xref: /petsc/src/ts/utils/dmplexlandau/plexland.c (revision dfd57a172ac9fa6c7b5fe6de6ab5df85cefc2996)
1 #include <petsc/private/dmpleximpl.h>   /*I "petscdmplex.h" I*/
2 #include <petsclandau.h>                /*I "petsclandau.h"   I*/
3 #include <petscts.h>
4 #include <petscdmforest.h>
5 /* Landau collision operator */
6 
7 /* relativistic terms */
8 #define SPEED_OF_LIGHT 299792458
9 #if defined(PETSC_USE_REAL_SINGLE)
10 #define C_0(v0) (SPEED_OF_LIGHT/v0) /* needed for relativistic tensor on all architectures */
11 #else
12 #define C_0(v0) (SPEED_OF_LIGHT/v0) /* needed for relativistic tensor on all architectures */
13 #endif
14 
15 #define PETSC_THREAD_SYNC
16 #include "land_tensors.h"
17 
18 /* vector padding not supported */
19 #define LANDAU_VL  1
20 
21 static PetscErrorCode LandauGPUMapsDestroy(void *ptr)
22 {
23   P4estVertexMaps *maps = (P4estVertexMaps *)ptr;
24   PetscErrorCode  ierr;
25   PetscFunctionBegin;
26   if (maps->deviceType != LANDAU_CPU) {
27 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
28     if (maps->deviceType == LANDAU_KOKKOS) {
29       ierr = LandauKokkosDestroyMatMaps(maps);CHKERRQ(ierr); // imples Kokkos does
30     } // else could be CUDA
31 #elif defined(PETSC_HAVE_CUDA)
32     if (maps->deviceType == LANDAU_CUDA) {
33       ierr = LandauCUDADestroyMatMaps(maps);CHKERRQ(ierr);
34     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps->deviceType %D ?????",maps->deviceType);
35 #endif
36   }
37   ierr = PetscFree(maps->c_maps);CHKERRQ(ierr);
38   ierr = PetscFree(maps->gIdx);CHKERRQ(ierr);
39   ierr = PetscFree(maps);CHKERRQ(ierr);
40   PetscFunctionReturn(0);
41 }
42 static PetscErrorCode energy_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
43 {
44   PetscReal     v2 = 0;
45   PetscFunctionBegin;
46   /* compute v^2 / 2 */
47   for (int i = 0; i < dim; ++i) v2 += x[i]*x[i];
48   /* evaluate the Maxwellian */
49   u[0] = v2/2;
50   PetscFunctionReturn(0);
51 }
52 
53 /* needs double */
54 static PetscErrorCode gamma_m1_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
55 {
56   PetscReal     *c2_0_arr = ((PetscReal*)actx);
57   double        u2 = 0, c02 = (double)*c2_0_arr, xx;
58 
59   PetscFunctionBegin;
60   /* compute u^2 / 2 */
61   for (int i = 0; i < dim; ++i) u2 += x[i]*x[i];
62   /* gamma - 1 = g_eps, for conditioning and we only take derivatives */
63   xx = u2/c02;
64 #if defined(PETSC_USE_DEBUG)
65   u[0] = PetscSqrtReal(1. + xx);
66 #else
67   u[0] = xx/(PetscSqrtReal(1. + xx) + 1.) - 1.; // better conditioned. -1 might help condition and only used for derivative
68 #endif
69   PetscFunctionReturn(0);
70 }
71 
72 /* ------------------------------------------------------------------- */
73 /*
74  LandauFormJacobian_Internal - Evaluates Jacobian matrix.
75 
76  Input Parameters:
77  .  globX - input vector
78  .  actx - optional user-defined context
79  .  dim - dimension
80 
81  Output Parameters:
82  .  J0acP - Jacobian matrix filled, not created
83  */
84 static PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, PetscReal shift, void *a_ctx)
85 {
86   LandauCtx         *ctx = (LandauCtx*)a_ctx;
87   PetscErrorCode    ierr;
88   PetscInt          cStart, cEnd, elemMatSize;
89   PetscDS           prob;
90   PetscSection      section,globsection;
91   PetscInt          numCells,totDim,ej,Nq,*Nbf,*Ncf,Nb,Ncx,Nf,d,f,fieldA,qj,N;
92   PetscQuadrature   quad;
93   const PetscReal   *quadWeights;
94   PetscTabulation   *Tf; // used for CPU and print info
95   PetscReal         Eq_m[LANDAU_MAX_SPECIES], m_0=ctx->m_0; /* normalize mass -- not needed! */
96   PetscScalar       *IPf=NULL;
97   const PetscScalar *xdata=NULL;
98   PetscLogDouble    flops;
99   PetscContainer    container;
100   P4estVertexMaps   *maps=NULL;
101 
102   PetscFunctionBegin;
103   PetscValidHeaderSpecific(a_X,VEC_CLASSID,1);
104   PetscValidHeaderSpecific(JacP,MAT_CLASSID,2);
105   PetscValidPointer(ctx,5);
106   /* check for matrix container for GPU assembly */
107   ierr = PetscLogEventBegin(ctx->events[10],0,0,0,0);CHKERRQ(ierr);
108   ierr = PetscObjectQuery((PetscObject) JacP, "assembly_maps", (PetscObject *) &container);CHKERRQ(ierr);
109   if (container /* && ctx->deviceType != LANDAU_CPU */) {
110     if (!ctx->gpu_assembly) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"GPU matrix container but no GPU assembly");
111     ierr = PetscContainerGetPointer(container, (void **) &maps);CHKERRQ(ierr);
112     if (!maps) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"empty GPU matrix container");
113   }
114   if (ctx->plex == NULL) {
115     ierr = DMConvert(ctx->dmv, DMPLEX, &ctx->plex);CHKERRQ(ierr);
116   }
117   ierr = DMPlexGetHeightStratum(ctx->plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
118   ierr = DMGetLocalSection(ctx->plex, &section);CHKERRQ(ierr);
119   ierr = DMGetGlobalSection(ctx->plex, &globsection);CHKERRQ(ierr);
120   ierr = DMGetDS(ctx->plex, &prob);CHKERRQ(ierr);
121   ierr = PetscDSGetTabulation(prob, &Tf);CHKERRQ(ierr); // Bf, &Df
122   ierr = PetscDSGetDimensions(prob, &Nbf);CHKERRQ(ierr); Nb = Nbf[0]; /* number of vertices*S */
123   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
124   if (Nf!=ctx->num_species) SETERRQ1(ctx->comm, PETSC_ERR_PLIB, "Nf %D != S",Nf);
125   ierr = PetscDSGetComponents(prob, &Ncf);CHKERRQ(ierr);
126   Ncx = Ncf[0];
127   if (Ncx!=1) SETERRQ1(ctx->comm, PETSC_ERR_PLIB, "Nc %D != 1",Ncx);
128   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
129   numCells = cEnd - cStart;
130   ierr = PetscFEGetQuadrature(ctx->fe[0], &quad);CHKERRQ(ierr);
131   ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, &quadWeights);CHKERRQ(ierr);
132   if (Nb!=Nq) SETERRQ4(ctx->comm, PETSC_ERR_PLIB, "Nb!=Nq %D %D over integration or simplices? Tf[0]->Nb=%D dim=%D",Nb,Nq,Tf[0]->Nb,dim);
133   if (Nq >LANDAU_MAX_NQ) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"Order too high. Nq = %D > LANDAU_MAX_NQ (%D)",Nq,LANDAU_MAX_NQ);
134   if (LANDAU_DIM != dim) SETERRQ2(ctx->comm, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim,LANDAU_DIM);
135   if (!ctx->SData_d) {
136     ierr = PetscNew(&ctx->SData_d);CHKERRQ(ierr);
137   }
138   elemMatSize = totDim*totDim; // used for CPU and print info
139   ierr = PetscLogEventEnd(ctx->events[10],0,0,0,0);CHKERRQ(ierr);
140   ierr = VecGetSize(a_X,&N);CHKERRQ(ierr);
141   if (!ctx->init) { /* create static point data, Jacobian called first */
142     PetscReal       *invJ,*ww,*xx,*yy,*zz=NULL,*mass_w,*invJ_a;
143     const PetscInt  nip = Nq*numCells;
144     Vec             v2_2 = NULL; // projected function: v^2/2 ofr non-relativistic, gamma... for relativistic
145     PetscSection    e_section;
146     DM              dmEnergy=NULL;
147     ierr = PetscLogEventBegin(ctx->events[7],0,0,0,0);CHKERRQ(ierr);
148     ctx->init = PETSC_TRUE;
149     ierr = PetscInfo(ctx->plex, "Initialize static data\n");CHKERRQ(ierr);
150     /* collect f data, first time is for Jacobian, but make mass now */
151     if (ctx->verbose > 1 || ctx->verbose > 0) {
152       ierr = PetscPrintf(ctx->comm,"[%D]%s: %D IPs, %D cells, totDim=%D, Nb=%D, Nq=%D, elemMatSize=%D, dim=%D, Tab: Nb=%D Nf=%D Np=%D cdim=%D N=%D shift=%g\n",
153                          0,"FormLandau",Nq*numCells,numCells, totDim, Nb, Nq, elemMatSize, dim, Tf[0]->Nb, Nf, Tf[0]->Np, Tf[0]->cdim, N, shift);CHKERRQ(ierr);
154     }
155     ierr = PetscMalloc5(nip,&mass_w,nip,&ww,nip,&xx,nip,&yy,nip*dim*dim,&invJ_a);CHKERRQ(ierr);
156     if (dim==3) {
157       ierr = PetscMalloc1(nip,&zz);CHKERRQ(ierr);
158     }
159     // prep energy trick, get v^2 / 2 vector
160     if (ctx->use_energy_tensor_trick) {
161       PetscErrorCode (*energyf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {ctx->use_relativistic_corrections ? gamma_m1_f : energy_f};
162       PetscFE        fe;
163       Vec            glob_v2;
164       PetscReal      *c2_0[1], data[1] = {PetscSqr(C_0(ctx->v_0))};
165 
166       ierr = DMClone(ctx->plex, &dmEnergy);CHKERRQ(ierr);
167       ierr = PetscObjectSetName((PetscObject) dmEnergy, "energy");CHKERRQ(ierr);
168       ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &fe);CHKERRQ(ierr);
169       ierr = PetscObjectSetName((PetscObject) fe, "energy");CHKERRQ(ierr);
170       ierr = DMSetField(dmEnergy, 0, NULL, (PetscObject)fe);CHKERRQ(ierr);
171       ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
172       ierr = DMCreateDS(dmEnergy);CHKERRQ(ierr);
173       ierr = DMGetSection(dmEnergy, &e_section);CHKERRQ(ierr);
174       ierr = DMGetGlobalVector(dmEnergy,&glob_v2);CHKERRQ(ierr);
175       ierr = PetscObjectSetName((PetscObject) glob_v2, "v^2/2");CHKERRQ(ierr);
176       c2_0[0] = &data[0];
177       ierr = DMProjectFunction(dmEnergy, 0., energyf, (void**)c2_0, INSERT_ALL_VALUES, glob_v2);CHKERRQ(ierr);
178       ierr = DMGetLocalVector(dmEnergy, &v2_2);CHKERRQ(ierr);
179       ierr = VecZeroEntries(v2_2);CHKERRQ(ierr); /* zero BCs so don't set */
180       ierr = DMGlobalToLocalBegin(dmEnergy, glob_v2, INSERT_VALUES, v2_2);CHKERRQ(ierr);
181       ierr = DMGlobalToLocalEnd  (dmEnergy, glob_v2, INSERT_VALUES, v2_2);CHKERRQ(ierr);
182       ierr = DMViewFromOptions(dmEnergy,NULL, "-energy_dm_view");CHKERRQ(ierr);
183       ierr = VecViewFromOptions(glob_v2,NULL, "-energy_vec_view");CHKERRQ(ierr);
184       ierr = DMRestoreGlobalVector(dmEnergy, &glob_v2);CHKERRQ(ierr);
185     }
186     for (ej = 0 ; ej < numCells; ++ej) {
187       PetscScalar *coefs = NULL;
188       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);
189       invJ = invJ_a ? invJ_a + ej * Nq*dim*dim : NULL;
190       ierr = DMPlexComputeCellGeometryFEM(ctx->plex, cStart+ej, quad, vj, Jdummy, invJ, detJj);CHKERRQ(ierr);
191       if (ctx->use_energy_tensor_trick) {
192         ierr = DMPlexVecGetClosure(dmEnergy, e_section, v2_2, cStart+ej, NULL, &coefs);CHKERRQ(ierr);
193       }
194       /* create dynamic point data */
195       for (qj = 0; qj < Nq; ++qj) {
196         PetscInt         gidx = (ej*Nq + qj);
197         mass_w[gidx] = detJj[qj] * quadWeights[qj];
198         if (dim==2) mass_w[gidx] *=  2.*PETSC_PI*vj[qj * dim + 0]; /* cylindrical coordinate, w/o 2pi */
199         // get xx, yy, zz
200         if (ctx->use_energy_tensor_trick) {
201           double                  refSpaceDer[3],eGradPhi[3];
202           const PetscReal * const DD = Tf[0]->T[1];
203           const PetscReal         *Dq = &DD[qj*Nb*dim];
204           for (int d = 0; d < 3; ++d) refSpaceDer[d] = eGradPhi[d] = 0.0;
205           for (int b = 0; b < Nb; ++b) {
206             for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[b*dim+d]*PetscRealPart(coefs[b]);
207             //PetscPrintf(ctx->comm,"%12.5e ", coefs[b]);
208           }
209           //PetscPrintf(ctx->comm,"\n");
210           xx[gidx] = 1e10;
211           if (ctx->use_relativistic_corrections) {
212             double dg2_c2 = 0;
213             //for (int d = 0; d < dim; ++d) refSpaceDer[d] *= c02;
214             for (int d = 0; d < dim; ++d) dg2_c2 += PetscSqr(refSpaceDer[d]);
215             dg2_c2 *= (double)c02;
216             if (dg2_c2 >= .999) {
217               xx[gidx] = vj[qj * dim + 0]; /* coordinate */
218               yy[gidx] = vj[qj * dim + 1];
219               if (dim==3) zz[gidx] = vj[qj * dim + 2];
220               PetscPrintf(ctx->comm,"Error: %12.5e %D.%D) dg2/c02 = %12.5e x= %12.5e %12.5e %12.5e\n",PetscSqrtReal(xx[gidx]*xx[gidx] + yy[gidx]*yy[gidx] + zz[gidx]*zz[gidx]), ej, qj, dg2_c2, xx[gidx],yy[gidx],zz[gidx]);
221             } else {
222               PetscReal fact = c02/PetscSqrtReal(1. - dg2_c2);
223               for (int d = 0; d < dim; ++d) refSpaceDer[d] *= fact;
