetscOptionsReal("-dm_landau_z_radius1", "velocity range to refine r=0 axis (for electrons)", "plexland.c", ctx->vperp0_radius1, &ctx->vperp0_radius1, &flg));
1427   PetscCall(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));
1428   /* spherical domain (not used) */
1429   PetscCall(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));
1430   PetscCall(PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, &sph_flg));
1431   PetscCall(PetscOptionsBool("-dm_landau_inflate", "With sphere, inflate for curved edges", "plexland.c", ctx->inflate, &ctx->inflate, &flg));
1432   PetscCall(PetscOptionsReal("-dm_landau_e_radius", "Electron thermal velocity, used for circular meshes", "plexland.c", ctx->e_radius, &ctx->e_radius, &flg));
1433   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an e radius but did not set sphere, user error really */
1434   if (!flg) ctx->e_radius = 1.5 * PetscSqrtReal(8 * ctx->k * ctx->thermal_temps[0] / ctx->masses[0] / PETSC_PI) / ctx->v_0;
1435   nt = LANDAU_MAX_GRIDS;
1436   PetscCall(PetscOptionsRealArray("-dm_landau_i_radius", "Ion thermal velocity, used for circular meshes", "plexland.c", ctx->i_radius, &nt, &flg));
1437   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE;
1438   if (!flg) {
1439     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
1440   }
1441   if (flg) PetscCheck(ctx->num_grids == nt, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_i_radius: %" PetscInt_FMT " != num_species = %" PetscInt_FMT, nt, ctx->num_grids);
1442   if (ctx->sphere) PetscCheck(ctx->e_radius > ctx->i_radius[0], ctx->comm, PETSC_ERR_ARG_WRONG, "bad radii: %g < %g < %g", (double)ctx->i_radius[0], (double)ctx->e_radius, (double)ctx->radius[0]);
1443   /* processing options */
1444   PetscCall(PetscOptionsBool("-dm_landau_gpu_assembly", "Assemble Jacobian on GPU", "plexland.c", ctx->gpu_assembly, &ctx->gpu_assembly, NULL));
1445   if (ctx->deviceType == LANDAU_CPU || ctx->deviceType == LANDAU_KOKKOS) { // make Kokkos
1446     PetscCall(PetscOptionsBool("-dm_landau_coo_assembly", "Assemble Jacobian with Kokkos on 'device'", "plexland.c", ctx->coo_assembly, &ctx->coo_assembly, NULL));
1447     if (ctx->coo_assembly) PetscCheck(ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "COO assembly requires 'gpu assembly' even if Kokkos 'CPU' back-end %d", ctx->coo_assembly);
1448   }
1449   PetscCall(PetscOptionsBool("-dm_landau_jacobian_field_major_order", "Reorder Jacobian for GPU assembly with field major, or block diagonal, ordering (DEPRECATED)", "plexland.c", ctx->jacobian_field_major_order, &ctx->jacobian_field_major_order, NULL));
1450   if (ctx->jacobian_field_major_order) PetscCheck(ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_jacobian_field_major_order requires -dm_landau_gpu_assembly");
1451   PetscCheck(!ctx->jacobian_field_major_order, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_jacobian_field_major_order DEPRECATED");
1452   PetscOptionsEnd();
1453 
1454   for (ii = ctx->num_species; ii < LANDAU_MAX_SPECIES; ii++) ctx->masses[ii] = ctx->thermal_temps[ii] = ctx->charges[ii] = 0;
1455   if (ctx->verbose > 0) {
1456     PetscCall(PetscPrintf(ctx->comm, "masses:        e=%10.3e; ions in proton mass units:   %10.3e %10.3e ...\n", (double)ctx->masses[0], (double)(ctx->masses[1] / 1.6720e-27), (double)(ctx->num_species > 2 ? ctx->masses[2] / 1.6720e-27 : 0)));
1457     PetscCall(PetscPrintf(ctx->comm, "charges:       e=%10.3e; charges in elementary units: %10.3e %10.3e\n", (double)ctx->charges[0], (double)(-ctx->charges[1] / ctx->charges[0]), (double)(ctx->num_species > 2 ? -ctx->charges[2] / ctx->charges[0] : 0)));
1458     PetscCall(PetscPrintf(ctx->comm, "n:             e: %10.3e                           i: %10.3e %10.3e\n", (double)ctx->n[0], (double)ctx->n[1], (double)(ctx->num_species > 2 ? ctx->n[2] : 0)));
1459     PetscCall(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", (double)ctx->thermal_temps[0], (double)ctx->thermal_temps[1],
1460                           (double)((ctx->num_species > 2) ? ctx->thermal_temps[2] : 0), (double)ctx->v_0, (double)(ctx->v_0 / SPEED_OF_LIGHT), (double)ctx->n_0, (double)ctx->t_0, ctx->use_relativistic_corrections ? "relativistic" : "classical", ctx->use_energy_tensor_trick ? "Use trick" : "Intuitive",
1461                           ctx->batch_sz));
1462     PetscCall(PetscPrintf(ctx->comm, "Domain radius (AMR levels) grid %d: par=%10.3e, perp=%10.3e (%" PetscInt_FMT ") ", 0, (double)ctx->radius_par[0], (double)ctx->radius_perp[0], ctx->numAMRRefine[0]));
1463     for (ii = 1; ii < ctx->num_grids; ii++) PetscCall(PetscPrintf(ctx->comm, ", %" PetscInt_FMT ": par=%10.3e, perp=%10.3e (%" PetscInt_FMT ") ", ii, (double)ctx->radius_par[ii], (double)ctx->radius_perp[ii], ctx->numAMRRefine[ii]));
1464     PetscCall(PetscPrintf(ctx->comm, "\n"));
1465     if (ctx->jacobian_field_major_order) {
1466       PetscCall(PetscPrintf(ctx->comm, "Using field major order for GPU Jacobian\n"));
1467     } else {
1468       PetscCall(PetscPrintf(ctx->comm, "Using default Plex order for all matrices\n"));
1469     }
1470   }
1471   PetscCall(DMDestroy(&dummy));
1472   {
1473     PetscMPIInt rank;
1474     PetscCallMPI(MPI_Comm_rank(ctx->comm, &rank));
1475     ctx->stage = 0;
1476     PetscCall(PetscLogEventRegister("Landau Create", DM_CLASSID, &ctx->events[13]));   /* 13 */
1477     PetscCall(PetscLogEventRegister(" GPU ass. setup", DM_CLASSID, &ctx->events[2]));  /* 2 */
1478     PetscCall(PetscLogEventRegister(" Build matrix", DM_CLASSID, &ctx->events[12]));   /* 12 */
1479     PetscCall(PetscLogEventRegister(" Assembly maps", DM_CLASSID, &ctx->events[15]));  /* 15 */
1480     PetscCall(PetscLogEventRegister("Landau Mass mat", DM_CLASSID, &ctx->events[14])); /* 14 */
1481     PetscCall(PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[11])); /* 11 */
1482     PetscCall(PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[0]));  /* 0 */
1483     PetscCall(PetscLogEventRegister("Landau Mass", DM_CLASSID, &ctx->events[9]));      /* 9 */
1484     PetscCall(PetscLogEventRegister(" Preamble", DM_CLASSID, &ctx->events[10]));       /* 10 */
1485     PetscCall(PetscLogEventRegister(" static IP Data", DM_CLASSID, &ctx->events[7]));  /* 7 */
1486     PetscCall(PetscLogEventRegister(" dynamic IP-Jac", DM_CLASSID, &ctx->events[1]));  /* 1 */
1487     PetscCall(PetscLogEventRegister(" Kernel-init", DM_CLASSID, &ctx->events[3]));     /* 3 */
1488     PetscCall(PetscLogEventRegister(" Jac-f-df (GPU)", DM_CLASSID, &ctx->events[8]));  /* 8 */
1489     PetscCall(PetscLogEventRegister(" J Kernel (GPU)", DM_CLASSID, &ctx->events[4]));  /* 4 */
1490     PetscCall(PetscLogEventRegister(" M Kernel (GPU)", DM_CLASSID, &ctx->events[16])); /* 16 */
1491     PetscCall(PetscLogEventRegister(" Copy to CPU", DM_CLASSID, &ctx->events[5]));     /* 5 */
1492     PetscCall(PetscLogEventRegister(" CPU assemble", DM_CLASSID, &ctx->events[6]));    /* 6 */
1493 
1494     if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
1495       PetscCall(PetscOptionsClearValue(NULL, "-snes_converged_reason"));
1496       PetscCall(PetscOptionsClearValue(NULL, "-ksp_converged_reason"));
1497       PetscCall(PetscOptionsClearValue(NULL, "-snes_monitor"));
1498       PetscCall(PetscOptionsClearValue(NULL, "-ksp_monitor"));
1499       PetscCall(PetscOptionsClearValue(NULL, "-ts_monitor"));
1500       PetscCall(PetscOptionsClearValue(NULL, "-ts_view"));
1501       PetscCall(PetscOptionsClearValue(NULL, "-ts_adapt_monitor"));
1502       PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_amr_dm_view"));
1503       PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_amr_vec_view"));
1504       PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_mass_dm_view"));
1505       PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_mass_view"));
1506       PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_jacobian_view"));
1507       PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_mat_view"));
1508       PetscCall(PetscOptionsClearValue(NULL, "-pc_bjkokkos_ksp_converged_reason"));
1509       PetscCall(PetscOptionsClearValue(NULL, "-pc_bjkokkos_ksp_monitor"));
1510       PetscCall(PetscOptionsClearValue(NULL, "-"));
1511       PetscCall(PetscOptionsClearValue(NULL, "-info"));
1512     }
1513   }
1514   PetscFunctionReturn(PETSC_SUCCESS);
1515 }
1516 
1517 static PetscErrorCode CreateStaticGPUData(PetscInt dim, IS grid_batch_is_inv[], LandauCtx *ctx)
1518 {
1519   PetscSection     section[LANDAU_MAX_GRIDS], globsection[LANDAU_MAX_GRIDS];
1520   PetscQuadrature  quad;
1521   const PetscReal *quadWeights;
1522   PetscInt         numCells[LANDAU_MAX_GRIDS], Nq, Nf[LANDAU_MAX_GRIDS], ncellsTot = 0, MAP_BF_SIZE = 64 * LANDAU_DIM * LANDAU_DIM * LANDAU_MAX_Q_FACE * LANDAU_MAX_SPECIES;
1523   PetscTabulation *Tf;
1524   PetscDS          prob;
1525 
1526   PetscFunctionBegin;
1527   PetscCall(DMGetDS(ctx->plex[0], &prob));    // same DS for all grids
1528   PetscCall(PetscDSGetTabulation(prob, &Tf)); // Bf, &Df same for all grids
1529   /* DS, Tab and quad is same on all grids */
1530   PetscCheck(ctx->plex[0], ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
1531   PetscCall(PetscFEGetQuadrature(ctx->fe[0], &quad));
1532   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, &quadWeights));