224               // could test with other point u' that (grad - grad') * U (refSpaceDer, refSpaceDer') == 0
225             }
226           }
227           if (xx[gidx] == 1e10) {
228             for (int d = 0; d < dim; ++d) {
229               for (int e = 0 ; e < dim; ++e) {
230                 eGradPhi[d] += invJ[qj * dim * dim + e*dim+d]*refSpaceDer[e];
231               }
232             }
233             xx[gidx] = eGradPhi[0];
234             yy[gidx] = eGradPhi[1];
235             if (dim==3) zz[gidx] = eGradPhi[2];
236           }
237         } else {
238           xx[gidx] = vj[qj * dim + 0]; /* coordinate */
239           yy[gidx] = vj[qj * dim + 1];
240           if (dim==3) zz[gidx] = vj[qj * dim + 2];
241         }
242         //ierr = PetscPrintf(ctx->comm,"%D.%D) %12.5e %12.5e %12.5e\n", ej, qj, xx[gidx], yy[gidx], zz ? zz[gidx] : -0);CHKERRQ(ierr);
243         ww[gidx] = detJj[qj] * quadWeights[qj];
244         if (dim==2) ww[gidx] *= vj[qj * dim + 0];  /* cylindrical coordinate, w/o 2pi */
245       } /* q */
246       if (ctx->use_energy_tensor_trick) {
247         ierr = DMPlexVecRestoreClosure(dmEnergy, e_section, v2_2, cStart+ej, NULL, &coefs);CHKERRQ(ierr);
248       }
249     } /* ej */
250     if (ctx->use_energy_tensor_trick) {
251       ierr = DMRestoreLocalVector(dmEnergy, &v2_2);CHKERRQ(ierr);
252       ierr = DMDestroy(&dmEnergy);CHKERRQ(ierr);
253     }
254     /* cache static data */
255     if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
256 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_KOKKOS)
257       PetscReal invMass[LANDAU_MAX_SPECIES],nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
258       for (fieldA=0;fieldA<Nf;fieldA++) {
259         invMass[fieldA] = m_0/ctx->masses[fieldA];
260         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/m_0)*m_0/ctx->masses[fieldA];
261         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);
262       }
263       if (ctx->deviceType == LANDAU_CUDA) {
264 #if defined(PETSC_HAVE_CUDA)
265         ierr = LandauCUDAStaticDataSet(ctx->plex,Nq,nu_alpha,nu_beta,invMass,invJ_a,mass_w,xx,yy,zz,ww,ctx->SData_d);CHKERRQ(ierr);
266 #else
267         SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
268 #endif
269       } else if (ctx->deviceType == LANDAU_KOKKOS) {
270 #if defined(PETSC_HAVE_KOKKOS)
271         ierr = LandauKokkosStaticDataSet(ctx->plex,Nq,nu_alpha,nu_beta,invMass,invJ_a,mass_w,xx,yy,zz,ww,ctx->SData_d);CHKERRQ(ierr);
272 #else
273         SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
274 #endif
275       }
276 #endif
277       /* free */
278       ierr = PetscFree5(mass_w,ww,xx,yy,invJ_a);CHKERRQ(ierr);
279       if (dim==3) {
280         ierr = PetscFree(zz);CHKERRQ(ierr);
281       }
282     } else { /* CPU version, just copy in, only use part */
283       ctx->SData_d->w = (void*)ww;
284       ctx->SData_d->x = (void*)xx;
285       ctx->SData_d->y = (void*)yy;
286       ctx->SData_d->z = (void*)zz;
287       ctx->SData_d->invJ = (void*)invJ_a;
288       ctx->SData_d->mass_w = (void*)mass_w;
289     }
290     ierr = PetscLogEventEnd(ctx->events[7],0,0,0,0);CHKERRQ(ierr);
291   }
292   if (shift==0) { /* create dynamic point data */
293     ierr = PetscLogEventBegin(ctx->events[1],0,0,0,0);CHKERRQ(ierr);
294     ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
295     flops = (PetscLogDouble)numCells*(PetscLogDouble)Nq*(PetscLogDouble)(5*dim*dim*Nf*Nf + 165);
296     for (fieldA=0;fieldA<Nf;fieldA++) {
297       Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
298       if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
299     }
300     if (!ctx->gpu_assembly || !container) {
301       Vec locX;
302       ierr = DMGetLocalVector(ctx->plex, &locX);CHKERRQ(ierr);
303       ierr = VecZeroEntries(locX);CHKERRQ(ierr); /* zero BCs so don't set */
304       ierr = DMGlobalToLocalBegin(ctx->plex, a_X, INSERT_VALUES, locX);CHKERRQ(ierr);
305       ierr = DMGlobalToLocalEnd  (ctx->plex, a_X, INSERT_VALUES, locX);CHKERRQ(ierr);
306       ierr = PetscMalloc1(Nq*numCells*Nf,&IPf);CHKERRQ(ierr);
307       for (ej = 0 ; ej < numCells; ++ej) {
308         PetscScalar *coef = NULL;
309         ierr = DMPlexVecGetClosure(ctx->plex, section, locX, cStart+ej, NULL, &coef);CHKERRQ(ierr);
310         ierr = PetscMemcpy(&IPf[ej*Nb*Nf],coef,Nb*Nf*sizeof(PetscScalar));CHKERRQ(ierr); /* change if LandauIPReal != PetscScalar */
311         ierr = DMPlexVecRestoreClosure(ctx->plex, section, locX, cStart+ej, NULL, &coef);CHKERRQ(ierr);
312       } /* ej */
313       ierr = DMRestoreLocalVector(ctx->plex, &locX);CHKERRQ(ierr);
314     } else {
315       PetscMemType mtype;
316       ierr = VecGetArrayReadAndMemType(a_X,&xdata,&mtype);CHKERRQ(ierr);
317       if (mtype!=PETSC_MEMTYPE_HOST && ctx->deviceType == LANDAU_CPU) {
318         SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"CPU run with device data: use -mat_type aij");
319       }
320     }
321     ierr = PetscLogEventEnd(ctx->events[1],0,0,0,0);CHKERRQ(ierr);
322   } else {
323     flops = (PetscLogDouble)numCells*(PetscLogDouble)Nq*(PetscLogDouble)(5*dim*dim*Nf*Nf);
324   }
325   /* do it */
326   if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
327     if (ctx->deviceType == LANDAU_CUDA) {
328 #if defined(PETSC_HAVE_CUDA)
329       ierr = LandauCUDAJacobian(ctx->plex,Nq,Eq_m,IPf,N,xdata,ctx->SData_d,ctx->subThreadBlockSize,shift,ctx->events,JacP);CHKERRQ(ierr);
330 #else
331       SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
332 #endif
333     } else if (ctx->deviceType == LANDAU_KOKKOS) {
334 #if defined(PETSC_HAVE_KOKKOS)
335       ierr = LandauKokkosJacobian(ctx->plex,Nq,Eq_m,IPf,N,xdata,ctx->SData_d,ctx->subThreadBlockSize,shift,ctx->events,JacP);CHKERRQ(ierr);
336 #else
337       SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
338 #endif
339     }
340   } else { /* CPU version */
341     PetscInt        ei, qi;
342     PetscScalar     *elemMat,coef_buff[LANDAU_MAX_SPECIES*LANDAU_MAX_NQ];
343     PetscReal       *ff, *dudx, *dudy, *dudz, *invJ, *invJ_a = (PetscReal*)ctx->SData_d->invJ, *xx = (PetscReal*)ctx->SData_d->x, *yy = (PetscReal*)ctx->SData_d->y, *zz = (PetscReal*)ctx->SData_d->z, *ww = (PetscReal*)ctx->SData_d->w, *mass_w = (PetscReal*)ctx->SData_d->mass_w;
344     const PetscInt  nip = Nq*numCells, mask_factor = (ctx->use_energy_tensor_trick && (Nq==8 || Nq==4)) ? Nq : 1; // 3D Q1
345     const PetscReal *const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
346     PetscReal       Eq_m[LANDAU_MAX_SPECIES], invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
347     if (shift!=0.0) { // mass
348       ierr = PetscMalloc1(elemMatSize, &elemMat);CHKERRQ(ierr);
349     } else {      /* compute f and df and init data for Jacobian */
350       ierr = PetscLogEventBegin(ctx->events[8],0,0,0,0);CHKERRQ(ierr);
351       for (fieldA=0;fieldA<Nf;fieldA++) {
352         invMass[fieldA] = m_0/ctx->masses[fieldA];
353         Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
354         if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
355         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/m_0)*m_0/ctx->masses[fieldA];
356         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);
357       }
358       ierr = PetscMalloc5(elemMatSize, &elemMat, nip*Nf, &ff, nip*Nf, &dudx, nip*Nf, &dudy, dim==3 ? nip*Nf : 0, &dudz);CHKERRQ(ierr);
359       for (ei = cStart, invJ = invJ_a; ei < cEnd; ++ei, invJ += Nq*dim*dim) {
360         PetscScalar *coef;
361         PetscInt     b,f,idx,q;
362         PetscReal    u_x[LANDAU_MAX_SPECIES][LANDAU_DIM];
363         if (IPf) {
364           coef = &IPf[ei*Nb*Nf]; // this is const
365         } else {
366           if (!maps) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"!maps");
367           coef = coef_buff;
368           for (f = 0; f < Nf; ++f) {
369             LandauIdx *const Idxs = &maps->gIdx[ei-cStart][f][0];
370             for (b = 0; b < Nb; ++b) {
371               idx = Idxs[b];
372               if (idx >= 0) {
373                 coef[f*Nb+b] = xdata[idx];
374               } else {
375                 idx = -idx - 1;
376                 coef[f*Nb+b] = 0;
377                 for (q = 0; q < maps->num_face; q++) {
378                   PetscInt    id = maps->c_maps[idx][q].gid;
379                   PetscScalar scale = maps->c_maps[idx][q].scale;
380                   coef[f*Nb+b] += scale*xdata[id];
381                 }
382               }
383             }
384           }
385         }
386         /* get f and df */
387         for (qi = 0; qi < Nq; ++qi) {
388           const PetscReal  *Bq = &BB[qi*Nb];
389           const PetscReal  *Dq = &DD[qi*Nb*dim];
390           const PetscInt   gidx = ei*Nq + qi;
391           /* get f & df */
392           for (f = 0; f < Nf; ++f) {
393             PetscInt   b, e;
394             PetscReal  refSpaceDer[LANDAU_DIM];
395             ff[gidx + f*nip] = 0.0;
396             for (d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
397             for (b = 0; b < Nb; ++b) {
398               const PetscInt    cidx = b;
399               ff[gidx + f*nip] += Bq[cidx]*PetscRealPart(coef[f*Nb+cidx]);
400               for (d = 0; d < dim; ++d) refSpaceDer[d] += Dq[cidx*dim+d]*PetscRealPart(coef[f*Nb+cidx]);
401             }
402             for (d = 0; d < dim; ++d) {
403               for (e = 0, u_x[f][d] = 0.0; e < dim; ++e) {
404                 u_x[f][d] += invJ[qi * dim * dim + e*dim+d]*refSpaceDer[e];
405               }
406             }
407           }
408           for (f=0;f<Nf;f++) {
409             dudx[gidx + f*nip] = u_x[f][0];
410             dudy[gidx + f*nip] = u_x[f][1];
411 #if LANDAU_DIM==3
412             dudz[gidx + f*nip] = u_x[f][2];
413 #endif
414           }
415         }
416       }
417       ierr = PetscLogEventEnd(ctx->events[8],0,0,0,0);CHKERRQ(ierr);
418     }
419     for (ej = cStart, invJ = invJ_a; ej < cEnd; ++ej, invJ += Nq*dim*dim) {
420       ierr = PetscMemzero(elemMat, totDim *totDim * sizeof(PetscScalar));CHKERRQ(ierr);
421       ierr = PetscLogEventBegin(ctx->events[4],0,0,0,0);CHKERRQ(ierr);
422       ierr = PetscLogFlops((PetscLogDouble)Nq*flops);CHKERRQ(ierr);
423       //printf("\t:%d.%d) Invj[0] = %e (%d)\n",ej,qj,invJ[0],(int)(invJ-invJ_a));
424       for (qj = 0; qj < Nq; ++qj) {
425         const PetscReal * const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
426         PetscReal               g0[LANDAU_MAX_SPECIES], g2[LANDAU_MAX_SPECIES][LANDAU_DIM], g3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM];
427         PetscInt                d,d2,dp,d3,ipidx,fieldA;
428         const PetscInt          jpidx = Nq*(ej-cStart) + qj;
429         if (shift==0.0) {
430           const PetscReal * const invJj = &invJ[qj*dim*dim];
431           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];
432           const PetscReal         vj[3] = {xx[jpidx], yy[jpidx], zz ? zz[jpidx] : 0}, wj = ww[jpidx];
433 
434           // create g2 & g3
435           for (d=0;d<dim;d++) { // clear accumulation data D & K
436             gg2_temp[d] = 0;
437             for (d2=0;d2<dim;d2++) gg3_temp[d][d2] = 0;
438           }
439           for (ipidx = 0; ipidx < nip; ipidx++) {
440             const PetscReal wi = ww[ipidx], x = xx[ipidx], y = yy[ipidx];
441             PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
442 #if LANDAU_DIM==2
443             PetscReal       Ud[2][2], Uk[2][2];
444             LandauTensor2D(vj, x, y, Ud, Uk, (ipidx/mask_factor==jpidx/mask_factor) ? 0. : 1.);
445 #else
446             PetscReal U[3][3], z = zz[ipidx];
447             if (ctx->use_relativistic_corrections) {