1533   PetscCheck(Nq <= LANDAU_MAX_NQ, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nq = %" PetscInt_FMT " > LANDAU_MAX_NQ (%d)", Nq, LANDAU_MAX_NQ);
1534   /* setup each grid */
1535   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
1536     PetscInt cStart, cEnd;
1537     PetscCheck(ctx->plex[grid] != NULL, ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
1538     PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
1539     numCells[grid] = cEnd - cStart; // grids can have different topology
1540     PetscCall(DMGetLocalSection(ctx->plex[grid], &section[grid]));
1541     PetscCall(DMGetGlobalSection(ctx->plex[grid], &globsection[grid]));
1542     PetscCall(PetscSectionGetNumFields(section[grid], &Nf[grid]));
1543     ncellsTot += numCells[grid];
1544   }
1545   /* create GPU assembly data */
1546   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
1547     PetscContainer container;
1548     PetscScalar   *elemMatrix, *elMat;
1549     pointInterpolationP4est(*pointMaps)[LANDAU_MAX_Q_FACE];
1550     P4estVertexMaps *maps;
1551     const PetscInt  *plex_batch = NULL, Nb = Nq, elMatSz = Nq * Nq * ctx->num_species * ctx->num_species; // tensor elements;
1552     LandauIdx       *coo_elem_offsets = NULL, *coo_elem_fullNb = NULL, (*coo_elem_point_offsets)[LANDAU_MAX_NQ + 1] = NULL;
1553     /* create GPU assembly data */
1554     PetscCall(PetscInfo(ctx->plex[0], "Make GPU maps %d\n", 1));
1555     PetscCall(PetscLogEventBegin(ctx->events[2], 0, 0, 0, 0));
1556     PetscCall(PetscMalloc(sizeof(*maps) * ctx->num_grids, &maps));
1557     PetscCall(PetscMalloc(sizeof(*pointMaps) * MAP_BF_SIZE, &pointMaps));
1558     PetscCall(PetscMalloc(sizeof(*elemMatrix) * elMatSz, &elemMatrix));
1559 
1560     if (ctx->coo_assembly) {                                                                                                      // setup COO assembly -- put COO metadata directly in ctx->SData_d
1561       PetscCall(PetscMalloc3(ncellsTot + 1, &coo_elem_offsets, ncellsTot, &coo_elem_fullNb, ncellsTot, &coo_elem_point_offsets)); // array of integer pointers
1562       coo_elem_offsets[0] = 0;                                                                                                    // finish later
1563       PetscCall(PetscInfo(ctx->plex[0], "COO initialization, %" PetscInt_FMT " cells\n", ncellsTot));
1564       ctx->SData_d.coo_n_cellsTot         = ncellsTot;
1565       ctx->SData_d.coo_elem_offsets       = (void *)coo_elem_offsets;
1566       ctx->SData_d.coo_elem_fullNb        = (void *)coo_elem_fullNb;
1567       ctx->SData_d.coo_elem_point_offsets = (void *)coo_elem_point_offsets;
1568     } else {
1569       ctx->SData_d.coo_elem_offsets = ctx->SData_d.coo_elem_fullNb = NULL;
1570       ctx->SData_d.coo_elem_point_offsets                          = NULL;
1571       ctx->SData_d.coo_n_cellsTot                                  = 0;
1572     }
1573 
1574     ctx->SData_d.coo_max_fullnb = 0;
1575     for (PetscInt grid = 0, glb_elem_idx = 0; grid < ctx->num_grids; grid++) {
1576       PetscInt cStart, cEnd, Nfloc = Nf[grid], totDim = Nfloc * Nq;
1577       if (grid_batch_is_inv[grid]) PetscCall(ISGetIndices(grid_batch_is_inv[grid], &plex_batch));
1578       PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
1579       // make maps
1580       maps[grid].d_self       = NULL;
1581       maps[grid].num_elements = numCells[grid];
1582       maps[grid].num_face     = (PetscInt)(pow(Nq, 1. / ((double)dim)) + .001);                 // Q
1583       maps[grid].num_face     = (PetscInt)(pow(maps[grid].num_face, (double)(dim - 1)) + .001); // Q^2
1584       maps[grid].num_reduced  = 0;
1585       maps[grid].deviceType   = ctx->deviceType;
1586       maps[grid].numgrids     = ctx->num_grids;
1587       // count reduced and get
1588       PetscCall(PetscMalloc(maps[grid].num_elements * sizeof(*maps[grid].gIdx), &maps[grid].gIdx));
1589       for (int ej = cStart, eidx = 0; ej < cEnd; ++ej, ++eidx, glb_elem_idx++) {
1590         if (coo_elem_offsets) coo_elem_offsets[glb_elem_idx + 1] = coo_elem_offsets[glb_elem_idx]; // start with last one, then add
1591         for (int fieldA = 0; fieldA < Nf[grid]; fieldA++) {
1592           int fullNb = 0;
1593           for (int q = 0; q < Nb; ++q) {
1594             PetscInt     numindices, *indices;
1595             PetscScalar *valuesOrig = elMat = elemMatrix;
1596             PetscCall(PetscArrayzero(elMat, totDim * totDim));
1597             elMat[(fieldA * Nb + q) * totDim + fieldA * Nb + q] = 1;
1598             PetscCall(DMPlexGetClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **)&elMat));
1599             for (PetscInt f = 0; f < numindices; ++f) { // look for a non-zero on the diagonal
1600               if (PetscAbs(PetscRealPart(elMat[f * numindices + f])) > PETSC_MACHINE_EPSILON) {
1601                 // found it
1602                 if (PetscAbs(PetscRealPart(elMat[f * numindices + f] - 1.)) < PETSC_MACHINE_EPSILON) { // normal vertex 1.0
1603                   if (plex_batch) {
1604                     maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)plex_batch[indices[f]];
1605                   } else {
1606                     maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)indices[f];
1607                   }
1608                   fullNb++;
1609                 } else { //found a constraint
1610                   int            jj                = 0;
1611                   PetscReal      sum               = 0;
1612                   const PetscInt ff                = f;
1613                   maps[grid].gIdx[eidx][fieldA][q] = -maps[grid].num_reduced - 1; // store (-)index: id = -(idx+1): idx = -id - 1
1614 
1615                   do {                                                                                              // constraints are continuous in Plex - exploit that here
1616                     int ii;                                                                                         // get 'scale'
1617                     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
1618                       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
1619                         pointMaps[maps[grid].num_reduced][jj].scale += PetscRealPart(elMat[f * numindices + ff + ii]);
1620                       }
1621                     }
1622                     sum += pointMaps[maps[grid].num_reduced][jj].scale; // diagnostic
1623                     // get 'gid'
1624                     if (pointMaps[maps[grid].num_reduced][jj].scale == 0) pointMaps[maps[grid].num_reduced][jj].gid = -1; // 3D has Q and Q^2 interps
1625                     else {
1626                       if (plex_batch) {
1627                         pointMaps[maps[grid].num_reduced][jj].gid = plex_batch[indices[f]];
1628                       } else {
1629                         pointMaps[maps[grid].num_reduced][jj].gid = indices[f];
1630                       }
1631                       fullNb++;
1632                     }
1633                   } while (++jj < maps[grid].num_face && ++f < numindices); // jj is incremented if we hit the end
1634                   while (jj < maps[grid].num_face) {
1635                     pointMaps[maps[grid].num_reduced][jj].scale = 0;
1636                     pointMaps[maps[grid].num_reduced][jj].gid   = -1;
1637                     jj++;
1638                   }
1639                   if (PetscAbs(sum - 1.0) > 10 * PETSC_MACHINE_EPSILON) { // debug
1640                     int       d, f;
1641                     PetscReal tmp = 0;
1642                     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\t\t%d.%d.%d) ERROR total I = %22.16e (LANDAU_MAX_Q_FACE=%d, #face=%d)\n", eidx, q, fieldA, (double)sum, LANDAU_MAX_Q_FACE, maps[grid].num_face));
1643                     for (d = 0, tmp = 0; d < numindices; ++d) {
1644                       if (tmp != 0 && PetscAbs(tmp - 1.0) > 10 * PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%3d) %3" PetscInt_FMT ": ", d, indices[d]));
1645                       for (f = 0; f < numindices; ++f) tmp += PetscRealPart(elMat[d * numindices + f]);
1646                       if (tmp != 0) PetscCall(PetscPrintf(ctx->comm, " | %22.16e\n", (double)tmp));
1647                     }
1648                   }
1649                   maps[grid].num_reduced++;
1650                   PetscCheck(maps[grid].num_reduced < MAP_BF_SIZE, PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps[grid].num_reduced %d > %" PetscInt_FMT, maps[grid].num_reduced, MAP_BF_SIZE);
1651                 }
1652                 break;
1653               }
1654             }
1655             // cleanup
1656             PetscCall(DMPlexRestoreClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **)&elMat));
1657             if (elMat != valuesOrig) PetscCall(DMRestoreWorkArray(ctx->plex[grid], numindices * numindices, MPIU_SCALAR, &elMat));
1658           }
1659           if (ctx->coo_assembly) {                                 // setup COO assembly
1660             coo_elem_offsets[glb_elem_idx + 1] += fullNb * fullNb; // one species block, adds a block for each species, on this element in this grid
1661             if (fieldA == 0) {                                     // cache full Nb for this element, on this grid per species
1662               coo_elem_fullNb[glb_elem_idx] = fullNb;
1663               if (fullNb > ctx->SData_d.coo_max_fullnb) ctx->SData_d.coo_max_fullnb = fullNb;