448               PetscReal U2[3][3];
449               LandauTensor3DRelativistic(vj, x, y, z, U, (ipidx/mask_factor==jpidx/mask_factor) ? 0. : 1., C_0(ctx->v_0));
450             } else {
451               LandauTensor3D(vj, x, y, z, U, (ipidx==jpidx) ? 0. : 1.);
452             }
453 #endif
454             for (fieldA = 0; fieldA < Nf; ++fieldA) {
455               temp1[0] += dudx[ipidx + fieldA*nip]*nu_beta[fieldA]*invMass[fieldA];
456               temp1[1] += dudy[ipidx + fieldA*nip]*nu_beta[fieldA]*invMass[fieldA];
457 #if LANDAU_DIM==3
458               temp1[2] += dudz[ipidx + fieldA*nip]*nu_beta[fieldA]*invMass[fieldA];
459 #endif
460               temp2    += ff[ipidx + fieldA*nip]*nu_beta[fieldA];
461             }
462             temp1[0] *= wi;
463             temp1[1] *= wi;
464 #if LANDAU_DIM==3
465             temp1[2] *= wi;
466 #endif
467             temp2    *= wi;
468 #if LANDAU_DIM==2
469             for (d2 = 0; d2 < 2; d2++) {
470               for (d3 = 0; d3 < 2; ++d3) {
471                 /* K = U * grad(f): g2=e: i,A */
472                 gg2_temp[d2] += Uk[d2][d3]*temp1[d3];
473                 /* D = -U * (I \kron (fx)): g3=f: i,j,A */
474                 gg3_temp[d2][d3] += Ud[d2][d3]*temp2;
475               }
476             }
477 #else
478             for (d2 = 0; d2 < 3; ++d2) {
479               for (d3 = 0; d3 < 3; ++d3) {
480                 /* K = U * grad(f): g2 = e: i,A */
481                 gg2_temp[d2] += U[d2][d3]*temp1[d3];
482                 /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
483                 gg3_temp[d2][d3] += U[d2][d3]*temp2;
484               }
485             }
486 #endif
487           } /* IPs */
488           // add alpha and put in gg2/3
489           for (fieldA = 0; fieldA < Nf; ++fieldA) {
490             for (d2 = 0; d2 < dim; d2++) {
491               gg2[fieldA][d2] = gg2_temp[d2]*nu_alpha[fieldA];
492               for (d3 = 0; d3 < dim; d3++) {
493                 gg3[fieldA][d2][d3] = -gg3_temp[d2][d3]*nu_alpha[fieldA]*invMass[fieldA];
494               }
495             }
496           }
497           /* add electric field term once per IP */
498           for (fieldA = 0; fieldA < Nf; ++fieldA) {
499             gg2[fieldA][dim-1] += Eq_m[fieldA];
500           }
501           /* Jacobian transform - g2, g3 */
502           for (fieldA = 0; fieldA < Nf; ++fieldA) {
503             for (d = 0; d < dim; ++d) {
504               g2[fieldA][d] = 0.0;
505               for (d2 = 0; d2 < dim; ++d2) {
506                 g2[fieldA][d] += invJj[d*dim+d2]*gg2[fieldA][d2];
507                 g3[fieldA][d][d2] = 0.0;
508                 for (d3 = 0; d3 < dim; ++d3) {
509                   for (dp = 0; dp < dim; ++dp) {
510                     g3[fieldA][d][d2] += invJj[d*dim + d3]*gg3[fieldA][d3][dp]*invJj[d2*dim + dp];
511                   }
512                 }
513                 g3[fieldA][d][d2] *= wj;
514               }
515               g2[fieldA][d] *= wj;
516             }
517           }
518         } else { // mass
519           /* Jacobian transform - g0 */
520           for (fieldA = 0; fieldA < Nf; ++fieldA) {
521             g0[fieldA] = mass_w[jpidx] * shift; // move this to below and remove g0
522           }
523         }
524         /* FE matrix construction */
525         {
526           PetscInt  fieldA,d,f,d2,g;
527           const PetscReal *BJq = &BB[qj*Nb], *DIq = &DD[qj*Nb*dim];
528           /* assemble - on the diagonal (I,I) */
529           for (fieldA = 0; fieldA < Nf ; fieldA++) {
530             for (f = 0; f < Nb ; f++) {
531               const PetscInt i = fieldA*Nb + f; /* Element matrix row */
532               for (g = 0; g < Nb; ++g) {
533                 const PetscInt j    = fieldA*Nb + g; /* Element matrix column */
534                 const PetscInt fOff = i*totDim + j;
535                 if (shift==0.0) {
536                   for (d = 0; d < dim; ++d) {
537                     elemMat[fOff] += DIq[f*dim+d]*g2[fieldA][d]*BJq[g];
538                     //printf("\t:%d.%d.%d.%d.%d.%d) elemMat=%e += %e %e %e\n",ej,qj,fieldA,f,g,d,elemMat[fOff],DIq[f*dim+d],g2[fieldA][d],BJq[g]);
539                     for (d2 = 0; d2 < dim; ++d2) {
540                       elemMat[fOff] += DIq[f*dim + d]*g3[fieldA][d][d2]*DIq[g*dim + d2];
541                     }
542                   }
543                 } else { // mass
544                   elemMat[fOff] += BJq[f]*g0[fieldA]*BJq[g];
545                 }
546               }
547             }
548           }
549         }
550       } /* qj loop */
551       ierr = PetscLogEventEnd(ctx->events[4],0,0,0,0);CHKERRQ(ierr);
552       /* assemble matrix */
553       ierr = PetscLogEventBegin(ctx->events[6],0,0,0,0);CHKERRQ(ierr);
554       if (!maps) {
555         ierr = DMPlexMatSetClosure(ctx->plex, section, globsection, JacP, ej, elemMat, ADD_VALUES);CHKERRQ(ierr);
556       } else {  // GPU like assembly for debugging
557         PetscInt      fieldA,idx,q,f,g,d,nr,nc,rows0[LANDAU_MAX_Q_FACE],cols0[LANDAU_MAX_Q_FACE]={0},rows[LANDAU_MAX_Q_FACE],cols[LANDAU_MAX_Q_FACE];
558         PetscScalar   vals[LANDAU_MAX_Q_FACE*LANDAU_MAX_Q_FACE],row_scale[LANDAU_MAX_Q_FACE],col_scale[LANDAU_MAX_Q_FACE]={0};
559         /* assemble - from the diagonal (I,I) in this format for DMPlexMatSetClosure */
560         for (fieldA = 0; fieldA < Nf ; fieldA++) {
561           LandauIdx *const Idxs = &maps->gIdx[ej-cStart][fieldA][0];
562           for (f = 0; f < Nb ; f++) {
563             idx = Idxs[f];
564             if (idx >= 0) {
565               nr = 1;
566               rows0[0] = idx;
567               row_scale[0] = 1.;
568             } else {
569               idx = -idx - 1;
570               nr = maps->num_face;
571               for (q = 0; q < maps->num_face; q++) {
572                 rows0[q]     = maps->c_maps[idx][q].gid;
573                 row_scale[q] = maps->c_maps[idx][q].scale;
574               }
575             }
576             for (g = 0; g < Nb; ++g) {
577               idx = Idxs[g];
578               if (idx >= 0) {
579                 nc = 1;
580                 cols0[0] = idx;
581                 col_scale[0] = 1.;
582               } else {
583                 idx = -idx - 1;
584                 nc = maps->num_face;
585                 for (q = 0; q < maps->num_face; q++) {
586                   cols0[q]     = maps->c_maps[idx][q].gid;
587                   col_scale[q] = maps->c_maps[idx][q].scale;
588                 }
589               }
590               const PetscInt    i = fieldA*Nb + f; /* Element matrix row */
591               const PetscInt    j = fieldA*Nb + g; /* Element matrix column */
592               const PetscScalar Aij = elemMat[i*totDim + j];
593               for (q = 0; q < nr; q++) rows[q] = rows0[q];
594               for (q = 0; q < nc; q++) cols[q] = cols0[q];
595               for (q = 0; q < nr; q++) {
596                 for (d = 0; d < nc; d++) {
597                   vals[q*nc + d] = row_scale[q]*col_scale[d]*Aij;
598                 }
599               }
600               ierr = MatSetValues(JacP,nr,rows,nc,cols,vals,ADD_VALUES);CHKERRQ(ierr);
601             }
602           }
603         }
604       }
605       if (ej==-1) {
606         PetscErrorCode    ierr2;
607         ierr2 = PetscPrintf(ctx->comm,"CPU Element matrix\n");CHKERRQ(ierr2);
608         for (d = 0; d < totDim; ++d) {
609           for (f = 0; f < totDim; ++f) {ierr2 = PetscPrintf(ctx->comm," %12.5e",  PetscRealPart(elemMat[d*totDim + f]));CHKERRQ(ierr2);}
610           ierr2 = PetscPrintf(ctx->comm,"\n");CHKERRQ(ierr2);
611         }
612         exit(12);
613       }
614       ierr = PetscLogEventEnd(ctx->events[6],0,0,0,0);CHKERRQ(ierr);
615     } /* ej cells loop, not cuda */
616     if (shift!=0.0) { // mass
617       ierr = PetscFree(elemMat);CHKERRQ(ierr);
618     } else {
619       ierr = PetscFree5(elemMat, ff, dudx, dudy, dudz);CHKERRQ(ierr);
620     }
621   } /* CPU version */
622 
623   /* assemble matrix or vector */
624   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
625   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
626 #define MAP_BF_SIZE (64*LANDAU_DIM*LANDAU_DIM*LANDAU_MAX_Q_FACE*LANDAU_MAX_SPECIES)
627   if (ctx->gpu_assembly && !container) {
628     PetscScalar             elemMatrix[LANDAU_MAX_NQ*LANDAU_MAX_NQ*LANDAU_MAX_SPECIES*LANDAU_MAX_SPECIES], *elMat;
629     pointInterpolationP4est pointMaps[MAP_BF_SIZE][LANDAU_MAX_Q_FACE];
630     PetscInt                q,eidx,fieldA;
631     MatType                 type;
632     ierr = PetscInfo1(ctx->plex, "Make GPU maps %D\n",1);CHKERRQ(ierr);
633     ierr = MatGetType(JacP,&type);CHKERRQ(ierr);
634     ierr = PetscLogEventBegin(ctx->events[2],0,0,0,0);CHKERRQ(ierr);
635     ierr = PetscMalloc(sizeof(P4estVertexMaps), &maps);CHKERRQ(ierr);
636     ierr = PetscContainerCreate(PETSC_COMM_SELF, &container);CHKERRQ(ierr);
637     ierr = PetscContainerSetPointer(container, (void *)maps);CHKERRQ(ierr);
638     ierr = PetscContainerSetUserDestroy(container, LandauGPUMapsDestroy);CHKERRQ(ierr);
639     ierr = PetscObjectCompose((PetscObject) JacP, "assembly_maps", (PetscObject) container);CHKERRQ(ierr);
640     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
641     // make maps
642     maps->data = NULL;
643     maps->num_elements = numCells;
644     maps->num_face = (PetscInt)(pow(Nq,1./((double)dim))+.001); // Q
645     maps->num_face = (PetscInt)(pow(maps->num_face,(double)(dim-1))+.001); // Q^2
646     maps->num_reduced = 0;
647     maps->deviceType = ctx->deviceType;
648 
649     // count reduced and get
650     ierr = PetscMalloc(maps->num_elements * sizeof *maps->gIdx, &maps->gIdx);CHKERRQ(ierr);
651     for (fieldA=0;fieldA<Nf;fieldA++) {
652       for (ej = cStart, eidx = 0 ; ej < cEnd; ++ej, ++eidx) {
653         for (q = 0; q < Nb; ++q) {
654           PetscInt    numindices,*indices;
655           PetscScalar *valuesOrig = elMat = elemMatrix;
656           ierr = PetscMemzero(elMat, totDim*totDim*sizeof(PetscScalar));CHKERRQ(ierr);
657           elMat[ (fieldA*Nb + q)*totDim + fieldA*Nb + q] = 1;
658           ierr = DMPlexGetClosureIndices(ctx->plex, section, globsection, ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
659           for (f = 0 ; f < numindices ; ++f) { // look for a non-zero on the diagonal
660             if (PetscAbs(PetscRealPart(elMat[f*numindices + f])) > PETSC_MACHINE_EPSILON) {
661               // found it
662               if (PetscAbs(PetscRealPart(elMat[f*numindices + f] - 1.)) < PETSC_MACHINE_EPSILON) {
663                 maps->gIdx[eidx][fieldA][q] = (LandauIdx)indices[f]; // normal vertex 1.0
664               } else { //found a constraint
665                 int       jj = 0;
666                 PetscReal sum = 0;
667                 const PetscInt ff = f;
668                 maps->gIdx[eidx][fieldA][q] = -maps->num_reduced - 1; // gid = -(idx+1): idx = -gid - 1
669                 do {  // constraints are continous in Plex - exploit that here
670                   int ii;
671                   for (ii = 0, pointMaps[maps->num_reduced][jj].scale = 0; ii < maps->num_face; ii++) { // DMPlex puts them all together
672                     if (ff + ii < numindices) {
673                       pointMaps[maps->num_reduced][jj].scale += PetscRealPart(elMat[f*numindices + ff + ii]);
674                     }
675                   }
676                   sum += pointMaps[maps->num_reduced][jj].scale;
677                   if (pointMaps[maps->num_reduced][jj].scale == 0) pointMaps[maps->num_reduced][jj].gid = -1; // 3D has Q and Q^2 interps -- all contiguous???
678                   else                                             pointMaps[maps->num_reduced][jj].gid = indices[f];
679                 } while (++jj < maps->num_face && ++f < numindices); // jj is incremented if we hit the end
680                 while (jj++ < maps->num_face) {
681                   pointMaps[maps->num_reduced][jj].scale = 0;
682                   pointMaps[maps->num_reduced][jj].gid = -1;
683                 }
684                 if (PetscAbs(sum-1.0) > 10*PETSC_MACHINE_EPSILON) { // debug
685                   int       d,f;
686                   PetscReal tmp = 0;
687                   PetscPrintf(PETSC_COMM_SELF,"\t\t%D.%D.%D) ERROR total I = %22.16e (LANDAU_MAX_Q_FACE=%d, #face=%D)\n",eidx,q,fieldA,sum,LANDAU_MAX_Q_FACE,maps->num_face);
688                   for (d = 0, tmp = 0; d < numindices; ++d) {
689                     if (tmp!=0 && PetscAbs(tmp-1.0) > 10*PETSC_MACHINE_EPSILON) ierr = PetscPrintf(PETSC_COMM_WORLD,"%3D) %3D: ",d,indices[d]);CHKERRQ(ierr);
690                     for (f = 0; f < numindices; ++f) {
691                       tmp += PetscRealPart(elMat[d*numindices + f]);
692                     }
693                     if (tmp!=0) ierr = PetscPrintf(ctx->comm," | %22.16e\n",tmp);CHKERRQ(ierr);
694                   }
695                 }
696                 maps->num_reduced++;
697                 if (maps->num_reduced>=MAP_BF_SIZE) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps->num_reduced %d > %d",maps->num_reduced,MAP_BF_SIZE);
698               }
699               break;
700             }
701           }
702           // cleanup
703           ierr = DMPlexRestoreClosureIndices(ctx->plex, section, globsection, ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
704           if (elMat != valuesOrig) {ierr = DMRestoreWorkArray(ctx->plex, numindices*numindices, MPIU_SCALAR, &elMat);CHKERRQ(ierr);}
705         }
706       }
707     }
708     // allocate and copy point datamaps->gIdx[eidx][field][q] -- for CPU version of this code, for debugging
709     ierr = PetscMalloc(maps->num_reduced * sizeof *maps->c_maps, &maps->c_maps);CHKERRQ(ierr);
710     for (ej = 0; ej < maps->num_reduced; ++ej) {
711       for (q = 0; q < maps->num_face; ++q) {
712         maps->c_maps[ej][q].scale = pointMaps[ej][q].scale;
713         maps->c_maps[ej][q].gid = pointMaps[ej][q].gid;
714       }
715     }
716 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
717     if (ctx->deviceType == LANDAU_KOKKOS) {
718       ierr = LandauKokkosCreateMatMaps(maps, pointMaps,Nf,Nq);CHKERRQ(ierr); // imples Kokkos does
719     } // else could be CUDA
720 #endif
721 #if defined(PETSC_HAVE_CUDA)
722     if (ctx->deviceType == LANDAU_CUDA) {
723       ierr = LandauCUDACreateMatMaps(maps, pointMaps,Nf,Nq);CHKERRQ(ierr);
724     }
725 #endif
726 
727     ierr = PetscLogEventEnd(ctx->events[2],0,0,0,0);CHKERRQ(ierr);
728   }
729   /* clean up */
730   if (IPf) {
731     ierr = PetscFree(IPf);CHKERRQ(ierr);
732   }
733   if (xdata) {
734     ierr = VecRestoreArrayReadAndMemType(a_X,&xdata);CHKERRQ(ierr);
735   }
736 
737   PetscFunctionReturn(0);
738 }
739 
740 #if defined(LANDAU_ADD_BCS)
741 static void zero_bc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
742                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
743                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
744                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
745 {
746   uexact[0] = 0;
747 }
748 #endif
749 
750 #define MATVEC2(__a,__x,__p) {int i,j; for (i=0.; i<2; i++) {__p[i] = 0; for (j=0.; j<2; j++) __p[i] += __a[i][j]*__x[j]; }}
751 static void CircleInflate(PetscReal r1, PetscReal r2, PetscReal r0, PetscInt num_sections, PetscReal x, PetscReal y,
752                           PetscReal *outX, PetscReal *outY)
753 {
754   PetscReal rr = PetscSqrtReal(x*x + y*y), outfact, efact;
755   if (rr < r1 + PETSC_SQRT_MACHINE_EPSILON) {
756     *outX = x; *outY = y;
757   } else {
758     const PetscReal xy[2] = {x,y}, sinphi=y/rr, cosphi=x/rr;
759     PetscReal       cth,sth,xyprime[2],Rth[2][2],rotcos,newrr;
760     if (num_sections==2) {
761       rotcos = 0.70710678118654;
762       outfact = 1.5; efact = 2.5;
763       /* rotate normalized vector into [-pi/4,pi/4) */
764       if (sinphi >= 0.) {         /* top cell, -pi/2 */
765         cth = 0.707106781186548; sth = -0.707106781186548;
766       } else {                    /* bottom cell -pi/8 */
767         cth = 0.707106781186548; sth = .707106781186548;
768       }
769     } else if (num_sections==3) {
770       rotcos = 0.86602540378443;
771       outfact = 1.5; efact = 2.5;
772       /* rotate normalized vector into [-pi/6,pi/6) */
773       if (sinphi >= 0.5) {         /* top cell, -pi/3 */
774         cth = 0.5; sth = -0.866025403784439;
775       } else if (sinphi >= -.5) {  /* mid cell 0 */
776         cth = 1.; sth = .0;
777       } else { /* bottom cell +pi/3 */
778         cth = 0.5; sth = 0.866025403784439;
779       }
780     } else if (num_sections==4) {
781       rotcos = 0.9238795325112;
782       outfact = 1.5; efact = 3;
783       /* rotate normalized vector into [-pi/8,pi/8) */
784       if (sinphi >= 0.707106781186548) {         /* top cell, -3pi/8 */
785         cth = 0.38268343236509; sth = -0.923879532511287;
786       } else if (sinphi >= 0.) {                 /* mid top cell -pi/8 */
787         cth = 0.923879532511287; sth = -.38268343236509;
788       } else if (sinphi >= -0.707106781186548) { /* mid bottom cell + pi/8 */
789         cth = 0.923879532511287; sth = 0.38268343236509;
790       } else {                                   /* bottom cell + 3pi/8 */
791         cth = 0.38268343236509; sth = .923879532511287;
792       }
793     } else {
794       cth = 0.; sth = 0.; rotcos = 0; efact = 0;
795     }
796     Rth[0][0] = cth; Rth[0][1] =-sth;
797     Rth[1][0] = sth; Rth[1][1] = cth;
798     MATVEC2(Rth,xy,xyprime);
799     if (num_sections==2) {
800       newrr = xyprime[0]/rotcos;
801     } else {
802       PetscReal newcosphi=xyprime[0]/rr, rin = r1, rout = rr - rin;
803       PetscReal routmax = r0*rotcos/newcosphi - rin, nroutmax = r0 - rin, routfrac = rout/routmax;
804       newrr = rin + routfrac*nroutmax;
805     }
806     *outX = cosphi*newrr; *outY = sinphi*newrr;
807     /* grade */
808     PetscReal fact,tt,rs,re, rr = PetscSqrtReal(PetscSqr(*outX) + PetscSqr(*outY));
809     if (rr > r2) { rs = r2; re = r0; fact = outfact;} /* outer zone */
810     else {         rs = r1; re = r2; fact = efact;} /* electron zone */
811     tt = (rs + PetscPowReal((rr - rs)/(re - rs),fact) * (re-rs)) / rr;
812     *outX *= tt;
813     *outY *= tt;
814   }
815 }
816 
817 static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
818 {
819   LandauCtx   *ctx = (LandauCtx*)a_ctx;
820   PetscReal   r = abc[0], z = abc[1];
821   if (ctx->inflate) {
822     PetscReal absR, absZ;
823     absR = PetscAbs(r);
824     absZ = PetscAbs(z);
825     CircleInflate(ctx->i_radius,ctx->e_radius,ctx->radius,ctx->num_sections,absR,absZ,&absR,&absZ);
826     r = (r > 0) ? absR : -absR;
827     z = (z > 0) ? absZ : -absZ;
828   }
829   xyz[0] = r;
830   xyz[1] = z;
831   if (dim==3) xyz[2] = abc[2];
832 
833   PetscFunctionReturn(0);
834 }
835 
836 static PetscErrorCode ErrorIndicator_Simple(PetscInt dim, PetscReal volume, PetscReal x[], PetscInt Nc, const PetscInt Nf[], const PetscScalar u[], const PetscScalar u_x[], PetscReal *error, void *actx)
837 {
838   PetscReal err = 0.0;
839   PetscInt  f = *(PetscInt*)actx, j;
840   PetscFunctionBegin;
841   for (j = 0; j < dim; ++j) {
842     err += PetscSqr(PetscRealPart(u_x[f*dim+j]));
843   }
844   err = PetscRealPart(u[f]); /* just use rho */
845   *error = volume * err; /* * (ctx->axisymmetric ? 2.*PETSC_PI * r : 1); */
846   PetscFunctionReturn(0);
847 }
848 
849 static PetscErrorCode LandauDMCreateVMesh(MPI_Comm comm, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM *dm)
850 {
851   PetscErrorCode ierr;
852   PetscReal      radius = ctx->radius;
853   size_t         len;
854   char           fname[128] = ""; /* we can add a file if we want */
855 
856   PetscFunctionBegin;
857   /* create DM */
858   ierr = PetscStrlen(fname, &len);CHKERRQ(ierr);
859   if (len) {
860     PetscInt dim2;
861     ierr = DMPlexCreateFromFile(comm, fname, ctx->interpolate, dm);CHKERRQ(ierr);
862     ierr = DMGetDimension(*dm, &dim2);CHKERRQ(ierr);
863     if (LANDAU_DIM != dim2) SETERRQ2(comm, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim2,LANDAU_DIM);
864   } else {    /* p4est, quads */
865     /* Create plex mesh of Landau domain */
866     if (!ctx->sphere) {
867       PetscInt       cells[] = {2,2,2};
868       PetscReal      lo[] = {-radius,-radius,-radius}, hi[] = {radius,radius,radius};
869       DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim==2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
870       for (int i=0;i<ctx->preAMRRefine;i++) for (int j=0;j<3;j++) cells[j] *= 2;
871       if (dim==2) { lo[0] = 0; cells[0] /= 2; }
872       ierr = DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, cells, lo, hi, periodicity, PETSC_TRUE, dm);CHKERRQ(ierr);
873       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr); /* needed for periodic */
874       if (dim==3) {ierr = PetscObjectSetName((PetscObject) *dm, "cube");CHKERRQ(ierr);}
875       else {ierr = PetscObjectSetName((PetscObject) *dm, "half-plane");CHKERRQ(ierr);}
876     } else if (dim==2) {
877       PetscInt       numCells,cells[16][4],i,j;
878       PetscInt       numVerts;
879       PetscReal      inner_radius1 = ctx->i_radius, inner_radius2 = ctx->e_radius;
880       PetscReal      *flatCoords = NULL;
881       PetscInt       *flatCells = NULL, *pcell;
882       if (ctx->num_sections==2) {
883 #if 1
884         numCells = 5;
885         numVerts = 10;
886         int cells2[][4] = { {0,1,4,3},
887                             {1,2,5,4},
888                             {3,4,7,6},
889                             {4,5,8,7},
890                             {6,7,8,9} };
891         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
892         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
893         {
894           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
895           for (j = 0; j < numVerts-1; j++) {
896             PetscReal z, r, theta = -PETSC_PI/2 + (j%3) * PETSC_PI/2;
897             PetscReal rad = (j >= 6) ? inner_radius1 : (j >= 3) ? inner_radius2 : ctx->radius;
898             z = rad * PetscSinReal(theta);
899             coords[j][1] = z;
900             r = rad * PetscCosReal(theta);
901             coords[j][0] = r;
902           }
903           coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
904         }
905 #else
906         numCells = 4;
907         numVerts = 8;
908         static int     cells2[][4] = {{0,1,2,3},
909                                       {4,5,1,0},
910                                       {5,6,2,1},
911                                       {6,7,3,2}};
912         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
913         ierr = loc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
914         {
915           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
916           PetscInt j;
917           for (j = 0; j < 8; j++) {
918             PetscReal z, r;
919             PetscReal theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3.;
920             PetscReal rad = ctx->radius * ((j < 4) ? 0.5 : 1.0);
921             z = rad * PetscSinReal(theta);
922             coords[j][1] = z;
923             r = rad * PetscCosReal(theta);
924             coords[j][0] = r;
925           }
926         }
927 #endif
928       } else if (ctx->num_sections==3) {
929         numCells = 7;
930         numVerts = 12;
931         int cells2[][4] = { {0,1,5,4},
932                             {1,2,6,5},
933                             {2,3,7,6},
934                             {4,5,9,8},
935                             {5,6,10,9},
936                             {6,7,11,10},
937                             {8,9,10,11} };
938         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
939         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
940         {
941           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
942           for (j = 0; j < numVerts; j++) {
943             PetscReal z, r, theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3;
944             PetscReal rad = (j >= 8) ? inner_radius1 : (j >= 4) ? inner_radius2 : ctx->radius;
945             z = rad * PetscSinReal(theta);
946             coords[j][1] = z;
947             r = rad * PetscCosReal(theta);
948             coords[j][0] = r;
949           }
950         }
951       } else if (ctx->num_sections==4) {
952         numCells = 10;
953         numVerts = 16;
954         int cells2[][4] = { {0,1,6,5},
955                             {1,2,7,6},
956                             {2,3,8,7},
957                             {3,4,9,8},
958                             {5,6,11,10},
959                             {6,7,12,11},
960                             {7,8,13,12},
961                             {8,9,14,13},
962                             {10,11,12,15},
963                             {12,13,14,15}};
964         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
965         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
966         {
967           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
968           for (j = 0; j < numVerts-1; j++) {
969             PetscReal z, r, theta = -PETSC_PI/2 + (j%5) * PETSC_PI/4;
970             PetscReal rad = (j >= 10) ? inner_radius1 : (j >= 5) ? inner_radius2 : ctx->radius;