1664             } else PetscCheck(coo_elem_fullNb[glb_elem_idx] == fullNb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "full element size change with species %d %d", coo_elem_fullNb[glb_elem_idx], fullNb);
1665           }
1666         } // field
1667       }   // cell
1668       // allocate and copy point data maps[grid].gIdx[eidx][field][q]
1669       PetscCall(PetscMalloc(maps[grid].num_reduced * sizeof(*maps[grid].c_maps), &maps[grid].c_maps));
1670       for (int ej = 0; ej < maps[grid].num_reduced; ++ej) {
1671         for (int q = 0; q < maps[grid].num_face; ++q) {
1672           maps[grid].c_maps[ej][q].scale = pointMaps[ej][q].scale;
1673           maps[grid].c_maps[ej][q].gid   = pointMaps[ej][q].gid;
1674         }
1675       }
1676 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1677       if (ctx->deviceType == LANDAU_KOKKOS) {
1678         PetscCall(LandauKokkosCreateMatMaps(maps, pointMaps, Nf, Nq, grid)); // implies Kokkos does
1679       }                                                                      // else could be CUDA
1680 #endif
1681 #if defined(PETSC_HAVE_CUDA)
1682       if (ctx->deviceType == LANDAU_CUDA) PetscCall(LandauCUDACreateMatMaps(maps, pointMaps, Nf, Nq, grid));
1683 #endif
1684       if (plex_batch) {
1685         PetscCall(ISRestoreIndices(grid_batch_is_inv[grid], &plex_batch));
1686         PetscCall(ISDestroy(&grid_batch_is_inv[grid])); // we are done with this
1687       }
1688     } /* grids */
1689     // finish COO
1690     if (ctx->coo_assembly) { // setup COO assembly
1691       PetscInt *oor, *ooc;
1692       ctx->SData_d.coo_size = coo_elem_offsets[ncellsTot] * ctx->batch_sz;
1693       PetscCall(PetscMalloc2(ctx->SData_d.coo_size, &oor, ctx->SData_d.coo_size, &ooc));
1694       for (int i = 0; i < ctx->SData_d.coo_size; i++) oor[i] = ooc[i] = -1;
1695       // get
1696       for (int grid = 0, glb_elem_idx = 0; grid < ctx->num_grids; grid++) {
1697         for (int ej = 0; ej < numCells[grid]; ++ej, glb_elem_idx++) {
1698           const int              fullNb           = coo_elem_fullNb[glb_elem_idx];
1699           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
1700           coo_elem_point_offsets[glb_elem_idx][0] = 0;
1701           for (int f = 0, cnt2 = 0; f < Nb; f++) {
1702             int idx                                     = Idxs[f];
1703             coo_elem_point_offsets[glb_elem_idx][f + 1] = coo_elem_point_offsets[glb_elem_idx][f]; // start at last
1704             if (idx >= 0) {
1705               cnt2++;
1706               coo_elem_point_offsets[glb_elem_idx][f + 1]++; // inc
1707             } else {
1708               idx = -idx - 1;
1709               for (int q = 0; q < maps[grid].num_face; q++) {
1710                 if (maps[grid].c_maps[idx][q].gid < 0) break;
1711                 cnt2++;
1712                 coo_elem_point_offsets[glb_elem_idx][f + 1]++; // inc
1713               }
1714             }
1715             PetscCheck(cnt2 <= fullNb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "wrong count %d < %d", fullNb, cnt2);
1716           }
1717           PetscCheck(coo_elem_point_offsets[glb_elem_idx][Nb] == fullNb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "coo_elem_point_offsets size %d != fullNb=%d", coo_elem_point_offsets[glb_elem_idx][Nb], fullNb);
1718         }
1719       }
1720       // set
1721       for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
1722         for (int grid = 0, glb_elem_idx = 0; grid < ctx->num_grids; grid++) {
1723           const PetscInt moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
1724           for (int ej = 0; ej < numCells[grid]; ++ej, glb_elem_idx++) {
1725             const int fullNb = coo_elem_fullNb[glb_elem_idx], fullNb2 = fullNb * fullNb;
1726             // set (i,j)
1727             for (int fieldA = 0; fieldA < Nf[grid]; fieldA++) {
1728               const LandauIdx *const Idxs = &maps[grid].gIdx[ej][fieldA][0];
1729               int                    rows[LANDAU_MAX_Q_FACE], cols[LANDAU_MAX_Q_FACE];
1730               for (int f = 0; f < Nb; ++f) {
1731                 const int nr = coo_elem_point_offsets[glb_elem_idx][f + 1] - coo_elem_point_offsets[glb_elem_idx][f];
1732                 if (nr == 1) rows[0] = Idxs[f];
1733                 else {
1734                   const int idx = -Idxs[f] - 1;
1735                   for (int q = 0; q < nr; q++) rows[q] = maps[grid].c_maps[idx][q].gid;
1736                 }
1737                 for (int g = 0; g < Nb; ++g) {
1738                   const int nc = coo_elem_point_offsets[glb_elem_idx][g + 1] - coo_elem_point_offsets[glb_elem_idx][g];
1739                   if (nc == 1) cols[0] = Idxs[g];
1740                   else {
1741                     const int idx = -Idxs[g] - 1;
1742                     for (int q = 0; q < nc; q++) cols[q] = maps[grid].c_maps[idx][q].gid;
1743                   }
1744                   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];
1745                   for (int q = 0, idx = idx0; q < nr; q++) {
1746                     for (int d = 0; d < nc; d++, idx++) {
1747                       oor[idx] = rows[q] + moffset;
1748                       ooc[idx] = cols[d] + moffset;
1749                     }
1750                   }
1751                 }
1752               }
1753             }
1754           } // cell
1755         }   // grid
1756       }     // batch
1757       PetscCall(MatSetPreallocationCOO(ctx->J, ctx->SData_d.coo_size, oor, ooc));
1758       PetscCall(PetscFree2(oor, ooc));
1759     }
1760     PetscCall(PetscFree(pointMaps));
1761     PetscCall(PetscFree(elemMatrix));
1762     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
1763     PetscCall(PetscContainerSetPointer(container, (void *)maps));
1764     PetscCall(PetscContainerSetUserDestroy(container, LandauGPUMapsDestroy));
1765     PetscCall(PetscObjectCompose((PetscObject)ctx->J, "assembly_maps", (PetscObject)container));
1766     PetscCall(PetscContainerDestroy(&container));
1767     PetscCall(PetscLogEventEnd(ctx->events[2], 0, 0, 0, 0));
1768   } // end GPU assembly
1769   { /* create static point data, Jacobian called first, only one vertex copy */
1770     PetscReal     *invJe, *ww, *xx, *yy, *zz = NULL, *invJ_a;
1771     PetscInt       outer_ipidx, outer_ej, grid, nip_glb = 0;
1772     PetscFE        fe;
1773     const PetscInt Nb = Nq;
1774     PetscCall(PetscLogEventBegin(ctx->events[7], 0, 0, 0, 0));
1775     PetscCall(PetscInfo(ctx->plex[0], "Initialize static data\n"));
1776     for (PetscInt grid = 0; grid < ctx->num_grids; grid++) nip_glb += Nq * numCells[grid];
1777     /* collect f data, first time is for Jacobian, but make mass now */
1778     if (ctx->verbose > 0) {
1779       PetscInt ncells = 0, N;
1780       PetscCall(MatGetSize(ctx->J, &N, NULL));
1781       for (PetscInt grid = 0; grid < ctx->num_grids; grid++) ncells += numCells[grid];
1782       PetscCall(PetscPrintf(ctx->comm, "%d) %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,
1783                             ctx->num_species, Nb, dim, N));
1784     }
1785     PetscCall(PetscMalloc4(nip_glb, &ww, nip_glb, &xx, nip_glb, &yy, nip_glb * dim * dim, &invJ_a));
1786     if (dim == 3) PetscCall(PetscMalloc1(nip_glb, &zz));
1787     if (ctx->use_energy_tensor_trick) {
1788       PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &fe));
1789       PetscCall(PetscObjectSetName((PetscObject)fe, "energy"));
1790     }
1791     /* init each grids static data - no batch */
1792     for (grid = 0, outer_ipidx = 0, outer_ej = 0; grid < ctx->num_grids; grid++) { // OpenMP (once)
1793       Vec          v2_2 = NULL;                                                    // projected function: v^2/2 for non-relativistic, gamma... for relativistic
1794       PetscSection e_section;
1795       DM           dmEnergy;
1796       PetscInt     cStart, cEnd, ej;
1797 
1798       PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
1799       // prep energy trick, get v^2 / 2 vector
1800       if (ctx->use_energy_tensor_trick) {
1801         PetscErrorCode (*energyf[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *) = {ctx->use_relativistic_corrections ? gamma_m1_f : energy_f};
1802         Vec        glob_v2;
1803         PetscReal *c2_0[1], data[1] = {PetscSqr(C_0(ctx->v_0))};
1804 
1805         PetscCall(DMClone(ctx->plex[grid], &dmEnergy));
1806         PetscCall(PetscObjectSetName((PetscObject)dmEnergy, "energy"));
1807         PetscCall(DMSetField(dmEnergy, 0, NULL, (PetscObject)fe));
1808         PetscCall(DMCreateDS(dmEnergy));
1809         PetscCall(DMGetSection(dmEnergy, &e_section));
1810         PetscCall(DMGetGlobalVector(dmEnergy, &glob_v2));
1811         PetscCall(PetscObjectSetName((PetscObject)glob_v2, "trick"));
1812         c2_0[0] = &data[0];
1813         PetscCall(DMProjectFunction(dmEnergy, 0., energyf, (void **)c2_0, INSERT_ALL_VALUES, glob_v2));
1814         PetscCall(DMGetLocalVector(dmEnergy, &v2_2));
1815         PetscCall(VecZeroEntries(v2_2)); /* zero BCs so don't set */
1816         PetscCall(DMGlobalToLocalBegin(dmEnergy, glob_v2, INSERT_VALUES, v2_2));
1817         PetscCall(DMGlobalToLocalEnd(dmEnergy, glob_v2, INSERT_VALUES, v2_2));
1818         PetscCall(DMViewFromOptions(dmEnergy, NULL, "-energy_dm_view"));
1819         PetscCall(VecViewFromOptions(glob_v2, NULL, "-energy_vec_view"));
1820         PetscCall(DMRestoreGlobalVector(dmEnergy, &glob_v2));
1821       }
1822       /* append part of the IP data for each grid */
1823       for (ej = 0; ej < numCells[grid]; ++ej, ++outer_ej) {
1824         PetscScalar *coefs = NULL;
1825         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);
1826         invJe = invJ_a + outer_ej * Nq * dim * dim;
1827         PetscCall(DMPlexComputeCellGeometryFEM(ctx->plex[grid], ej + cStart, quad, vj, Jdummy, invJe, detJj));
1828         if (ctx->use_energy_tensor_trick) PetscCall(DMPlexVecGetClosure(dmEnergy, e_section, v2_2, ej + cStart, NULL, &coefs));
1829         /* create static point data */
1830         for (PetscInt qj = 0; qj < Nq; qj++, outer_ipidx++) {
1831           const PetscInt   gidx = outer_ipidx;
1832           const PetscReal *invJ = &invJe[qj * dim * dim];
1833           ww[gidx]              = detJj[qj] * quadWeights[qj];
1834           if (dim == 2) ww[gidx] *= vj[qj * dim + 0]; /* cylindrical coordinate, w/o 2pi */
1835           // get xx, yy, zz
1836           if (ctx->use_energy_tensor_trick) {
1837             double                 refSpaceDer[3], eGradPhi[3];
1838             const PetscReal *const DD = Tf[0]->T[1];
1839             const PetscReal       *Dq = &DD[qj * Nb * dim];
1840             for (int d = 0; d < 3; ++d) refSpaceDer[d] = eGradPhi[d] = 0.0;
1841             for (int b = 0; b < Nb; ++b) {
1842               for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[b * dim + d] * PetscRealPart(coefs[b]);
1843             }
1844             xx[gidx] = 1e10;
1845             if (ctx->use_relativistic_corrections) {
1846               double dg2_c2 = 0;
1847               //for (int d = 0; d < dim; ++d) refSpaceDer[d] *= c02;
1848               for (int d = 0; d < dim; ++d) dg2_c2 += PetscSqr(refSpaceDer[d]);
1849               dg2_c2 *= (double)c02;
1850               if (dg2_c2 >= .999) {
1851                 xx[gidx] = vj[qj * dim + 0]; /* coordinate */
1852                 yy[gidx] = vj[qj * dim + 1];
1853                 if (dim == 3) zz[gidx] = vj[qj * dim + 2];
1854                 PetscCall(PetscPrintf(ctx->comm, "Error: %12.5e %" PetscInt_FMT ".%" PetscInt_FMT ") dg2/c02 = %12.5e x= %12.5e %12.5e %12.5e\n", (double)PetscSqrtReal(xx[gidx] * xx[gidx] + yy[gidx] * yy[gidx] + zz[gidx] * zz[gidx]), ej, qj, dg2_c2, (double)xx[gidx], (double)yy[gidx], (double)zz[gidx]));
1855               } else {
1856                 PetscReal fact = c02 / PetscSqrtReal(1. - dg2_c2);
1857                 for (int d = 0; d < dim; ++d) refSpaceDer[d] *= fact;
1858                 // could test with other point u' that (grad - grad') * U (refSpaceDer, refSpaceDer') == 0
1859               }
1860             }
1861             if (xx[gidx] == 1e10) {
1862               for (int d = 0; d < dim; ++d) {
1863                 for (int e = 0; e < dim; ++e) eGradPhi[d] += invJ[e * dim + d] * refSpaceDer[e];
1864               }
1865               xx[gidx] = eGradPhi[0];
1866               yy[gidx] = eGradPhi[1];
1867               if (dim == 3) zz[gidx] = eGradPhi[2];
1868             }
1869           } else {
1870             xx[gidx] = vj[qj * dim + 0]; /* coordinate */
1871             yy[gidx] = vj[qj * dim + 1];
1872             if (dim == 3) zz[gidx] = vj[qj * dim + 2];
1873           }
1874         } /* q */
1875         if (ctx->use_energy_tensor_trick) PetscCall(DMPlexVecRestoreClosure(dmEnergy, e_section, v2_2, ej + cStart, NULL, &coefs));
1876       } /* ej */
1877       if (ctx->use_energy_tensor_trick) {
1878         PetscCall(DMRestoreLocalVector(dmEnergy, &v2_2));
1879         PetscCall(DMDestroy(&dmEnergy));
1880       }
1881     } /* grid */
1882     if (ctx->use_energy_tensor_trick) PetscCall(PetscFEDestroy(&fe));
1883     /* cache static data */
1884     if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
1885 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_KOKKOS_KERNELS)
1886       PetscReal invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
1887       for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
1888         for (PetscInt ii = ctx->species_offset[grid]; ii < ctx->species_offset[grid + 1]; ii++) {
1889           invMass[ii]  = ctx->m_0 / ctx->masses[ii];
1890           nu_alpha[ii] = PetscSqr(ctx->charges[ii] / ctx->m_0) * ctx->m_0 / ctx->masses[ii];
1891           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);
1892         }
1893       }
1894       if (ctx->deviceType == LANDAU_CUDA) {
1895   #if defined(PETSC_HAVE_CUDA)
1896         PetscCall(LandauCUDAStaticDataSet(ctx->plex[0], Nq, ctx->batch_sz, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset, nu_alpha, nu_beta, invMass, invJ_a, xx, yy, zz, ww, &ctx->SData_d));
1897   #else
1898         SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type cuda not built");
1899   #endif
1900       } else if (ctx->deviceType == LANDAU_KOKKOS) {
1901   #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1902         PetscCall(LandauKokkosStaticDataSet(ctx->plex[0], Nq, ctx->batch_sz, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset, nu_alpha, nu_beta, invMass, invJ_a, xx, yy, zz, ww, &ctx->SData_d));
1903   #else
1904         SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type kokkos not built");
1905   #endif
1906       }
1907 #endif
1908       /* free */
1909       PetscCall(PetscFree4(ww, xx, yy, invJ_a));
1910       if (dim == 3) PetscCall(PetscFree(zz));
1911     } else { /* CPU version, just copy in, only use part */
1912       ctx->SData_d.w    = (void *)ww;
1913       ctx->SData_d.x    = (void *)xx;
1914       ctx->SData_d.y    = (void *)yy;
1915       ctx->SData_d.z    = (void *)zz;
1916       ctx->SData_d.invJ = (void *)invJ_a;
1917     }
1918     PetscCall(PetscLogEventEnd(ctx->events[7], 0, 0, 0, 0));
1919   } // initialize
1920   PetscFunctionReturn(PETSC_SUCCESS);
1921 }
1922 
1923 /* < v, u > */
1924 static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
1925 {
1926   g0[0] = 1.;
1927 }
1928 
1929 /* < v, u > */
1930 static void g0_fake(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
1931 {
1932   static double ttt = 1e-12;
1933   g0[0]             = ttt++;
1934 }
1935 
1936 /* < v, u > */
1937 static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
1938 {
1939   g0[0] = 2. * PETSC_PI * x[0];
1940 }
1941 
1942 static PetscErrorCode MatrixNfDestroy(void *ptr)
1943 {
1944   PetscInt *nf = (PetscInt *)ptr;
1945   PetscFunctionBegin;
1946   PetscCall(PetscFree(nf));
1947   PetscFunctionReturn(PETSC_SUCCESS);
1948 }
1949 
1950 /*
1951  LandauCreateJacobianMatrix - creates ctx->J with without real data. Hard to keep sparse.
1952   - Like DMPlexLandauCreateMassMatrix. Should remove one and combine
1953   - has old support for field major ordering
1954  */
1955 static PetscErrorCode LandauCreateJacobianMatrix(MPI_Comm comm, Vec X, IS grid_batch_is_inv[LANDAU_MAX_GRIDS], LandauCtx *ctx)
1956 {
1957   PetscInt *idxs = NULL;
1958   Mat       subM[LANDAU_MAX_GRIDS];
1959 
1960   PetscFunctionBegin;
1961   if (!ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
1962     PetscFunctionReturn(PETSC_SUCCESS);
1963   }
1964   // get the RCM for this grid to separate out species into blocks -- create 'idxs' & 'ctx->batch_is' -- not used
1965   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) PetscCall(PetscMalloc1(ctx->mat_offset[ctx->num_grids] * ctx->batch_sz, &idxs));
1966   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
1967     const PetscInt *values, n = ctx->mat_offset[grid + 1] - ctx->mat_offset[grid];
1968     Mat             gMat;
1969     DM              massDM;
1970     PetscDS         prob;
1971     Vec             tvec;
1972     // get "mass" matrix for reordering
1973     PetscCall(DMClone(ctx->plex[grid], &massDM));
1974     PetscCall(DMCopyFields(ctx->plex[grid], massDM));
1975     PetscCall(DMCreateDS(massDM));
1976     PetscCall(DMGetDS(massDM, &prob));
1977     for (int ix = 0, ii = ctx->species_offset[grid]; ii < ctx->species_offset[grid + 1]; ii++, ix++) PetscCall(PetscDSSetJacobian(prob, ix, ix, g0_fake, NULL, NULL, NULL));
1978     PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only")); // this trick is need to both sparsify the matrix and avoid runtime error
1979     PetscCall(DMCreateMatrix(massDM, &gMat));
1980     PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only false"));
1981     PetscCall(MatSetOption(gMat, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
1982     PetscCall(MatSetOption(gMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
1983     PetscCall(DMCreateLocalVector(ctx->plex[grid], &tvec));
1984     PetscCall(DMPlexSNESComputeJacobianFEM(massDM, tvec, gMat, gMat, ctx));
1985     PetscCall(MatViewFromOptions(gMat, NULL, "-dm_landau_reorder_mat_view"));
1986     PetscCall(DMDestroy(&massDM));
1987     PetscCall(VecDestroy(&tvec));
1988     subM[grid] = gMat;
1989     if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
1990       MatOrderingType rtype = MATORDERINGRCM;
1991       IS              isrow, isicol;
1992       PetscCall(MatGetOrdering(gMat, rtype, &isrow, &isicol));
1993       PetscCall(ISInvertPermutation(isrow, PETSC_DECIDE, &grid_batch_is_inv[grid]));
1994       PetscCall(ISGetIndices(isrow, &values));
1995       for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // add batch size DMs for this species grid