971             z = rad * PetscSinReal(theta);
972             coords[j][1] = z;
973             r = rad * PetscCosReal(theta);
974             coords[j][0] = r;
975           }
976           coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
977         }
978       } else {
979         numCells = 0;
980         numVerts = 0;
981       }
982       for (j = 0, pcell = flatCells; j < numCells; j++, pcell += 4) {
983         pcell[0] = cells[j][0]; pcell[1] = cells[j][1];
984         pcell[2] = cells[j][2]; pcell[3] = cells[j][3];
985       }
986       ierr = DMPlexCreateFromCellListPetsc(comm,2,numCells,numVerts,4,ctx->interpolate,flatCells,2,flatCoords,dm);CHKERRQ(ierr);
987       ierr = PetscFree2(flatCoords,flatCells);CHKERRQ(ierr);
988       ierr = PetscObjectSetName((PetscObject) *dm, "semi-circle");CHKERRQ(ierr);
989     } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Velocity space meshes does not support cubed sphere");
990   }
991   ierr = PetscObjectSetOptionsPrefix((PetscObject)*dm,prefix);CHKERRQ(ierr);
992 
993   ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); /* Plex refine */
994 
995   { /* p4est? */
996     char      convType[256];
997     PetscBool flg;
998     ierr = PetscOptionsBegin(ctx->comm, prefix, "Mesh conversion options", "DMPLEX");CHKERRQ(ierr);
999     ierr = PetscOptionsFList("-dm_landau_type","Convert DMPlex to another format (should not be Plex!)","plexland.c",DMList,DMPLEX,convType,256,&flg);CHKERRQ(ierr);
1000     ierr = PetscOptionsEnd();CHKERRQ(ierr);
1001     if (flg) {
1002       DM dmforest;
1003       ierr = DMConvert(*dm,convType,&dmforest);CHKERRQ(ierr);
1004       if (dmforest) {
1005         PetscBool isForest;
1006         if (dmforest->prealloc_only != (*dm)->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"plex->prealloc_only != dm->prealloc_only");
1007         ierr = PetscObjectSetOptionsPrefix((PetscObject)dmforest,prefix);CHKERRQ(ierr);
1008         ierr = DMIsForest(dmforest,&isForest);CHKERRQ(ierr);
1009         if (isForest) {
1010           if (ctx->sphere && ctx->inflate) {
1011             ierr = DMForestSetBaseCoordinateMapping(dmforest,GeometryDMLandau,ctx);CHKERRQ(ierr);
1012           }
1013           if (dmforest->prealloc_only != (*dm)->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"plex->prealloc_only != dm->prealloc_only");
1014           ierr = DMDestroy(dm);CHKERRQ(ierr);
1015           *dm = dmforest;
1016           ctx->errorIndicator = ErrorIndicator_Simple; /* flag for Forest */
1017         } else SETERRQ(ctx->comm, PETSC_ERR_USER, "Converted to non Forest?");
1018       } else SETERRQ(ctx->comm, PETSC_ERR_USER, "Convert failed?");
1019     }
1020   }
1021   ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr);
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 static PetscErrorCode SetupDS(DM dm, PetscInt dim, LandauCtx *ctx)
1026 {
1027   PetscErrorCode  ierr;
1028   PetscInt        ii;
1029   PetscFunctionBegin;
1030   for (ii=0;ii<ctx->num_species;ii++) {
1031     char     buf[256];
1032     if (ii==0) ierr = PetscSNPrintf(buf, 256, "e");
1033     else {ierr = PetscSNPrintf(buf, 256, "i%D", ii);CHKERRQ(ierr);}
1034     /* Setup Discretization - FEM */
1035     ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &ctx->fe[ii]);CHKERRQ(ierr);
1036     ierr = PetscObjectSetName((PetscObject) ctx->fe[ii], buf);CHKERRQ(ierr);
1037     ierr = DMSetField(dm, ii, NULL, (PetscObject) ctx->fe[ii]);CHKERRQ(ierr);
1038   }
1039   ierr = DMCreateDS(dm);CHKERRQ(ierr);
1040   if (1) {
1041     PetscInt        ii;
1042     PetscSection    section;
1043     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1044     for (ii=0;ii<ctx->num_species;ii++) {
1045       char buf[256];
1046       if (ii==0) ierr = PetscSNPrintf(buf, 256, "se");
1047       else ierr = PetscSNPrintf(buf, 256, "si%D", ii);
1048       ierr = PetscSectionSetComponentName(section, ii, 0, buf);CHKERRQ(ierr);
1049     }
1050   }
1051   PetscFunctionReturn(0);
1052 }
1053 
1054 /* Define a Maxwellian function for testing out the operator. */
1055 
1056 /* Using cartesian velocity space coordinates, the particle */
1057 /* density, [1/m^3], is defined according to */
1058 
1059 /* $$ n=\int_{R^3} dv^3 \left(\frac{m}{2\pi T}\right)^{3/2}\exp [- mv^2/(2T)] $$ */
1060 
1061 /* Using some constant, c, we normalize the velocity vector into a */
1062 /* dimensionless variable according to v=c*x. Thus the density, $n$, becomes */
1063 
1064 /* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */
1065 
1066 /* Defining $\theta=2T/mc^2$, we thus find that the probability density */
1067 /* for finding the particle within the interval in a box dx^3 around x is */
1068 
1069 /* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */
1070 
1071 typedef struct {
1072   LandauCtx   *ctx;
1073   PetscReal kT_m;
1074   PetscReal n;
1075   PetscReal shift;
1076 } MaxwellianCtx;
1077 
1078 static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
1079 {
1080   MaxwellianCtx *mctx = (MaxwellianCtx*)actx;
1081   LandauCtx     *ctx = mctx->ctx;
1082   PetscInt      i;
1083   PetscReal     v2 = 0, theta = 2*mctx->kT_m/(ctx->v_0*ctx->v_0); /* theta = 2kT/mc^2 */
1084   PetscFunctionBegin;
1085   /* compute the exponents, v^2 */
1086   for (i = 0; i < dim; ++i) v2 += x[i]*x[i];
1087   /* evaluate the Maxwellian */
1088   u[0] = mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
1089   if (mctx->shift!=0.) {
1090     v2 = 0;
1091     for (i = 0; i < dim-1; ++i) v2 += x[i]*x[i];
1092     v2 += (x[dim-1]-mctx->shift)*(x[dim-1]-mctx->shift);
1093     /* evaluate the shifted Maxwellian */
1094     u[0] += mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
1095   }
1096   PetscFunctionReturn(0);
1097 }
1098 
1099 /*@
1100  LandauAddMaxwellians - Add a Maxwellian distribution to a state
1101 
1102  Collective on X
1103 
1104  Input Parameters:
1105  .   dm - The mesh
1106  +   time - Current time
1107  -   temps - Temperatures of each species
1108  .   ns - Number density of each species
1109  +   actx - Landau context
1110 
1111  Output Parameter:
1112  .   X  - The state
1113 
1114  Level: beginner
1115 
1116  .keywords: mesh
1117  .seealso: LandauCreateVelocitySpace()
1118  @*/
1119 PetscErrorCode LandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], void *actx)
1120 {
1121   LandauCtx      *ctx = (LandauCtx*)actx;
1122   PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *);
1123   PetscErrorCode ierr,ii;
1124   PetscInt       dim;
1125   MaxwellianCtx  *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];
1126 
1127   PetscFunctionBegin;
1128   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1129   if (!ctx) { ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr); }
1130   for (ii=0;ii<ctx->num_species;ii++) {
1131     mctxs[ii] = &data[ii];
1132     data[ii].ctx = ctx;
1133     data[ii].kT_m = ctx->k*temps[ii]/ctx->masses[ii]; /* kT/m */
1134     data[ii].n = ns[ii];
1135     initu[ii] = maxwellian;
1136     data[ii].shift = 0;
1137   }
1138   data[0].shift = ctx->electronShift;
1139   /* need to make ADD_ALL_VALUES work - TODO */
1140   ierr = DMProjectFunction(dm, time, initu, (void**)mctxs, INSERT_ALL_VALUES, X);CHKERRQ(ierr);
1141   PetscFunctionReturn(0);
1142 }
1143 
1144 /*
1145  LandauSetInitialCondition - Addes Maxwellians with context
1146 
1147  Collective on X
1148 
1149  Input Parameters:
1150  .   dm - The mesh
1151  +   actx - Landau context with T and n
1152 
1153  Output Parameter:
1154  .   X  - The state
1155 
1156  Level: beginner
1157 
1158  .keywords: mesh
1159  .seealso: LandauCreateVelocitySpace(), LandauAddMaxwellians()
1160  */
1161 static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, void *actx)
1162 {
1163   LandauCtx        *ctx = (LandauCtx*)actx;
1164   PetscErrorCode ierr;
1165   PetscFunctionBegin;
1166   if (!ctx) { ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr); }
1167   ierr = VecZeroEntries(X);CHKERRQ(ierr);
1168   ierr = LandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, ctx);CHKERRQ(ierr);
1169   PetscFunctionReturn(0);
1170 }
1171 
1172 static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscReal refineTol[], PetscReal coarsenTol[], PetscInt type, LandauCtx *ctx, DM *newDM)
1173 {
1174   DM               dm, plex, adaptedDM = NULL;
1175   PetscDS          prob;
1176   PetscBool        isForest;
1177   PetscQuadrature  quad;
1178   PetscInt         Nq, *Nb, cStart, cEnd, c, dim, qj, k;
1179   DMLabel          adaptLabel = NULL;
1180   PetscErrorCode   ierr;
1181 
1182   PetscFunctionBegin;
1183   ierr = VecGetDM(sol, &dm);CHKERRQ(ierr);
1184   ierr = DMCreateDS(dm);CHKERRQ(ierr);
1185   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1186   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1187   ierr = DMIsForest(dm, &isForest);CHKERRQ(ierr);
1188   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1189   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1190   ierr = DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);CHKERRQ(ierr);
1191   ierr = PetscFEGetQuadrature(fem, &quad);CHKERRQ(ierr);
1192   ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1193   if (Nq >LANDAU_MAX_NQ) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"Order too high. Nq = %D > LANDAU_MAX_NQ (%D)",Nq,LANDAU_MAX_NQ);
1194   ierr = PetscDSGetDimensions(prob, &Nb);CHKERRQ(ierr);
1195   if (type==4) {
1196     for (c = cStart; c < cEnd; c++) {
1197       ierr = DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);CHKERRQ(ierr);
1198     }
1199     ierr = PetscInfo1(sol, "Phase:%s: Uniform refinement\n","adaptToleranceFEM");CHKERRQ(ierr);
1200   } else if (type==2) {
1201     PetscInt  rCellIdx[8], eCellIdx[64], iCellIdx[64], eMaxIdx = -1, iMaxIdx = -1, nr = 0, nrmax = (dim==3) ? 8 : 2;
1202     PetscReal minRad = PETSC_INFINITY, r, eMinRad = PETSC_INFINITY, iMinRad = PETSC_INFINITY;
1203     for (c = 0; c < 64; c++) { eCellIdx[c] = iCellIdx[c] = -1; }
1204     for (c = cStart; c < cEnd; c++) {
1205       PetscReal    tt, v0[LANDAU_MAX_NQ*3], detJ[LANDAU_MAX_NQ];
1206       ierr = DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ);CHKERRQ(ierr);
1207       for (qj = 0; qj < Nq; ++qj) {
1208         tt = PetscSqr(v0[dim*qj+0]) + PetscSqr(v0[dim*qj+1]) + PetscSqr(((dim==3) ? v0[dim*qj+2] : 0));
1209         r = PetscSqrtReal(tt);
1210         if (r < minRad - PETSC_SQRT_MACHINE_EPSILON*10.) {
1211           minRad = r;
1212           nr = 0;
1213           rCellIdx[nr++]= c;
1214           ierr = PetscInfo4(sol, "\t\tPhase: adaptToleranceFEM Found first inner r=%e, cell %D, qp %D/%D\n", r, c, qj+1, Nq);CHKERRQ(ierr);
1215         } else if ((r-minRad) < PETSC_SQRT_MACHINE_EPSILON*100. && nr < nrmax) {
1216           for (k=0;k<nr;k++) if (c == rCellIdx[k]) break;
1217           if (k==nr) {
1218             rCellIdx[nr++]= c;
1219             ierr = PetscInfo5(sol, "\t\t\tPhase: adaptToleranceFEM Found another inner r=%e, cell %D, qp %D/%D, d=%e\n", r, c, qj+1, Nq, r-minRad);CHKERRQ(ierr);
1220           }
1221         }
1222         if (ctx->sphere) {
1223           if ((tt=r-ctx->e_radius) > 0) {
1224             PetscInfo2(sol, "\t\t\t %D cell r=%g\n",c,tt);
1225             if (tt < eMinRad - PETSC_SQRT_MACHINE_EPSILON*100.) {
1226               eMinRad = tt;
1227               eMaxIdx = 0;
1228               eCellIdx[eMaxIdx++] = c;
1229             } else if (eMaxIdx > 0 && (tt-eMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != eCellIdx[eMaxIdx-1]) {
1230               eCellIdx[eMaxIdx++] = c;
1231             }
1232           }
1233           if ((tt=r-ctx->i_radius) > 0) {
1234             if (tt < iMinRad - 1.e-5) {
1235               iMinRad = tt;
1236               iMaxIdx = 0;
1237               iCellIdx[iMaxIdx++] = c;
1238             } else if (iMaxIdx > 0 && (tt-iMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != iCellIdx[iMaxIdx-1]) {
1239               iCellIdx[iMaxIdx++] = c;
1240             }
1241           }
1242         }
1243       }
1244     }
1245     for (k=0;k<nr;k++) {
1246       ierr = DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE);CHKERRQ(ierr);
1247     }
1248     if (ctx->sphere) {
1249       for (c = 0; c < eMaxIdx; c++) {
1250         ierr = DMLabelSetValue(adaptLabel, eCellIdx[c], DM_ADAPT_REFINE);CHKERRQ(ierr);
1251         ierr = PetscInfo3(sol, "\t\tPhase:%s: refine sphere e cell %D r=%g\n","adaptToleranceFEM",eCellIdx[c],eMinRad);CHKERRQ(ierr);
1252       }
1253       for (c = 0; c < iMaxIdx; c++) {
1254         ierr = DMLabelSetValue(adaptLabel, iCellIdx[c], DM_ADAPT_REFINE);CHKERRQ(ierr);
1255         ierr = PetscInfo3(sol, "\t\tPhase:%s: refine sphere i cell %D r=%g\n","adaptToleranceFEM",iCellIdx[c],iMinRad);CHKERRQ(ierr);
1256       }
1257     }
1258     ierr = PetscInfo4(sol, "Phase:%s: Adaptive refine origin cells %D,%D r=%g\n","adaptToleranceFEM",rCellIdx[0],rCellIdx[1],minRad);CHKERRQ(ierr);
1259   } else if (type==0 || type==1 || type==3) { /* refine along r=0 axis */
1260     PetscScalar  *coef = NULL;
1261     Vec          coords;
1262     PetscInt     csize,Nv,d,nz;
1263     DM           cdm;
1264     PetscSection cs;
1265     ierr = DMGetCoordinatesLocal(dm, &coords);CHKERRQ(ierr);
1266     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
1267     ierr = DMGetLocalSection(cdm, &cs);CHKERRQ(ierr);
1268     for (c = cStart; c < cEnd; c++) {
1269       PetscInt doit = 0, outside = 0;
1270       ierr = DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef);CHKERRQ(ierr);
1271       Nv = csize/dim;
1272       for (nz = d = 0; d < Nv; d++) {
1273         PetscReal z = PetscRealPart(coef[d*dim + (dim-1)]), x = PetscSqr(PetscRealPart(coef[d*dim + 0])) + ((dim==3) ? PetscSqr(PetscRealPart(coef[d*dim + 1])) : 0);
1274         x = PetscSqrtReal(x);
1275         if (x < PETSC_MACHINE_EPSILON*10. && PetscAbs(z)<PETSC_MACHINE_EPSILON*10.) doit = 1;             /* refine origin */
1276         else if (type==0 && (z < -PETSC_MACHINE_EPSILON*10. || z > ctx->re_radius+PETSC_MACHINE_EPSILON*10.)) outside++;   /* first pass don't refine bottom */
1277         else if (type==1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) outside++; /* don't refine outside electron refine radius */
1278         else if (type==3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) outside++; /* don't refine outside ion refine radius */
1279         if (x < PETSC_MACHINE_EPSILON*10.) nz++;
1280       }
1281       ierr = DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef);CHKERRQ(ierr);
1282       if (doit || (outside<Nv && nz)) {
1283         ierr = DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);CHKERRQ(ierr);
1284       }
1285     }
1286     ierr = PetscInfo1(sol, "Phase:%s: RE refinement\n","adaptToleranceFEM");CHKERRQ(ierr);
1287   }
1288   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1289   ierr = DMAdaptLabel(dm, adaptLabel, &adaptedDM);CHKERRQ(ierr);
1290   ierr = DMLabelDestroy(&adaptLabel);CHKERRQ(ierr);
1291   *newDM = adaptedDM;
1292   if (adaptedDM) {
1293     if (isForest) {
1294       ierr = DMForestSetAdaptivityForest(adaptedDM,NULL);CHKERRQ(ierr);
1295     }
1296     ierr = DMConvert(adaptedDM, DMPLEX, &plex);CHKERRQ(ierr);
1297     ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1298     ierr = PetscInfo2(sol, "\tPhase: adaptToleranceFEM: %D cells, %d total quadrature points\n",cEnd-cStart,Nq*(cEnd-cStart));CHKERRQ(ierr);
1299     ierr = DMDestroy(&plex);CHKERRQ(ierr);
1300   }
1301   PetscFunctionReturn(0);
1302 }
1303 
1304 static PetscErrorCode adapt(DM *dm, LandauCtx *ctx, Vec *uu)
1305 {
1306   PetscErrorCode  ierr;
1307   PetscInt        type, limits[5] = {ctx->numRERefine,ctx->nZRefine1,ctx->maxRefIts,ctx->nZRefine2,ctx->postAMRRefine};
1308   PetscInt        adaptIter;
1309 
1310   PetscFunctionBegin;
1311   for (type=0;type<5;type++) {
1312     for (adaptIter = 0; adaptIter<limits[type];adaptIter++) {
1313       DM  dmNew = NULL;
1314       ierr = adaptToleranceFEM(ctx->fe[0], *uu, ctx->refineTol, ctx->coarsenTol, type, ctx, &dmNew);CHKERRQ(ierr);
1315       if (dmNew)  { // can happen with no AMR and post refinement
1316         ierr = DMDestroy(dm);CHKERRQ(ierr);
1317         ierr = VecDestroy(uu);CHKERRQ(ierr);
1318         ierr = DMCreateGlobalVector(dmNew,uu);CHKERRQ(ierr);
1319         ierr = PetscObjectSetName((PetscObject) *uu, "u");CHKERRQ(ierr);
1320         ierr = LandauSetInitialCondition(dmNew, *uu, ctx);CHKERRQ(ierr);
1321         *dm = dmNew;
1322       }
1323     }
1324   }
1325   PetscFunctionReturn(0);
1326 }
1327 
1328 static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
1329 {
1330   PetscErrorCode    ierr;
1331   PetscBool         flg, sph_flg;
1332   PetscInt          ii,nt,nm,nc;
1333   DM                dummy;
1334 
1335   PetscFunctionBegin;
1336   ierr = DMCreate(ctx->comm,&dummy);CHKERRQ(ierr);
1337   /* get options - initialize context */
1338   ctx->verbose = 1;
1339   ctx->interpolate = PETSC_TRUE;
1340   ctx->gpu_assembly = PETSC_TRUE;
1341   ctx->sphere = PETSC_FALSE;
1342   ctx->inflate = PETSC_FALSE;
1343   ctx->electronShift = 0;
1344   ctx->errorIndicator = NULL;
1345   ctx->radius = 5.; /* electron thermal radius (velocity) */
1346   ctx->re_radius = 0.;
1347   ctx->vperp0_radius1 = 0;
1348   ctx->vperp0_radius2 = 0;
1349   ctx->e_radius = .1;
1350   ctx->i_radius = .01;
1351   ctx->maxRefIts = 5;
1352   ctx->postAMRRefine = 0;
1353   ctx->preAMRRefine = 0;
1354   ctx->nZRefine1 = 0;
1355   ctx->nZRefine2 = 0;
1356   ctx->numRERefine = 0;
1357   ctx->aux_bool = PETSC_FALSE;
1358   ctx->num_sections = 3; /* 2, 3 or 4 */
1359   /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
1360   ctx->charges[0] = -1;  /* electron charge (MKS) */
1361   ctx->masses[0] = 1/1835.5; /* temporary value in proton mass */
1362   ctx->n[0] = 1;
1363   ctx->thermal_temps[0] = 1;
1364   /* constants, etc. */
1365   ctx->epsilon0 = 8.8542e-12; /* permittivity of free space (MKS) F/m */
1366   ctx->k = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
1367   ctx->lnLam = 10;         /* cross section ratio large - small angle collisions */
1368   ctx->n_0 = 1.e20;        /* typical plasma n, but could set it to 1 */
1369   ctx->Ez = 0;
1370   ctx->v_0 = 1; /* in electron thermal velocity */
1371   ctx->subThreadBlockSize = 1; /* for device and maybe OMP */
1372   ctx->numConcurrency = 1; /* for device */
1373   ctx->SData_d = NULL;     /* for device */
1374   ctx->times[0] = 0;
1375   ctx->init = PETSC_FALSE; // doit first time
1376   ctx->use_matrix_mass = PETSC_FALSE; /* fast but slightly fragile */
1377   ctx->plex = NULL;     /* cache as expensive to Convert */
1378   ctx->use_relativistic_corrections = PETSC_FALSE;
1379   ctx->use_energy_tensor_trick = PETSC_FALSE; /* Use Eero's trick for energy conservation v --> grad(v^2/2) */
1380   ierr = PetscOptionsBegin(ctx->comm, prefix, "Options for Fokker-Plank-Landau collision operator", "none");CHKERRQ(ierr);
1381   {
1382     char opstring[256];
1383 #if defined(PETSC_HAVE_KOKKOS)
1384     ctx->deviceType = LANDAU_KOKKOS;
1385     ierr = PetscStrcpy(opstring,"kokkos");CHKERRQ(ierr);
1386 #if defined(PETSC_HAVE_CUDA)
1387     ctx->subThreadBlockSize = 16;
1388 #endif
1389 #elif defined(PETSC_HAVE_CUDA)
1390     ctx->deviceType = LANDAU_CUDA;
1391     ierr = PetscStrcpy(opstring,"cuda");CHKERRQ(ierr);
1392 #else
1393     ctx->deviceType = LANDAU_CPU;
1394     ierr = PetscStrcpy(opstring,"cpu");CHKERRQ(ierr);
1395     ctx->subThreadBlockSize = 0;
1396 #endif
1397     ierr = PetscOptionsString("-dm_landau_device_type","Use kernels on 'cpu', 'cuda', or 'kokkos'","plexland.c",opstring,opstring,256,NULL);CHKERRQ(ierr);
1398     ierr = PetscStrcmp("cpu",opstring,&flg);CHKERRQ(ierr);
1399     if (flg) {
1400       ctx->deviceType = LANDAU_CPU;
1401       ctx->subThreadBlockSize = 0;
1402     } else {
1403       ierr = PetscStrcmp("cuda",opstring,&flg);CHKERRQ(ierr);
1404       if (flg) {
1405         ctx->deviceType = LANDAU_CUDA;
1406         ctx->subThreadBlockSize = 0;
1407       } else {
1408         ierr = PetscStrcmp("kokkos",opstring,&flg);CHKERRQ(ierr);
1409         if (flg) ctx->deviceType = LANDAU_KOKKOS;
1410         else SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_device_type %s",opstring);
1411       }
1412     }
1413   }
1414   ierr = PetscOptionsBool("-dm_landau_gpu_assembly", "Assemble Jacobian on GPU", "plexland.c", ctx->gpu_assembly, &ctx->gpu_assembly, NULL);CHKERRQ(ierr);
1415   ierr = PetscOptionsReal("-dm_landau_electron_shift","Shift in thermal velocity of electrons","none",ctx->electronShift,&ctx->electronShift, NULL);CHKERRQ(ierr);
1416   ierr = PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, &sph_flg);CHKERRQ(ierr);
1417   ierr = PetscOptionsBool("-dm_landau_inflate", "With sphere, inflate for curved edges (no AMR)", "plexland.c", ctx->inflate, &ctx->inflate, NULL);CHKERRQ(ierr);
1418   ierr = PetscOptionsInt("-dm_landau_amr_re_levels", "Number of levels to refine along v_perp=0, z>0", "plexland.c", ctx->numRERefine, &ctx->numRERefine, NULL);CHKERRQ(ierr);
1419   ierr = PetscOptionsInt("-dm_landau_amr_z_refine1",  "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine1, &ctx->nZRefine1, NULL);CHKERRQ(ierr);
1420   ierr = PetscOptionsInt("-dm_landau_amr_z_refine2",  "Number of levels to refine along v_perp=0", "plexland.c", ctx->nZRefine2, &ctx->nZRefine2, NULL);CHKERRQ(ierr);
1421   ierr = PetscOptionsInt("-dm_landau_amr_levels_max", "Number of AMR levels of refinement around origin after r=0 refinements", "plexland.c", ctx->maxRefIts, &ctx->maxRefIts, NULL);CHKERRQ(ierr);
1422   ierr = PetscOptionsInt("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &ctx->postAMRRefine, NULL);CHKERRQ(ierr);
1423   ierr = PetscOptionsInt("-dm_landau_amr_pre_refine", "Number of levels to uniformly refine before AMR", "plexland.c", ctx->preAMRRefine, &ctx->preAMRRefine, NULL);CHKERRQ(ierr);
1424   ierr = PetscOptionsInt("-dm_landau_verbose", "", "plexland.c", ctx->verbose, &ctx->verbose, NULL);CHKERRQ(ierr);
1425   ierr = 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);CHKERRQ(ierr);
1426   ierr = PetscOptionsReal("-dm_landau_z_radius1","velocity range to refine r=0 axis (for electrons)","plexland.c",ctx->vperp0_radius1,&ctx->vperp0_radius1, &flg);CHKERRQ(ierr);
1427   ierr = 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);CHKERRQ(ierr);
1428   ierr = PetscOptionsReal("-dm_landau_Ez","Initial parallel electric field in unites of Conner-Hastie criticle field","plexland.c",ctx->Ez,&ctx->Ez, NULL);CHKERRQ(ierr);
1429   ierr = PetscOptionsReal("-dm_landau_n_0","Normalization constant for number density","plexland.c",ctx->n_0,&ctx->n_0, NULL);CHKERRQ(ierr);
1430   ierr = PetscOptionsReal("-dm_landau_ln_lambda","Cross section parameter","plexland.c",ctx->lnLam,&ctx->lnLam, NULL);CHKERRQ(ierr);
1431   ierr = 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);CHKERRQ(ierr);
1432   ierr = PetscOptionsInt("-dm_landau_num_thread_teams", "The number of other concurrent runs to make room for", "plexland.c", ctx->numConcurrency, &ctx->numConcurrency, NULL);CHKERRQ(ierr);
1433   ierr = 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);CHKERRQ(ierr);
1434   ierr = PetscOptionsBool("-dm_landau_use_relativistic_corrections", "Use relativistic corrections", "plexland.c", ctx->use_relativistic_corrections, &ctx->use_relativistic_corrections, NULL);CHKERRQ(ierr);
1435   ierr = PetscOptionsBool("-dm_landau_use_energy_tensor_trick", "Use Eero's trick of using grad(v^2/2) instead of v as args to Landau tensor to conserve energy with relativistic corrections and Q1 elements", "plexland.c", ctx->use_energy_tensor_trick, &ctx->use_energy_tensor_trick, NULL);CHKERRQ(ierr);
1436 
1437   /* get num species with temperature*/
1438   {
1439     PetscReal arr[100];
1440     nt = 100;
1441     ierr = PetscOptionsRealArray("-dm_landau_thermal_temps", "Temperature of each species [e,i_0,i_1,...] in keV", "plexland.c", arr, &nt, &flg);CHKERRQ(ierr);
1442     if (flg && nt > LANDAU_MAX_SPECIES) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"-thermal_temps ,t1,t2,.. number of species %D > MAX %D",nt,LANDAU_MAX_SPECIES);
1443   }
1444   nt = LANDAU_MAX_SPECIES;
1445   for (ii=1;ii<LANDAU_MAX_SPECIES;ii++) {
1446     ctx->thermal_temps[ii] = 1.;
1447     ctx->charges[ii] = 1;
1448     ctx->masses[ii] = 1;
1449     ctx->n[ii] = (ii==1) ? 1 : 0;
1450   }
1451   ierr = 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);CHKERRQ(ierr);
1452   if (flg) {
1453     PetscInfo1(dummy, "num_species set to number of thermal temps provided (%D)\n",nt);
1454     ctx->num_species = nt;
1455   } else SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
1456   for (ii=0;ii<ctx->num_species;ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
1457   nm = LANDAU_MAX_SPECIES-1;
1458   ierr = 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);CHKERRQ(ierr);
1459   if (flg && nm != ctx->num_species-1) {
1460     SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"num ion masses %D != num species %D",nm,ctx->num_species-1);
1461   }
1462   nm = LANDAU_MAX_SPECIES;
1463   ierr = PetscOptionsRealArray("-dm_landau_n", "Normalized (by -n_0) number density of each species", "plexland.c", ctx->n, &nm, &flg);CHKERRQ(ierr);
1464   if (flg && nm != ctx->num_species) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"wrong num n: %D != num species %D",nm,ctx->num_species);
1465   ctx->n_0 *= ctx->n[0]; /* normalized number density */
1466   for (ii=1;ii<ctx->num_species;ii++) ctx->n[ii] = ctx->n[ii]/ctx->n[0];
1467   ctx->n[0] = 1;
1468   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
1469   ctx->masses[0] = 9.10938356e-31; /* electron mass kg (should be about right already) */
1470   ctx->m_0 = ctx->masses[0]; /* arbitrary reference mass, electrons */
1471   ierr = PetscOptionsReal("-dm_landau_v_0","Velocity to normalize with in units of initial electrons thermal velocity (not recommended to change default)","plexland.c",ctx->v_0,&ctx->v_0, NULL);CHKERRQ(ierr);
1472   ctx->v_0 *= PetscSqrtReal(ctx->k*ctx->thermal_temps[0]/(ctx->masses[0])); /* electron mean velocity in 1D (need 3D form in computing T from FE integral) */
1473   nc = LANDAU_MAX_SPECIES-1;
1474   ierr = 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);CHKERRQ(ierr);
1475   if (flg && nc != ctx->num_species-1) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"num charges %D != num species %D",nc,ctx->num_species-1);
1476   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
1477   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 */
1478   /* geometry */
1479   for (ii=0;ii<ctx->num_species;ii++) ctx->refineTol[ii]  = PETSC_MAX_REAL;
1480   for (ii=0;ii<ctx->num_species;ii++) ctx->coarsenTol[ii] = 0.;
1481   ii = LANDAU_MAX_SPECIES;
1482   ierr = PetscOptionsRealArray("-dm_landau_refine_tol","tolerance for refining cells in AMR","plexland.c",ctx->refineTol, &ii, &flg);CHKERRQ(ierr);
1483   if (flg && ii != ctx->num_species) ierr = PetscInfo2(dummy, "Phase: Warning, #refine_tol %D != num_species %D\n",ii,ctx->num_species);CHKERRQ(ierr);
1484   ii = LANDAU_MAX_SPECIES;
1485   ierr = PetscOptionsRealArray("-dm_landau_coarsen_tol","tolerance for coarsening cells in AMR","plexland.c",ctx->coarsenTol, &ii, &flg);CHKERRQ(ierr);
1486   if (flg && ii != ctx->num_species) ierr = PetscInfo2(dummy, "Phase: Warning, #coarsen_tol %D != num_species %D\n",ii,ctx->num_species);CHKERRQ(ierr);
1487   ierr = PetscOptionsReal("-dm_landau_domain_radius","Phase space size in units of electron thermal velocity","plexland.c",ctx->radius,&ctx->radius, &flg);CHKERRQ(ierr);