1996 #if !defined(LANDAU_SPECIES_MAJOR)
1997         PetscInt N = ctx->mat_offset[ctx->num_grids], n0 = ctx->mat_offset[grid] + b_id * N;
1998         for (int ii = 0; ii < n; ++ii) idxs[n0 + ii] = values[ii] + n0;
1999 #else
2000         PetscInt n0 = ctx->mat_offset[grid] * ctx->batch_sz + b_id * n;
2001         for (int ii = 0; ii < n; ++ii) idxs[n0 + ii] = values[ii] + n0;
2002 #endif
2003       }
2004       PetscCall(ISRestoreIndices(isrow, &values));
2005       PetscCall(ISDestroy(&isrow));
2006       PetscCall(ISDestroy(&isicol));
2007     }
2008   }
2009   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) PetscCall(ISCreateGeneral(comm, ctx->mat_offset[ctx->num_grids] * ctx->batch_sz, idxs, PETSC_OWN_POINTER, &ctx->batch_is));
2010   // get a block matrix
2011   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2012     Mat      B = subM[grid];
2013     PetscInt nloc, nzl, *colbuf, row, COL_BF_SIZE = 1024;
2014     PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
2015     PetscCall(MatGetSize(B, &nloc, NULL));
2016     for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
2017       const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
2018       const PetscInt    *cols;
2019       const PetscScalar *vals;
2020       for (int i = 0; i < nloc; i++) {
2021         PetscCall(MatGetRow(B, i, &nzl, NULL, NULL));
2022         if (nzl > COL_BF_SIZE) {
2023           PetscCall(PetscFree(colbuf));
2024           PetscCall(PetscInfo(ctx->plex[grid], "Realloc buffer %" PetscInt_FMT " to %" PetscInt_FMT " (row size %" PetscInt_FMT ") \n", COL_BF_SIZE, 2 * COL_BF_SIZE, nzl));
2025           COL_BF_SIZE = nzl;
2026           PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
2027         }
2028         PetscCall(MatGetRow(B, i, &nzl, &cols, &vals));
2029         for (int j = 0; j < nzl; j++) colbuf[j] = cols[j] + moffset;
2030         row = i + moffset;
2031         PetscCall(MatSetValues(ctx->J, 1, &row, nzl, colbuf, vals, INSERT_VALUES));
2032         PetscCall(MatRestoreRow(B, i, &nzl, &cols, &vals));
2033       }
2034     }
2035     PetscCall(PetscFree(colbuf));
2036   }
2037   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(MatDestroy(&subM[grid]));
2038   PetscCall(MatAssemblyBegin(ctx->J, MAT_FINAL_ASSEMBLY));
2039   PetscCall(MatAssemblyEnd(ctx->J, MAT_FINAL_ASSEMBLY));
2040 
2041   // debug
2042   PetscCall(MatViewFromOptions(ctx->J, NULL, "-dm_landau_mat_view"));
2043   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
2044     Mat mat_block_order;
2045     PetscCall(MatCreateSubMatrix(ctx->J, ctx->batch_is, ctx->batch_is, MAT_INITIAL_MATRIX, &mat_block_order)); // use MatPermute
2046     PetscCall(MatViewFromOptions(mat_block_order, NULL, "-dm_landau_mat_view"));
2047     PetscCall(MatDestroy(&mat_block_order));
2048     PetscCall(VecScatterCreate(X, ctx->batch_is, X, NULL, &ctx->plex_batch));
2049     PetscCall(VecDuplicate(X, &ctx->work_vec));
2050   }
2051 
2052   PetscFunctionReturn(PETSC_SUCCESS);
2053 }
2054 
2055 PetscErrorCode DMPlexLandauCreateMassMatrix(DM pack, Mat *Amat);
2056 /*@C
2057  DMPlexLandauCreateVelocitySpace - Create a DMPlex velocity space mesh
2058 
2059  Collective
2060 
2061  Input Parameters:
2062  +   comm  - The MPI communicator
2063  .   dim - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
2064  -   prefix - prefix for options (not tested)
2065 
2066  Output Parameter:
2067  .   pack  - The DM object representing the mesh
2068  +   X - A vector (user destroys)
2069  -   J - Optional matrix (object destroys)
2070 
2071  Level: beginner
2072 
2073  .keywords: mesh
2074  .seealso: `DMPlexCreate()`, `DMPlexLandauDestroyVelocitySpace()`
2075  @*/
2076 PetscErrorCode DMPlexLandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *pack)
2077 {
2078   LandauCtx *ctx;
2079   Vec        Xsub[LANDAU_MAX_GRIDS];
2080   IS         grid_batch_is_inv[LANDAU_MAX_GRIDS];
2081 
2082   PetscFunctionBegin;
2083   PetscCheck(dim == 2 || dim == 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Only 2D and 3D supported");
2084   PetscCheck(LANDAU_DIM == dim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " != LANDAU_DIM %d", dim, LANDAU_DIM);
2085   PetscCall(PetscNew(&ctx));
2086   ctx->comm = comm; /* used for diagnostics and global errors */
2087   /* process options */
2088   PetscCall(ProcessOptions(ctx, prefix));
2089   if (dim == 2) ctx->use_relativistic_corrections = PETSC_FALSE;
2090   /* Create Mesh */
2091   PetscCall(DMCompositeCreate(PETSC_COMM_SELF, pack));
2092   PetscCall(PetscLogEventBegin(ctx->events[13], 0, 0, 0, 0));
2093   PetscCall(PetscLogEventBegin(ctx->events[15], 0, 0, 0, 0));
2094   PetscCall(LandauDMCreateVMeshes(PETSC_COMM_SELF, dim, prefix, ctx, *pack)); // creates grids (Forest of AMR)
2095   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2096     /* create FEM */
2097     PetscCall(SetupDS(ctx->plex[grid], dim, grid, ctx));
2098     /* set initial state */
2099     PetscCall(DMCreateGlobalVector(ctx->plex[grid], &Xsub[grid]));
2100     PetscCall(PetscObjectSetName((PetscObject)Xsub[grid], "u_orig"));
2101     /* initial static refinement, no solve */
2102     PetscCall(LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, 0, 1, ctx));
2103     /* forest refinement - forest goes in (if forest), plex comes out */
2104     if (ctx->use_p4est) {
2105       DM plex;
2106       PetscCall(adapt(grid, ctx, &Xsub[grid]));                                      // forest goes in, plex comes out
2107       PetscCall(DMViewFromOptions(ctx->plex[grid], NULL, "-dm_landau_amr_dm_view")); // need to differentiate - todo
2108       PetscCall(VecViewFromOptions(Xsub[grid], NULL, "-dm_landau_amr_vec_view"));
2109       // convert to plex, all done with this level
2110       PetscCall(DMConvert(ctx->plex[grid], DMPLEX, &plex));
2111       PetscCall(DMDestroy(&ctx->plex[grid]));
2112       ctx->plex[grid] = plex;
2113     }
2114 #if !defined(LANDAU_SPECIES_MAJOR)
2115     PetscCall(DMCompositeAddDM(*pack, ctx->plex[grid]));
2116 #else
2117     for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // add batch size DMs for this species grid
2118       PetscCall(DMCompositeAddDM(*pack, ctx->plex[grid]));
2119     }
2120 #endif
2121     PetscCall(DMSetApplicationContext(ctx->plex[grid], ctx));
2122   }
2123 #if !defined(LANDAU_SPECIES_MAJOR)
2124   // stack the batched DMs, could do it all here!!! b_id=0
2125   for (PetscInt b_id = 1; b_id < ctx->batch_sz; b_id++) {
2126     for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMCompositeAddDM(*pack, ctx->plex[grid]));
2127   }
2128 #endif
2129   // create ctx->mat_offset
2130   ctx->mat_offset[0] = 0;
2131   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2132     PetscInt n;
2133     PetscCall(VecGetLocalSize(Xsub[grid], &n));
2134     ctx->mat_offset[grid + 1] = ctx->mat_offset[grid] + n;
2135   }
2136   // creat DM & Jac
2137   PetscCall(DMSetApplicationContext(*pack, ctx));
2138   PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only"));
2139   PetscCall(DMCreateMatrix(*pack, &ctx->J));
2140   PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only false"));
2141   PetscCall(MatSetOption(ctx->J, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
2142   PetscCall(MatSetOption(ctx->J, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
2143   PetscCall(PetscObjectSetName((PetscObject)ctx->J, "Jac"));
2144   // construct initial conditions in X
2145   PetscCall(DMCreateGlobalVector(*pack, X));
2146   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2147     PetscInt n;
2148     PetscCall(VecGetLocalSize(Xsub[grid], &n));
2149     for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
2150       PetscScalar const *values;
2151       const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
2152       PetscCall(LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, b_id, ctx->batch_sz, ctx));
2153       PetscCall(VecGetArrayRead(Xsub[grid], &values)); // Drop whole grid in Plex ordering
2154       for (int i = 0, idx = moffset; i < n; i++, idx++) PetscCall(VecSetValue(*X, idx, values[i], INSERT_VALUES));
2155       PetscCall(VecRestoreArrayRead(Xsub[grid], &values));
2156     }
2157   }
2158   // cleanup
2159   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(VecDestroy(&Xsub[grid]));
2160   /* check for correct matrix type */
2161   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
2162     PetscBool flg;
2163     if (ctx->deviceType == LANDAU_CUDA) {
2164       PetscCall(PetscObjectTypeCompareAny((PetscObject)ctx->J, &flg, MATSEQAIJCUSPARSE, MATMPIAIJCUSPARSE, MATAIJCUSPARSE, ""));
2165       PetscCheck(flg, ctx->comm, PETSC_ERR_ARG_WRONG, "must use '-dm_mat_type aijcusparse -dm_vec_type cuda' for GPU assembly and Cuda or use '-dm_landau_device_type cpu'");
2166     } else if (ctx->deviceType == LANDAU_KOKKOS) {
2167       PetscCall(PetscObjectTypeCompareAny((PetscObject)ctx->J, &flg, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, MATAIJKOKKOS, ""));
2168 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
2169       PetscCheck(flg, ctx->comm, PETSC_ERR_ARG_WRONG, "must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for GPU assembly and Kokkos or use '-dm_landau_device_type cpu'");
2170 #else
2171       PetscCheck(flg, ctx->comm, PETSC_ERR_ARG_WRONG, "must configure with '--download-kokkos-kernels' for GPU assembly and Kokkos or use '-dm_landau_device_type cpu'");