1488   if (flg && ctx->radius <= 0) { /* negative is ratio of c */
1489     if (ctx->radius == 0) ctx->radius = 0.75;
1490     else ctx->radius = -ctx->radius;
1491     ctx->radius = ctx->radius*C_0(ctx->v_0);
1492     ierr = PetscInfo1(dummy, "Change domain radius to %e\n",ctx->radius);CHKERRQ(ierr);
1493   }
1494   ierr = PetscOptionsReal("-dm_landau_i_radius","Ion thermal velocity, used for circular meshes","plexland.c",ctx->i_radius,&ctx->i_radius, &flg);CHKERRQ(ierr);
1495   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an ion radius but did not set sphere, user error really */
1496   if (!flg) {
1497     ctx->i_radius = 1.5*PetscSqrtReal(8*ctx->k*ctx->thermal_temps[1]/ctx->masses[1]/PETSC_PI)/ctx->v_0; /* normalized radius with thermal velocity of first ion */
1498   }
1499   ierr = PetscOptionsReal("-dm_landau_e_radius","Electron thermal velocity, used for circular meshes","plexland.c",ctx->e_radius,&ctx->e_radius, &flg);CHKERRQ(ierr);
1500   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an e radius but did not set sphere, user error really */
1501   if (!flg) {
1502     ctx->e_radius = 1.5*PetscSqrtReal(8*ctx->k*ctx->thermal_temps[0]/ctx->masses[0]/PETSC_PI)/ctx->v_0; /* normalized radius with thermal velocity of electrons */
1503   }
1504   if (ctx->sphere && (ctx->e_radius <= ctx->i_radius || ctx->radius <= ctx->e_radius)) SETERRQ3(ctx->comm,PETSC_ERR_ARG_WRONG,"bad radii: %g < %g < %g",ctx->i_radius,ctx->e_radius,ctx->radius);
1505   ierr = PetscOptionsInt("-dm_landau_sub_thread_block_size", "Number of threads in Kokkos integration point subblock", "plexland.c", ctx->subThreadBlockSize, &ctx->subThreadBlockSize, NULL);CHKERRQ(ierr);
1506   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1507   for (ii=ctx->num_species;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] = ctx->thermal_temps[ii]  = ctx->charges[ii] = 0;
1508   if (ctx->verbose > 0) {
1509     ierr = PetscPrintf(ctx->comm, "masses:        e=%10.3e; ions in proton mass units:   %10.3e %10.3e ...\n",ctx->masses[0],ctx->masses[1]/1.6720e-27,ctx->num_species>2 ? ctx->masses[2]/1.6720e-27 : 0);CHKERRQ(ierr);
1510     ierr = PetscPrintf(ctx->comm, "charges:       e=%10.3e; charges in elementary units: %10.3e %10.3e\n", ctx->charges[0],-ctx->charges[1]/ctx->charges[0],ctx->num_species>2 ? -ctx->charges[2]/ctx->charges[0] : 0);CHKERRQ(ierr);
1511     ierr = PetscPrintf(ctx->comm, "thermal T (K): e=%10.3e i=%10.3e imp=%10.3e. v_0=%10.3e (%10.3ec) n_0=%10.3e t_0=%10.3e domain=%10.3e c_0=%22.15e, %s, %s\n",ctx->thermal_temps[0],ctx->thermal_temps[1],ctx->num_species>2 ? ctx->thermal_temps[2] : 0,ctx->v_0,ctx->v_0/299792458.,ctx->n_0,ctx->t_0,ctx->radius,C_0(ctx->v_0),ctx->use_relativistic_corrections ? "relativistic" : "classical", ctx->use_energy_tensor_trick ? "Use trick" : "Intuitive");CHKERRQ(ierr);
1512   }
1513   ierr = DMDestroy(&dummy);CHKERRQ(ierr);
1514   {
1515     PetscMPIInt    rank;
1516     ierr = MPI_Comm_rank(ctx->comm, &rank);CHKERRMPI(ierr);
1517     /* PetscLogStage  setup_stage; */
1518     ierr = PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[11]);CHKERRQ(ierr); /* 11 */
1519     ierr = PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[0]);CHKERRQ(ierr); /* 0 */
1520     ierr = PetscLogEventRegister("Landau Mass", DM_CLASSID, &ctx->events[9]);CHKERRQ(ierr); /* 9 */
1521     ierr = PetscLogEventRegister(" Preamble", DM_CLASSID, &ctx->events[10]);CHKERRQ(ierr); /* 10 */
1522     ierr = PetscLogEventRegister(" static IP Data", DM_CLASSID, &ctx->events[7]);CHKERRQ(ierr); /* 7 */
1523     ierr = PetscLogEventRegister(" dynamic IP-Jac", DM_CLASSID, &ctx->events[1]);CHKERRQ(ierr); /* 1 */
1524     ierr = PetscLogEventRegister(" Kernel-init", DM_CLASSID, &ctx->events[3]);CHKERRQ(ierr); /* 3 */
1525     ierr = PetscLogEventRegister(" Jac-f-df (GPU)", DM_CLASSID, &ctx->events[8]);CHKERRQ(ierr); /* 8 */
1526     ierr = PetscLogEventRegister(" Kernel (GPU)", DM_CLASSID, &ctx->events[4]);CHKERRQ(ierr); /* 4 */
1527     ierr = PetscLogEventRegister(" Copy to CPU", DM_CLASSID, &ctx->events[5]);CHKERRQ(ierr); /* 5 */
1528     ierr = PetscLogEventRegister(" Jac-assemble", DM_CLASSID, &ctx->events[6]);CHKERRQ(ierr); /* 6 */
1529     ierr = PetscLogEventRegister(" Jac asmbl setup", DM_CLASSID, &ctx->events[2]);CHKERRQ(ierr); /* 2 */
1530     ierr = PetscLogEventRegister(" Other", DM_CLASSID, &ctx->events[13]);CHKERRQ(ierr); /* 13 */
1531 
1532     if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
1533       ierr = PetscOptionsClearValue(NULL,"-snes_converged_reason");CHKERRQ(ierr);
1534       ierr = PetscOptionsClearValue(NULL,"-ksp_converged_reason");CHKERRQ(ierr);
1535       ierr = PetscOptionsClearValue(NULL,"-snes_monitor");CHKERRQ(ierr);
1536       ierr = PetscOptionsClearValue(NULL,"-ksp_monitor");CHKERRQ(ierr);
1537       ierr = PetscOptionsClearValue(NULL,"-ts_monitor");CHKERRQ(ierr);
1538       ierr = PetscOptionsClearValue(NULL,"-ts_adapt_monitor");CHKERRQ(ierr);
1539       ierr = PetscOptionsClearValue(NULL,"-dm_landau_amr_dm_view");CHKERRQ(ierr);
1540       ierr = PetscOptionsClearValue(NULL,"-dm_landau_amr_vec_view");CHKERRQ(ierr);
1541       ierr = PetscOptionsClearValue(NULL,"-dm_landau_pre_dm_view");CHKERRQ(ierr);
1542       ierr = PetscOptionsClearValue(NULL,"-dm_landau_pre_vec_view");CHKERRQ(ierr);
1543       ierr = PetscOptionsClearValue(NULL,"-info");CHKERRQ(ierr);
1544     }
1545   }
1546   PetscFunctionReturn(0);
1547 }
1548 
1549 /*@C
1550  LandauCreateVelocitySpace - Create a DMPlex velocity space mesh
1551 
1552  Collective on comm
1553 
1554  Input Parameters:
1555  +   comm  - The MPI communicator
1556  .   dim - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
1557  -   prefix - prefix for options
1558 
1559  Output Parameter:
1560  .   dm  - The DM object representing the mesh
1561  +   X - A vector (user destroys)
1562  -   J - Optional matrix (object destroys)
1563 
1564  Level: beginner
1565 
1566  .keywords: mesh
1567  .seealso: DMPlexCreate(), LandauDestroyVelocitySpace()
1568  @*/
1569 PetscErrorCode LandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *dm)
1570 {
1571   PetscErrorCode ierr;
1572   LandauCtx      *ctx;
1573   PetscBool      prealloc_only,flg;
1574 
1575   PetscFunctionBegin;
1576   if (dim!=2 && dim!=3) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Only 2D and 3D supported");
1577   ierr = PetscNew(&ctx);CHKERRQ(ierr);
1578   ctx->comm = comm; /* used for diagnostics and global errors */
1579   /* process options */
1580   ierr = ProcessOptions(ctx,prefix);CHKERRQ(ierr);
1581   if (dim==2) ctx->use_relativistic_corrections = PETSC_FALSE;
1582   /* Create Mesh */
1583   ierr = LandauDMCreateVMesh(PETSC_COMM_SELF, dim, prefix, ctx, dm);CHKERRQ(ierr);
1584   prealloc_only = (*dm)->prealloc_only;
1585   ierr = DMViewFromOptions(*dm,NULL,"-dm_landau_pre_dm_view");CHKERRQ(ierr);
1586   ierr = DMSetApplicationContext(*dm, ctx);CHKERRQ(ierr);
1587   /* create FEM */
1588   ierr = SetupDS(*dm,dim,ctx);CHKERRQ(ierr);
1589   /* set initial state */
1590   ierr = DMCreateGlobalVector(*dm,X);CHKERRQ(ierr);
1591   ierr = PetscObjectSetName((PetscObject) *X, "u");CHKERRQ(ierr);
1592   /* initial static refinement, no solve */
1593   ierr = LandauSetInitialCondition(*dm, *X, ctx);CHKERRQ(ierr);
1594   ierr = VecViewFromOptions(*X, NULL, "-dm_landau_pre_vec_view");CHKERRQ(ierr);
1595   /* forest refinement */
1596   if (ctx->errorIndicator) {
1597     /* AMR */
1598     ierr = adapt(dm,ctx,X);CHKERRQ(ierr);
1599     if ((*dm)->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"(*dm)->prealloc_only != prealloc_only");
1600     ierr = DMViewFromOptions(*dm,NULL,"-dm_landau_amr_dm_view");CHKERRQ(ierr);
1601     ierr = VecViewFromOptions(*X, NULL, "-dm_landau_amr_vec_view");CHKERRQ(ierr);
1602   }
1603   ierr = DMSetApplicationContext(*dm, ctx);CHKERRQ(ierr);
1604   ctx->dmv = *dm;
1605   if (ctx->dmv->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"ctx->dmv->prealloc_only != prealloc_only");
1606   ierr = DMCreateMatrix(ctx->dmv, &ctx->J);CHKERRQ(ierr);
1607   ierr = MatSetOption(ctx->J, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
1608   ierr = MatSetOption(ctx->J, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);CHKERRQ(ierr);
1609   if (J) *J = ctx->J;
1610   /* check for types that we need */
1611 #if defined(PETSC_HAVE_KOKKOS)
1612   if (ctx->deviceType == LANDAU_CPU) {
1613     ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,MATAIJKOKKOS,"");CHKERRQ(ierr);
1614   }
1615 #elif defined(PETSC_HAVE_CUDA)
1616   if (ctx->deviceType == LANDAU_CPU) {
1617     ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");CHKERRQ(ierr);
1618   }
1619 #endif
1620   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
1621     if (ctx->deviceType == LANDAU_CUDA) {
1622       ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");CHKERRQ(ierr);
1623       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must use '-dm_mat_type aijcusparse -dm_vec_type cuda' for GPU assembly and Cuda");
1624     } else if (ctx->deviceType == LANDAU_KOKKOS) {
1625       ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,MATAIJKOKKOS,"");CHKERRQ(ierr);
1626 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1627       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for GPU assembly and Kokkos");
1628 #else
1629       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must configure with '--download-kokkos-kernels=1' for GPU assembly and Kokkos");
1630 #endif
1631     }
1632   }
1633   PetscFunctionReturn(0);
1634 }
1635 
1636 /*@
1637  LandauDestroyVelocitySpace - Destroy a DMPlex velocity space mesh
1638 
1639  Collective on dm
1640 
1641  Input/Output Parameters:
1642  .   dm - the dm to destroy
1643 
1644  Level: beginner
1645 
1646  .keywords: mesh
1647  .seealso: LandauCreateVelocitySpace()
1648  @*/
1649 PetscErrorCode LandauDestroyVelocitySpace(DM *dm)
1650 {
1651   PetscErrorCode ierr,ii;
1652   LandauCtx      *ctx;
1653   PetscContainer container = NULL;
1654   PetscFunctionBegin;
1655   ierr = DMGetApplicationContext(*dm, &ctx);CHKERRQ(ierr);
1656   ierr = PetscObjectQuery((PetscObject)ctx->J,"coloring", (PetscObject*)&container);CHKERRQ(ierr);
1657   if (container) {
1658     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
1659   }
1660   ierr = MatDestroy(&ctx->M);CHKERRQ(ierr);
1661   ierr = MatDestroy(&ctx->J);CHKERRQ(ierr);
1662   for (ii=0;ii<ctx->num_species;ii++) {
1663     ierr = PetscFEDestroy(&ctx->fe[ii]);CHKERRQ(ierr);
1664   }
1665   if (ctx->deviceType == LANDAU_CUDA) {
1666 #if defined(PETSC_HAVE_CUDA)
1667     ierr = LandauCUDAStaticDataClear(ctx->SData_d);CHKERRQ(ierr);
1668 #else
1669     SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
1670 #endif
1671   } else if (ctx->deviceType == LANDAU_KOKKOS) {
1672 #if defined(PETSC_HAVE_KOKKOS)
1673     ierr = LandauKokkosStaticDataClear(ctx->SData_d);CHKERRQ(ierr);
1674 #else
1675     SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
1676 #endif
1677   } else {
1678     if (ctx->SData_d) { /* in a CPU run */
1679       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, *mass_w = (PetscReal*)ctx->SData_d->mass_w;
1680       ierr = PetscFree5(mass_w,ww,xx,yy,invJ);CHKERRQ(ierr);
1681       if (zz) {
1682         ierr = PetscFree(zz);CHKERRQ(ierr);
1683       }
1684     }
1685   }
1686   ierr = PetscFree(ctx->SData_d);CHKERRQ(ierr);
1687   if (ctx->times[0] > 0) {
1688     ierr = PetscPrintf(ctx->comm, "Landau Operator       %d 1.0 %10.3e ....\n",10000,ctx->times[0]);CHKERRQ(ierr);
1689   }
1690   if (ctx->plex != NULL) {
1691     ierr = DMDestroy(&ctx->plex);CHKERRQ(ierr);
1692   }
1693   PetscFree(ctx);
1694   ierr = DMDestroy(dm);CHKERRQ(ierr);
1695   PetscFunctionReturn(0);
1696 }
1697 
1698 /* < v, ru > */
1699 static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1700                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1701                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1702                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1703 {
1704   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1705   f0[0] = u[ii];
1706 }
1707 
1708 /* < v, ru > */
1709 static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1710                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1711                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1712                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1713 {
1714   PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
1715   f0[0] = x[jj]*u[ii]; /* x momentum */
1716 }
1717 
1718 static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1719                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1720                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1721                     PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1722 {
1723   PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
1724   double tmp1 = 0.;
1725   for (i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1726   f0[0] = tmp1*u[ii];
1727 }
1728 
1729 static PetscErrorCode gamma_n_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *actx)
1730 {
1731   const PetscReal *c2_0_arr = ((PetscReal*)actx);
1732   const PetscReal c02 = c2_0_arr[0];
1733 
1734   PetscFunctionBegin;
1735   for (int s = 0 ; s < Nf ; s++) {
1736     PetscReal tmp1 = 0.;
1737     for (int i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1738 #if defined(PETSC_USE_DEBUG)
1739     u[s] = PetscSqrtReal(1. + tmp1/c02);//  u[0] = PetscSqrtReal(1. + xx);
1740 #else
1741     {
1742       PetscReal xx = tmp1/c02;
1743       u[s] = xx/(PetscSqrtReal(1. + xx) + 1.); // better conditioned = xx/(PetscSqrtReal(1. + xx) + 1.)