2172 #endif
2173     }
2174   }
2175   PetscCall(PetscLogEventEnd(ctx->events[15], 0, 0, 0, 0));
2176 
2177   // create field major ordering
2178   ctx->work_vec   = NULL;
2179   ctx->plex_batch = NULL;
2180   ctx->batch_is   = NULL;
2181   for (int i = 0; i < LANDAU_MAX_GRIDS; i++) grid_batch_is_inv[i] = NULL;
2182   PetscCall(PetscLogEventBegin(ctx->events[12], 0, 0, 0, 0));
2183   PetscCall(LandauCreateJacobianMatrix(comm, *X, grid_batch_is_inv, ctx));
2184   PetscCall(PetscLogEventEnd(ctx->events[12], 0, 0, 0, 0));
2185 
2186   // create AMR GPU assembly maps and static GPU data
2187   PetscCall(CreateStaticGPUData(dim, grid_batch_is_inv, ctx));
2188 
2189   PetscCall(PetscLogEventEnd(ctx->events[13], 0, 0, 0, 0));
2190 
2191   // create mass matrix
2192   PetscCall(DMPlexLandauCreateMassMatrix(*pack, NULL));
2193 
2194   if (J) *J = ctx->J;
2195 
2196   if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
2197     PetscContainer container;
2198     // cache ctx for KSP with batch/field major Jacobian ordering -ksp_type gmres/etc -dm_landau_jacobian_field_major_order
2199     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
2200     PetscCall(PetscContainerSetPointer(container, (void *)ctx));
2201     PetscCall(PetscObjectCompose((PetscObject)ctx->J, "LandauCtx", (PetscObject)container));
2202     PetscCall(PetscContainerDestroy(&container));
2203     // batch solvers need to map -- can batch solvers work
2204     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
2205     PetscCall(PetscContainerSetPointer(container, (void *)ctx->plex_batch));
2206     PetscCall(PetscObjectCompose((PetscObject)ctx->J, "plex_batch_is", (PetscObject)container));
2207     PetscCall(PetscContainerDestroy(&container));
2208   }
2209   // for batch solvers
2210   {
2211     PetscContainer container;
2212     PetscInt      *pNf;
2213     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
2214     PetscCall(PetscMalloc1(sizeof(*pNf), &pNf));
2215     *pNf = ctx->batch_sz;
2216     PetscCall(PetscContainerSetPointer(container, (void *)pNf));
2217     PetscCall(PetscContainerSetUserDestroy(container, MatrixNfDestroy));
2218     PetscCall(PetscObjectCompose((PetscObject)ctx->J, "batch size", (PetscObject)container));
2219     PetscCall(PetscContainerDestroy(&container));
2220   }
2221 
2222   PetscFunctionReturn(PETSC_SUCCESS);
2223 }
2224 
2225 /*@
2226  DMPlexLandauAccess - Access to the distribution function with user callback
2227 
2228  Collective
2229 
2230  Input Parameters:
2231  .   pack - the DMComposite
2232  +   func - call back function
2233  .   user_ctx - user context
2234 
2235  Input/Output Parameters:
2236  +   X - Vector to data to
2237 
2238  Level: advanced
2239 
2240  .keywords: mesh
2241  .seealso: `DMPlexLandauCreateVelocitySpace()`
2242  @*/
2243 PetscErrorCode DMPlexLandauAccess(DM pack, Vec X, PetscErrorCode (*func)(DM, Vec, PetscInt, PetscInt, PetscInt, void *), void *user_ctx)
2244 {
2245   LandauCtx *ctx;
2246   PetscFunctionBegin;
2247   PetscCall(DMGetApplicationContext(pack, &ctx)); // uses ctx->num_grids; ctx->plex[grid]; ctx->batch_sz; ctx->mat_offset
2248   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2249     PetscInt dim, n;
2250     PetscCall(DMGetDimension(pack, &dim));
2251     for (PetscInt sp = ctx->species_offset[grid], i0 = 0; sp < ctx->species_offset[grid + 1]; sp++, i0++) {
2252       Vec      vec;
2253       PetscInt vf[1] = {i0};
2254       IS       vis;
2255       DM       vdm;
2256       PetscCall(DMCreateSubDM(ctx->plex[grid], 1, vf, &vis, &vdm));
2257       PetscCall(DMSetApplicationContext(vdm, ctx)); // the user might want this
2258       PetscCall(DMCreateGlobalVector(vdm, &vec));
2259       PetscCall(VecGetSize(vec, &n));
2260       for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
2261         const PetscInt moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
2262         PetscCall(VecZeroEntries(vec));
2263         /* Add your data with 'dm' for species 'sp' to 'vec' */
2264         PetscCall(func(vdm, vec, i0, grid, b_id, user_ctx));
2265         /* add to global */
2266         PetscScalar const *values;
2267         const PetscInt    *offsets;
2268         PetscCall(VecGetArrayRead(vec, &values));
2269         PetscCall(ISGetIndices(vis, &offsets));
2270         for (int i = 0; i < n; i++) PetscCall(VecSetValue(X, moffset + offsets[i], values[i], ADD_VALUES));
2271         PetscCall(VecRestoreArrayRead(vec, &values));
2272         PetscCall(ISRestoreIndices(vis, &offsets));
2273       } // batch
2274       PetscCall(VecDestroy(&vec));
2275       PetscCall(ISDestroy(&vis));
2276       PetscCall(DMDestroy(&vdm));
2277     }
2278   } // grid
2279   PetscFunctionReturn(PETSC_SUCCESS);
2280 }
2281 
2282 /*@
2283  DMPlexLandauDestroyVelocitySpace - Destroy a DMPlex velocity space mesh
2284 
2285  Collective
2286 
2287  Input/Output Parameters:
2288  .   dm - the dm to destroy
2289 
2290  Level: beginner
2291 
2292  .keywords: mesh
2293  .seealso: `DMPlexLandauCreateVelocitySpace()`
2294  @*/
2295 PetscErrorCode DMPlexLandauDestroyVelocitySpace(DM *dm)
2296 {
2297   LandauCtx *ctx;
2298   PetscFunctionBegin;
2299   PetscCall(DMGetApplicationContext(*dm, &ctx));
2300   PetscCall(MatDestroy(&ctx->M));
2301   PetscCall(MatDestroy(&ctx->J));
2302   for (PetscInt ii = 0; ii < ctx->num_species; ii++) PetscCall(PetscFEDestroy(&ctx->fe[ii]));
2303   PetscCall(ISDestroy(&ctx->batch_is));
2304   PetscCall(VecDestroy(&ctx->work_vec));
2305   PetscCall(VecScatterDestroy(&ctx->plex_batch));
2306   if (ctx->deviceType == LANDAU_CUDA) {
2307 #if defined(PETSC_HAVE_CUDA)
2308     PetscCall(LandauCUDAStaticDataClear(&ctx->SData_d));
2309 #else
2310     SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type %s not built", "cuda");
2311 #endif
2312   } else if (ctx->deviceType == LANDAU_KOKKOS) {
2313 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
2314     PetscCall(LandauKokkosStaticDataClear(&ctx->SData_d));
2315 #else
2316     SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type %s not built", "kokkos");
2317 #endif
2318   } else {
2319     if (ctx->SData_d.x) { /* in a CPU run */
2320       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;
2321       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;
2322       PetscCall(PetscFree4(ww, xx, yy, invJ));
2323       if (zz) PetscCall(PetscFree(zz));
2324       if (coo_elem_offsets) {
2325         PetscCall(PetscFree3(coo_elem_offsets, coo_elem_fullNb, coo_elem_point_offsets)); // could be NULL
2326       }
2327     }
2328   }
2329 
2330   if (ctx->times[LANDAU_MATRIX_TOTAL] > 0) { // OMP timings
2331     PetscCall(PetscPrintf(ctx->comm, "TSStep               N  1.0 %10.3e\n", ctx->times[LANDAU_EX2_TSSOLVE]));
2332     PetscCall(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));
2333     PetscCall(PetscPrintf(ctx->comm, "3:          Landau:  %10.3e\n", ctx->times[LANDAU_MATRIX_TOTAL]));
2334     PetscCall(PetscPrintf(ctx->comm, "Landau Jacobian       %" PetscInt_FMT " 1.0 %10.3e\n", (PetscInt)ctx->times[LANDAU_JACOBIAN_COUNT], ctx->times[LANDAU_JACOBIAN]));
2335     PetscCall(PetscPrintf(ctx->comm, "Landau Operator       N 1.0  %10.3e\n", ctx->times[LANDAU_OPERATOR]));
2336     PetscCall(PetscPrintf(ctx->comm, "Landau Mass           N 1.0  %10.3e\n", ctx->times[LANDAU_MASS]));
2337     PetscCall(PetscPrintf(ctx->comm, " Jac-f-df (GPU)       N 1.0  %10.3e\n", ctx->times[LANDAU_F_DF]));
2338     PetscCall(PetscPrintf(ctx->comm, " Kernel (GPU)         N 1.0  %10.3e\n", ctx->times[LANDAU_KERNEL]));
2339     PetscCall(PetscPrintf(ctx->comm, "MatLUFactorNum        X 1.0 %10.3e\n", ctx->times[KSP_FACTOR]));
2340     PetscCall(PetscPrintf(ctx->comm, "MatSolve              X 1.0 %10.3e\n", ctx->times[KSP_SOLVE]));
2341   }
2342   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMDestroy(&ctx->plex[grid]));
2343   PetscCall(PetscFree(ctx));
2344   PetscCall(DMDestroy(dm));
2345   PetscFunctionReturn(PETSC_SUCCESS);
2346 }
2347 
2348 /* < v, ru > */
2349 static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
2350 {
2351   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
2352   f0[0]       = u[ii];
2353 }
2354 
2355 /* < v, ru > */
2356 static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
2357 {
2358   PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
2359   f0[0] = x[jj] * u[ii]; /* x momentum */
2360 }
2361 
2362 static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
2363 {
2364   PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
2365   double   tmp1 = 0.;
2366   for (i = 0; i < dim; ++i) tmp1 += x[i] * x[i];
2367   f0[0] = tmp1 * u[ii];
2368 }
2369 
2370 static PetscErrorCode gamma_n_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *actx)
2371 {
2372   const PetscReal *c2_0_arr = ((PetscReal *)actx);
2373   const PetscReal  c02      = c2_0_arr[0];
2374 
2375   PetscFunctionBegin;
2376   for (int s = 0; s < Nf; s++) {
2377     PetscReal tmp1 = 0.;
2378     for (int i = 0; i < dim; ++i) tmp1 += x[i] * x[i];
2379 #if defined(PETSC_USE_DEBUG)
2380     u[s] = PetscSqrtReal(1. + tmp1 / c02); //  u[0] = PetscSqrtReal(1. + xx);
2381 #else
2382     {
2383       PetscReal xx = tmp1 / c02;
2384       u[s] = xx / (PetscSqrtReal(1. + xx) + 1.); // better conditioned = xx/(PetscSqrtReal(1. + xx) + 1.)
2385     }
2386 #endif
2387   }
2388   PetscFunctionReturn(PETSC_SUCCESS);
2389 }
2390 
2391 /* < v, ru > */
2392 static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
2393 {
2394   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
2395   f0[0]       = 2. * PETSC_PI * x[0] * u[ii];
2396 }
2397 
2398 /* < v, ru > */
2399 static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
2400 {
2401   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
2402   f0[0]       = 2. * PETSC_PI * x[0] * x[1] * u[ii];
2403 }
2404 
2405 static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
2406 {
2407   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
2408   f0[0]       = 2. * PETSC_PI * x[0] * (x[0] * x[0] + x[1] * x[1]) * u[ii];
2409 }
2410 
2411 /*@
2412  DMPlexLandauPrintNorms - collects moments and prints them
2413 
2414  Collective
2415 
2416  Input Parameters:
2417  +   X  - the state
2418  -   stepi - current step to print
2419 
2420  Level: beginner
2421 
2422  .keywords: mesh
2423  .seealso: `DMPlexLandauCreateVelocitySpace()`
2424  @*/
2425 PetscErrorCode DMPlexLandauPrintNorms(Vec X, PetscInt stepi)
2426 {
2427   LandauCtx  *ctx;
2428   PetscDS     prob;
2429   DM          pack;
2430   PetscInt    cStart, cEnd, dim, ii, i0, nDMs;
2431   PetscScalar xmomentumtot = 0, ymomentumtot = 0, zmomentumtot = 0, energytot = 0, densitytot = 0, tt[LANDAU_MAX_SPECIES];
2432   PetscScalar xmomentum[LANDAU_MAX_SPECIES], ymomentum[LANDAU_MAX_SPECIES], zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
2433   Vec        *globXArray;
2434 
2435   PetscFunctionBegin;
2436   PetscCall(VecGetDM(X, &pack));
2437   PetscCheck(pack, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Vector has no DM");
2438   PetscCall(DMGetDimension(pack, &dim));
2439   PetscCheck(dim == 2 || dim == 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " not in [2,3]", dim);
2440   PetscCall(DMGetApplicationContext(pack, &ctx));
2441   PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2442   /* print momentum and energy */
2443   PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
2444   PetscCheck(nDMs == ctx->num_grids * ctx->batch_sz, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "#DM wrong %" PetscInt_FMT " %" PetscInt_FMT, nDMs, ctx->num_grids * ctx->batch_sz);
2445   PetscCall(PetscMalloc(sizeof(*globXArray) * nDMs, &globXArray));
2446   PetscCall(DMCompositeGetAccessArray(pack, X, nDMs, NULL, globXArray));
2447   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2448     Vec Xloc = globXArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)];
2449     PetscCall(DMGetDS(ctx->plex[grid], &prob));
2450     for (ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
2451       PetscScalar user[2] = {(PetscScalar)i0, (PetscScalar)ctx->charges[ii]};
2452       PetscCall(PetscDSSetConstants(prob, 2, user));
2453       if (dim == 2) { /* 2/3X + 3V (cylindrical coordinates) */
2454         PetscCall(PetscDSSetObjective(prob, 0, &f0_s_rden));
2455         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2456         density[ii] = tt[0] * ctx->n_0 * ctx->charges[ii];
2457         PetscCall(PetscDSSetObjective(prob, 0, &f0_s_rmom));
2458         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2459         zmomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
2460         PetscCall(PetscDSSetObjective(prob, 0, &f0_s_rv2));
2461         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2462         energy[ii] = tt[0] * 0.5 * ctx->n_0 * ctx->v_0 * ctx->v_0 * ctx->masses[ii];
2463         zmomentumtot += zmomentum[ii];
2464         energytot += energy[ii];
2465         densitytot += density[ii];
2466         PetscCall(PetscPrintf(ctx->comm, "%3" PetscInt_FMT ") species-%" PetscInt_FMT ": charge density= %20.13e z-momentum= %20.13e energy= %20.13e", stepi, ii, (double)PetscRealPart(density[ii]), (double)PetscRealPart(zmomentum[ii]), (double)PetscRealPart(energy[ii])));
2467       } else { /* 2/3Xloc + 3V */
2468         PetscCall(PetscDSSetObjective(prob, 0, &f0_s_den));
2469         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2470         density[ii] = tt[0] * ctx->n_0 * ctx->charges[ii];
2471         PetscCall(PetscDSSetObjective(prob, 0, &f0_s_mom));
2472         user[1] = 0;
2473         PetscCall(PetscDSSetConstants(prob, 2, user));
2474         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2475         xmomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
2476         user[1]       = 1;
2477         PetscCall(PetscDSSetConstants(prob, 2, user));
2478         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2479         ymomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
2480         user[1]       = 2;
2481         PetscCall(PetscDSSetConstants(prob, 2, user));
2482         PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2483         zmomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
2484         if (ctx->use_relativistic_corrections) {
2485           /* gamma * M * f */
2486           if (ii == 0 && grid == 0) { // do all at once
2487             Vec Mf, globGamma, *globMfArray, *globGammaArray;
2488             PetscErrorCode (*gammaf[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *) = {gamma_n_f};
2489             PetscReal *c2_0[1], data[1];
2490 
2491             PetscCall(VecDuplicate(X, &globGamma));
2492             PetscCall(VecDuplicate(X, &Mf));
2493             PetscCall(PetscMalloc(sizeof(*globMfArray) * nDMs, &globMfArray));
2494             PetscCall(PetscMalloc(sizeof(*globMfArray) * nDMs, &globGammaArray));
2495             /* M * f */
2496             PetscCall(MatMult(ctx->M, X, Mf));
2497             /* gamma */
2498             PetscCall(DMCompositeGetAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
2499             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
2500               Vec v1  = globGammaArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)];
2501               data[0] = PetscSqr(C_0(ctx->v_0));
2502               c2_0[0] = &data[0];
2503               PetscCall(DMProjectFunction(ctx->plex[grid], 0., gammaf, (void **)c2_0, INSERT_ALL_VALUES, v1));
2504             }
2505             PetscCall(DMCompositeRestoreAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
2506             /* gamma * Mf */
2507             PetscCall(DMCompositeGetAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
2508             PetscCall(DMCompositeGetAccessArray(pack, Mf, nDMs, NULL, globMfArray));
2509             for (PetscInt grid = 0; grid < ctx->num_grids; grid++) { // yes a grid loop in a grid loop to print nice
2510               PetscInt Nf    = ctx->species_offset[grid + 1] - ctx->species_offset[grid], N, bs;
2511               Vec      Mfsub = globMfArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)], Gsub = globGammaArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)], v1, v2;
2512               // get each component
2513               PetscCall(VecGetSize(Mfsub, &N));
2514               PetscCall(VecCreate(ctx->comm, &v1));
2515               PetscCall(VecSetSizes(v1, PETSC_DECIDE, N / Nf));
2516               PetscCall(VecCreate(ctx->comm, &v2));
2517               PetscCall(VecSetSizes(v2, PETSC_DECIDE, N / Nf));
2518               PetscCall(VecSetFromOptions(v1)); // ???
2519               PetscCall(VecSetFromOptions(v2));
2520               // get each component
2521               PetscCall(VecGetBlockSize(Gsub, &bs));
2522               PetscCheck(bs == Nf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "bs %" PetscInt_FMT " != num_species %" PetscInt_FMT " in Gsub", bs, Nf);
2523               PetscCall(VecGetBlockSize(Mfsub, &bs));
2524               PetscCheck(bs == Nf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "bs %" PetscInt_FMT " != num_species %" PetscInt_FMT, bs, Nf);
2525               for (int i = 0, ix = ctx->species_offset[grid]; i < Nf; i++, ix++) {
2526                 PetscScalar val;
2527                 PetscCall(VecStrideGather(Gsub, i, v1, INSERT_VALUES)); // this is not right -- TODO
2528                 PetscCall(VecStrideGather(Mfsub, i, v2, INSERT_VALUES));
2529                 PetscCall(VecDot(v1, v2, &val));
2530                 energy[ix] = PetscRealPart(val) * ctx->n_0 * ctx->v_0 * ctx->v_0 * ctx->masses[ix];
2531               }
2532               PetscCall(VecDestroy(&v1));
2533               PetscCall(VecDestroy(&v2));
2534             } /* grids */
2535             PetscCall(DMCompositeRestoreAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
2536             PetscCall(DMCompositeRestoreAccessArray(pack, Mf, nDMs, NULL, globMfArray));
2537             PetscCall(PetscFree(globGammaArray));
2538             PetscCall(PetscFree(globMfArray));
2539             PetscCall(VecDestroy(&globGamma));
2540             PetscCall(VecDestroy(&Mf));
2541           }
2542         } else {
2543           PetscCall(PetscDSSetObjective(prob, 0, &f0_s_v2));
2544           PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
2545           energy[ii] = 0.5 * tt[0] * ctx->n_0 * ctx->v_0 * ctx->v_0 * ctx->masses[ii];
2546         }
2547         PetscCall(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, (double)PetscRealPart(density[ii]), (double)PetscRealPart(xmomentum[ii]), (double)PetscRealPart(ymomentum[ii]), (double)PetscRealPart(zmomentum[ii]), (double)PetscRealPart(energy[ii])));
2548         xmomentumtot += xmomentum[ii];
2549         ymomentumtot += ymomentum[ii];
2550         zmomentumtot += zmomentum[ii];
2551         energytot += energy[ii];
2552         densitytot += density[ii];
2553       }
2554       if (ctx->num_species > 1) PetscCall(PetscPrintf(ctx->comm, "\n"));
2555     }
2556   }
2557   PetscCall(DMCompositeRestoreAccessArray(pack, X, nDMs, NULL, globXArray));
2558   PetscCall(PetscFree(globXArray));
2559   /* totals */
2560   PetscCall(DMPlexGetHeightStratum(ctx->plex[0], 0, &cStart, &cEnd));
2561   if (ctx->num_species > 1) {
2562     if (dim == 2) {
2563       PetscCall(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),
2564                             (double)(ctx->masses[1] / ctx->masses[0]), cEnd - cStart));
2565     } else {
2566       PetscCall(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),
2567                             (double)(ctx->masses[1] / ctx->masses[0]), cEnd - cStart));
2568     }
2569   } else PetscCall(PetscPrintf(ctx->comm, " -- %" PetscInt_FMT " cells", cEnd - cStart));
2570   PetscCall(PetscPrintf(ctx->comm, "\n"));
2571   PetscFunctionReturn(PETSC_SUCCESS);
2572 }
2573 
2574 /*@
2575  DMPlexLandauCreateMassMatrix - Create mass matrix for Landau in Plex space (not field major order of Jacobian)
2576   - puts mass matrix into ctx->M
2577 
2578  Collective
2579 
2580  Input/Output Parameters:
2581 . pack     - the DM object. Puts matrix in Landau context M field
2582 
2583  Output Parameters:
2584 . Amat - The mass matrix (optional), mass matrix is added to the DM context
2585 
2586  Level: beginner
2587 
2588  .keywords: mesh
2589  .seealso: `DMPlexLandauCreateVelocitySpace()`
2590  @*/
2591 PetscErrorCode DMPlexLandauCreateMassMatrix(DM pack, Mat *Amat)
2592 {
2593   DM         mass_pack, massDM[LANDAU_MAX_GRIDS];
2594   PetscDS    prob;
2595   PetscInt   ii, dim, N1 = 1, N2;
2596   LandauCtx *ctx;
2597   Mat        packM, subM[LANDAU_MAX_GRIDS];
2598 
2599   PetscFunctionBegin;
2600   PetscValidHeaderSpecific(pack, DM_CLASSID, 1);
2601   if (Amat) PetscValidPointer(Amat, 2);
2602   PetscCall(DMGetApplicationContext(pack, &ctx));
2603   PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2604   PetscCall(PetscLogEventBegin(ctx->events[14], 0, 0, 0, 0));
2605   PetscCall(DMGetDimension(pack, &dim));
2606   PetscCall(DMCompositeCreate(PetscObjectComm((PetscObject)pack), &mass_pack));
2607   /* create pack mass matrix */
2608   for (PetscInt grid = 0, ix = 0; grid < ctx->num_grids; grid++) {
2609     PetscCall(DMClone(ctx->plex[grid], &massDM[grid]));
2610     PetscCall(DMCopyFields(ctx->plex[grid], massDM[grid]));
2611     PetscCall(DMCreateDS(massDM[grid]));
2612     PetscCall(DMGetDS(massDM[grid], &prob));
2613     for (ix = 0, ii = ctx->species_offset[grid]; ii < ctx->species_offset[grid + 1]; ii++, ix++) {
2614       if (dim == 3) PetscCall(PetscDSSetJacobian(prob, ix, ix, g0_1, NULL, NULL, NULL));
2615       else PetscCall(PetscDSSetJacobian(prob, ix, ix, g0_r, NULL, NULL, NULL));
2616     }
2617 #if !defined(LANDAU_SPECIES_MAJOR)
2618     PetscCall(DMCompositeAddDM(mass_pack, massDM[grid]));
2619 #else
2620     for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // add batch size DMs for this species grid
2621       PetscCall(DMCompositeAddDM(mass_pack, massDM[grid]));
2622     }
2623 #endif
2624     PetscCall(DMCreateMatrix(massDM[grid], &subM[grid]));
2625   }
2626 #if !defined(LANDAU_SPECIES_MAJOR)
2627   // stack the batched DMs
2628   for (PetscInt b_id = 1; b_id < ctx->batch_sz; b_id++) {
2629     for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMCompositeAddDM(mass_pack, massDM[grid]));
2630   }
2631 #endif
2632   PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only"));
2633   PetscCall(DMCreateMatrix(mass_pack, &packM));
2634   PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only false"));
2635   PetscCall(MatSetOption(packM, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
2636   PetscCall(MatSetOption(packM, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
2637   PetscCall(DMDestroy(&mass_pack));
2638   /* make mass matrix for each block */
2639   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2640     Vec locX;
2641     DM  plex = massDM[grid];
2642     PetscCall(DMGetLocalVector(plex, &locX));
2643     /* Mass matrix is independent of the input, so no need to fill locX */
2644     PetscCall(DMPlexSNESComputeJacobianFEM(plex, locX, subM[grid], subM[grid], ctx));
2645     PetscCall(DMRestoreLocalVector(plex, &locX));
2646     PetscCall(DMDestroy(&massDM[grid]));
2647   }
2648   PetscCall(MatGetSize(ctx->J, &N1, NULL));
2649   PetscCall(MatGetSize(packM, &N2, NULL));
2650   PetscCheck(N1 == N2, PetscObjectComm((PetscObject)pack), PETSC_ERR_PLIB, "Incorrect matrix sizes: |Jacobian| = %" PetscInt_FMT ", |Mass|=%" PetscInt_FMT, N1, N2);
2651   /* assemble block diagonals */
2652   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
2653     Mat      B = subM[grid];
2654     PetscInt nloc, nzl, *colbuf, COL_BF_SIZE = 1024, row;
2655     PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
2656     PetscCall(MatGetSize(B, &nloc, NULL));
2657     for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
2658       const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
2659       const PetscInt    *cols;
2660       const PetscScalar *vals;
2661       for (int i = 0; i < nloc; i++) {
2662         PetscCall(MatGetRow(B, i, &nzl, NULL, NULL));
2663         if (nzl > COL_BF_SIZE) {
2664           PetscCall(PetscFree(colbuf));
2665           PetscCall(PetscInfo(pack, "Realloc buffer %" PetscInt_FMT " to %" PetscInt_FMT " (row size %" PetscInt_FMT ") \n", COL_BF_SIZE, 2 * COL_BF_SIZE, nzl));
2666           COL_BF_SIZE = nzl;
2667           PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
2668         }
2669         PetscCall(MatGetRow(B, i, &nzl, &cols, &vals));
2670         for (int j = 0; j < nzl; j++) colbuf[j] = cols[j] + moffset;
2671         row = i + moffset;
2672         PetscCall(MatSetValues(packM, 1, &row, nzl, colbuf, vals, INSERT_VALUES));
2673         PetscCall(MatRestoreRow(B, i, &nzl, &cols, &vals));
2674       }
2675     }
2676     PetscCall(PetscFree(colbuf));
2677   }
2678   // cleanup
2679   for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(MatDestroy(&subM[grid]));
2680   PetscCall(MatAssemblyBegin(packM, MAT_FINAL_ASSEMBLY));
2681   PetscCall(MatAssemblyEnd(packM, MAT_FINAL_ASSEMBLY));
2682   PetscCall(PetscObjectSetName((PetscObject)packM, "mass"));
2683   PetscCall(MatViewFromOptions(packM, NULL, "-dm_landau_mass_view"));
2684   ctx->M = packM;
2685   if (Amat) *Amat = packM;
2686   PetscCall(PetscLogEventEnd(ctx->events[14], 0, 0, 0, 0));
2687   PetscFunctionReturn(PETSC_SUCCESS);
2688 }
2689 
2690 /*@
2691  DMPlexLandauIFunction - TS residual calculation, confusingly this computes the Jacobian w/o mass
2692 
2693  Collective
2694 
2695  Input Parameters:
2696 +   TS  - The time stepping context
2697 .   time_dummy - current time (not used)
2698 .   X - Current state
2699 .   X_t - Time derivative of current state
2700 -   actx - Landau context
2701 
2702  Output Parameter:
2703 .   F  - The residual
2704 
2705  Level: beginner
2706 
2707  .keywords: mesh
2708  .seealso: `DMPlexLandauCreateVelocitySpace()`, `DMPlexLandauIJacobian()`
2709  @*/
2710 PetscErrorCode DMPlexLandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
2711 {
2712   LandauCtx *ctx = (LandauCtx *)actx;
2713   PetscInt   dim;
2714   DM         pack;
2715 #if defined(PETSC_HAVE_THREADSAFETY)
2716   double starttime, endtime;
2717 #endif
2718   PetscObjectState state;
2719 
2720   PetscFunctionBegin;
2721   PetscCall(TSGetDM(ts, &pack));
2722   PetscCall(DMGetApplicationContext(pack, &ctx));
2723   PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2724   if (ctx->stage) PetscCall(PetscLogStagePush(ctx->stage));
2725   PetscCall(PetscLogEventBegin(ctx->events[11], 0, 0, 0, 0));
2726   PetscCall(PetscLogEventBegin(ctx->events[0], 0, 0, 0, 0));
2727 #if defined(PETSC_HAVE_THREADSAFETY)
2728   starttime = MPI_Wtime();
2729 #endif
2730   PetscCall(DMGetDimension(pack, &dim));
2731   PetscCall(PetscObjectStateGet((PetscObject)ctx->J, &state));
2732   if (state != ctx->norm_state) {
2733     PetscCall(PetscInfo(ts, "Create Landau Jacobian t=%g J.state %" PetscInt64_FMT " --> %" PetscInt64_FMT "\n", (double)time_dummy, ctx->norm_state, state));
2734     PetscCall(MatZeroEntries(ctx->J));
2735     PetscCall(LandauFormJacobian_Internal(X, ctx->J, dim, 0.0, (void *)ctx));
2736     PetscCall(MatViewFromOptions(ctx->J, NULL, "-dm_landau_jacobian_view"));
2737     PetscCall(PetscObjectStateGet((PetscObject)ctx->J, &state));
2738     ctx->norm_state = state;
2739   } else {
2740     PetscCall(PetscInfo(ts, "WARNING Skip forming Jacobian, has not changed %" PetscInt64_FMT "\n", state));
2741   }
2742   /* mat vec for op */
2743   PetscCall(MatMult(ctx->J, X, F)); /* C*f */
2744   /* add time term */
2745   if (X_t) PetscCall(MatMultAdd(ctx->M, X_t, F, F));
2746 #if defined(PETSC_HAVE_THREADSAFETY)
2747   if (ctx->stage) {
2748     endtime = MPI_Wtime();
2749     ctx->times[LANDAU_OPERATOR] += (endtime - starttime);
2750     ctx->times[LANDAU_JACOBIAN] += (endtime - starttime);
2751     ctx->times[LANDAU_MATRIX_TOTAL] += (endtime - starttime);
2752     ctx->times[LANDAU_JACOBIAN_COUNT] += 1;
2753   }
2754 #endif
2755   PetscCall(PetscLogEventEnd(ctx->events[0], 0, 0, 0, 0));
2756   PetscCall(PetscLogEventEnd(ctx->events[11], 0, 0, 0, 0));
2757   if (ctx->stage) PetscCall(PetscLogStagePop());
2758   PetscFunctionReturn(PETSC_SUCCESS);
2759 }
2760 
2761 /*@
2762  DMPlexLandauIJacobian - TS Jacobian construction, confusingly this adds mass
2763 
2764  Collective
2765 
2766  Input Parameters:
2767 +   TS  - The time stepping context
2768 .   time_dummy - current time (not used)
2769 .   X - Current state
2770 .   U_tdummy - Time derivative of current state (not used)
2771 .   shift - shift for du/dt term
2772 -   actx - Landau context
2773 
2774  Output Parameters:
2775 +   Amat  - Jacobian
2776 -   Pmat  - same as Amat
2777 
2778  Level: beginner
2779 
2780  .keywords: mesh
2781  .seealso: `DMPlexLandauCreateVelocitySpace()`, `DMPlexLandauIFunction()`
2782  @*/
2783 PetscErrorCode DMPlexLandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
2784 {
2785   LandauCtx *ctx = NULL;
2786   PetscInt   dim;
2787   DM         pack;
2788 #if defined(PETSC_HAVE_THREADSAFETY)
2789   double starttime, endtime;
2790 #endif
2791   PetscObjectState state;
2792 
2793   PetscFunctionBegin;
2794   PetscCall(TSGetDM(ts, &pack));
2795   PetscCall(DMGetApplicationContext(pack, &ctx));
2796   PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2797   PetscCheck(Amat == Pmat && Amat == ctx->J, ctx->comm, PETSC_ERR_PLIB, "Amat!=Pmat || Amat!=ctx->J");
2798   PetscCall(DMGetDimension(pack, &dim));
2799   /* get collision Jacobian into A */
2800   if (ctx->stage) PetscCall(PetscLogStagePush(ctx->stage));
2801   PetscCall(PetscLogEventBegin(ctx->events[11], 0, 0, 0, 0));
2802   PetscCall(PetscLogEventBegin(ctx->events[9], 0, 0, 0, 0));
2803 #if defined(PETSC_HAVE_THREADSAFETY)
2804   starttime = MPI_Wtime();
2805 #endif
2806   PetscCall(PetscInfo(ts, "Adding mass to Jacobian t=%g, shift=%g\n", (double)time_dummy, (double)shift));
2807   PetscCheck(shift != 0.0, ctx->comm, PETSC_ERR_PLIB, "zero shift");
2808   PetscCall(PetscObjectStateGet((PetscObject)ctx->J, &state));
2809   PetscCheck(state == ctx->norm_state, ctx->comm, PETSC_ERR_PLIB, "wrong state, %" PetscInt64_FMT " %" PetscInt64_FMT "", ctx->norm_state, state);
2810   if (!ctx->use_matrix_mass) {
2811     PetscCall(LandauFormJacobian_Internal(X, ctx->J, dim, shift, (void *)ctx));
2812   } else { /* add mass */
2813     PetscCall(MatAXPY(Pmat, shift, ctx->M, SAME_NONZERO_PATTERN));
2814   }
2815 #if defined(PETSC_HAVE_THREADSAFETY)
2816   if (ctx->stage) {
2817     endtime = MPI_Wtime();
2818     ctx->times[LANDAU_OPERATOR] += (endtime - starttime);
2819     ctx->times[LANDAU_MASS] += (endtime - starttime);
2820     ctx->times[LANDAU_MATRIX_TOTAL] += (endtime - starttime);
2821   }
2822 #endif
2823   PetscCall(PetscLogEventEnd(ctx->events[9], 0, 0, 0, 0));
2824   PetscCall(PetscLogEventEnd(ctx->events[11], 0, 0, 0, 0));
2825   if (ctx->stage) PetscCall(PetscLogStagePop());
2826   PetscFunctionReturn(PETSC_SUCCESS);
2827 }
2828