1744     }
1745 #endif
1746   }
1747   PetscFunctionReturn(0);
1748 }
1749 
1750 /* < v, ru > */
1751 static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1752                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1753                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1754                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1755 {
1756   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1757   f0[0] = 2.*PETSC_PI*x[0]*u[ii];
1758 }
1759 
1760 /* < v, ru > */
1761 static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1762                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1763                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1764                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1765 {
1766   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1767   f0[0] = 2.*PETSC_PI*x[0]*x[1]*u[ii];
1768 }
1769 
1770 static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1771                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1772                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1773                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1774 {
1775   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1776   f0[0] =  2.*PETSC_PI*x[0]*(x[0]*x[0] + x[1]*x[1])*u[ii];
1777 }
1778 
1779 /*@
1780  LandauPrintNorms - collects moments and prints them
1781 
1782  Collective on dm
1783 
1784  Input Parameters:
1785  +   X  - the state
1786  -   stepi - current step to print
1787 
1788  Level: beginner
1789 
1790  .keywords: mesh
1791  .seealso: LandauCreateVelocitySpace()
1792  @*/
1793 PetscErrorCode LandauPrintNorms(Vec X, PetscInt stepi)
1794 {
1795   PetscErrorCode ierr;
1796   LandauCtx      *ctx;
1797   PetscDS        prob;
1798   DM             dm;
1799   PetscInt       cStart, cEnd, dim, ii;
1800   PetscScalar    xmomentumtot=0, ymomentumtot=0, zmomentumtot=0, energytot=0, densitytot=0, tt[LANDAU_MAX_SPECIES];
1801   PetscScalar    xmomentum[LANDAU_MAX_SPECIES],  ymomentum[LANDAU_MAX_SPECIES],  zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
1802 
1803   PetscFunctionBegin;
1804   ierr = VecGetDM(X, &dm);CHKERRQ(ierr);
1805   if (!dm) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no DM");
1806   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1807   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
1808   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1809   if (!ctx->plex) {
1810     ierr = DMConvert(ctx->dmv, DMPLEX, &ctx->plex);CHKERRQ(ierr);
1811   }
1812   ierr = DMCreateDS(ctx->plex);CHKERRQ(ierr);
1813   ierr = DMGetDS(ctx->plex, &prob);CHKERRQ(ierr);
1814   /* print momentum and energy */
1815   for (ii=0;ii<ctx->num_species;ii++) {
1816     PetscScalar user[2] = { (PetscScalar)ii, (PetscScalar)ctx->charges[ii]};
1817     ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1818     if (dim==2) { /* 2/3X + 3V (cylindrical coordinates) */
1819       ierr = PetscDSSetObjective(prob, 0, &f0_s_rden);CHKERRQ(ierr);
1820       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1821       density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1822       ierr = PetscDSSetObjective(prob, 0, &f0_s_rmom);CHKERRQ(ierr);
1823       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1824       zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1825       ierr = PetscDSSetObjective(prob, 0, &f0_s_rv2);CHKERRQ(ierr);
1826       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1827       energy[ii] = tt[0]*0.5*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1828       zmomentumtot += zmomentum[ii];
1829       energytot  += energy[ii];
1830       densitytot += density[ii];
1831       ierr = PetscPrintf(ctx->comm, "%3D) species-%D: charge density= %20.13e z-momentum= %20.13e energy= %20.13e",stepi,ii,PetscRealPart(density[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));CHKERRQ(ierr);
1832     } else { /* 2/3X + 3V */
1833       ierr = PetscDSSetObjective(prob, 0, &f0_s_den);CHKERRQ(ierr);
1834       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1835       density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1836       ierr = PetscDSSetObjective(prob, 0, &f0_s_mom);CHKERRQ(ierr);
1837       user[1] = 0;
1838       ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1839       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1840       xmomentum[ii]  = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1841       user[1] = 1;
1842       ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1843       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1844       ymomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1845       user[1] = 2;
1846       ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1847       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1848       zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1849       if (ctx->use_relativistic_corrections) {
1850         if (ii==0) {
1851           Vec            gamma_glob,Mf,v1,v2;
1852           PetscErrorCode (*gammaf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {gamma_n_f};
1853           PetscReal      *c2_0[1], data[1];
1854           PetscInt       N;
1855 
1856           data[0] = PetscSqr(C_0(ctx->v_0));
1857           ierr = DMGetGlobalVector(dm,&gamma_glob);CHKERRQ(ierr);
1858           ierr = DMGetGlobalVector(dm,&Mf);CHKERRQ(ierr);
1859           c2_0[0] = &data[0];
1860           ierr = DMProjectFunction(dm, 0., gammaf, (void**)c2_0, INSERT_ALL_VALUES, gamma_glob);CHKERRQ(ierr);
1861           ierr = MatMult(ctx->M,X,Mf);CHKERRQ(ierr);
1862           // get each component
1863           ierr = VecGetSize(X,&N);CHKERRQ(ierr);
1864           ierr = VecCreate(ctx->comm,&v1);CHKERRQ(ierr);
1865           ierr = VecSetSizes(v1,PETSC_DECIDE,N/ctx->num_species);CHKERRQ(ierr);
1866           ierr = VecCreate(ctx->comm,&v2);CHKERRQ(ierr);
1867           ierr = VecSetSizes(v2,PETSC_DECIDE,N/ctx->num_species);CHKERRQ(ierr);
1868           ierr = VecGetBlockSize(gamma_glob,&N);CHKERRQ(ierr);
1869           ierr = VecSetFromOptions(v1);CHKERRQ(ierr);
1870           ierr = VecSetFromOptions(v2);CHKERRQ(ierr);
1871           for (int i=0;i<ctx->num_species;i++) {
1872             PetscScalar val;
1873             ierr = VecStrideGather(gamma_glob,i,v1,INSERT_VALUES);CHKERRQ(ierr);
1874             ierr = VecStrideGather(Mf,i,v2,INSERT_VALUES);CHKERRQ(ierr);
1875             ierr = VecDot(v1,v2,&val);CHKERRQ(ierr);
1876             energy[i] = PetscRealPart(val)*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[i];
1877           }
1878           ierr = DMRestoreGlobalVector(dm, &gamma_glob);CHKERRQ(ierr);
1879           ierr = DMRestoreGlobalVector(dm, &Mf);CHKERRQ(ierr);
1880           ierr = VecDestroy(&v1);CHKERRQ(ierr);
1881           ierr = VecDestroy(&v2);CHKERRQ(ierr);
1882          }
1883       } else {
1884         ierr = PetscDSSetObjective(prob, 0, &f0_s_v2);CHKERRQ(ierr);
1885         ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1886         energy[ii]    = 0.5*tt[0]*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1887       }
1888       ierr = PetscPrintf(ctx->comm, "%3D) species %D: density=%20.13e, x-momentum=%20.13e, y-momentum=%20.13e, z-momentum=%20.13e, energy=%21.13e",
1889                          stepi,ii,PetscRealPart(density[ii]),PetscRealPart(xmomentum[ii]),PetscRealPart(ymomentum[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));CHKERRQ(ierr);
1890       xmomentumtot += xmomentum[ii];
1891       ymomentumtot += ymomentum[ii];
1892       zmomentumtot += zmomentum[ii];
1893       energytot  += energy[ii];
1894       densitytot += density[ii];
1895     }
1896     if (ctx->num_species>1) PetscPrintf(ctx->comm, "\n");
1897   }
1898   /* totals */
1899   ierr = DMPlexGetHeightStratum(ctx->plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1900   if (ctx->num_species>1) {
1901     if (dim==2) {
1902       ierr = PetscPrintf(ctx->comm, "\t%3D) Total: charge density=%21.13e, momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %D cells)",
1903                          stepi,(double)PetscRealPart(densitytot),(double)PetscRealPart(zmomentumtot),(double)PetscRealPart(energytot),(double)(ctx->masses[1]/ctx->masses[0]),cEnd-cStart);CHKERRQ(ierr);
1904     } else {
1905       ierr = PetscPrintf(ctx->comm, "\t%3D) Total: charge density=%21.13e, x-momentum=%21.13e, y-momentum=%21.13e, z-momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %D cells)",
1906                          stepi,(double)PetscRealPart(densitytot),(double)PetscRealPart(xmomentumtot),(double)PetscRealPart(ymomentumtot),(double)PetscRealPart(zmomentumtot),(double)PetscRealPart(energytot),(double)(ctx->masses[1]/ctx->masses[0]),cEnd-cStart);CHKERRQ(ierr);
1907     }
1908   } else {
1909     ierr = PetscPrintf(ctx->comm, " -- %D cells",cEnd-cStart);CHKERRQ(ierr);
1910   }
1911   if (ctx->verbose > 1) {ierr = PetscPrintf(ctx->comm,", %D sub (vector) threads\n",ctx->subThreadBlockSize);CHKERRQ(ierr);}
1912   else {ierr = PetscPrintf(ctx->comm,"\n");CHKERRQ(ierr);}
1913   PetscFunctionReturn(0);
1914 }
1915 
1916 static PetscErrorCode destroy_coloring (void *is)
1917 {
1918   ISColoring tmp = (ISColoring)is;
1919   return ISColoringDestroy(&tmp);
1920 }
1921 
1922 /*@
1923  LandauCreateColoring - create a coloring and add to matrix (Landau context used just for 'print' flag, should be in DMPlex)
1924 
1925  Collective on JacP
1926 
1927  Input Parameters:
1928  +   JacP  - matrix to add coloring to
1929  -   plex - The DM
1930 
1931  Output Parameter:
1932  .   container  - Container with coloring
1933 
1934  Level: beginner
1935 
1936  .keywords: mesh
1937  .seealso: LandauCreateVelocitySpace()
1938  @*/
1939 PetscErrorCode LandauCreateColoring(Mat JacP, DM plex, PetscContainer *container)
1940 {
1941   PetscErrorCode  ierr;
1942   PetscInt        dim,cell,i,ej,nc,Nv,totDim,numGCells,cStart,cEnd;
1943   ISColoring      iscoloring = NULL;
1944   Mat             G,Q;
1945   PetscScalar     ones[128];
1946   MatColoring     mc;
1947   IS             *is;
1948   PetscInt        csize,colour,j,k;
1949   const PetscInt *indices;
1950   PetscInt       numComp[1];
1951   PetscInt       numDof[4];
1952   PetscFE        fe;
1953   DM             colordm;
1954   PetscSection   csection, section, globalSection;
1955   PetscDS        prob;
1956   LandauCtx      *ctx;
1957 
1958   PetscFunctionBegin;
1959   ierr = DMGetApplicationContext(plex, &ctx);CHKERRQ(ierr);
1960   ierr = DMGetLocalSection(plex, &section);CHKERRQ(ierr);
1961   ierr = DMGetGlobalSection(plex, &globalSection);CHKERRQ(ierr);
1962   ierr = DMGetDimension(plex, &dim);CHKERRQ(ierr);
1963   ierr = DMGetDS(plex, &prob);CHKERRQ(ierr);
1964   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1965   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1966   numGCells = cEnd - cStart;
1967   /* create cell centered DM */
1968   ierr = DMClone(plex, &colordm);CHKERRQ(ierr);
1969   ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, "color_", PETSC_DECIDE, &fe);CHKERRQ(ierr);
1970   ierr = PetscObjectSetName((PetscObject) fe, "color");CHKERRQ(ierr);
1971   ierr = DMSetField(colordm, 0, NULL, (PetscObject)fe);CHKERRQ(ierr);
1972   ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
1973   for (i = 0; i < (dim+1); ++i) numDof[i] = 0;
1974   numDof[dim] = 1;
1975   numComp[0] = 1;
1976   ierr = DMPlexCreateSection(colordm, NULL, numComp, numDof, 0, NULL, NULL, NULL, NULL, &csection);CHKERRQ(ierr);
1977   ierr = PetscSectionSetFieldName(csection, 0, "color");CHKERRQ(ierr);
1978   ierr = DMSetLocalSection(colordm, csection);CHKERRQ(ierr);
1979   ierr = DMViewFromOptions(colordm,NULL,"-color_dm_view");CHKERRQ(ierr);
1980   /* get vertex to element map Q and colroing graph G */
1981   ierr = MatGetSize(JacP,NULL,&Nv);CHKERRQ(ierr);
1982   ierr = MatCreateAIJ(PETSC_COMM_SELF,PETSC_DECIDE,PETSC_DECIDE,numGCells,Nv,totDim,NULL,0,NULL,&Q);CHKERRQ(ierr);
1983   for (i=0;i<128;i++) ones[i] = 1.0;
1984   for (cell = cStart, ej = 0 ; cell < cEnd; ++cell, ++ej) {
1985     PetscInt numindices,*indices;
1986     ierr = DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);CHKERRQ(ierr);
1987     if (numindices>128) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many indices. %D > %D",numindices,128);
1988     ierr = MatSetValues(Q,1,&ej,numindices,indices,ones,ADD_VALUES);CHKERRQ(ierr);
1989     ierr = DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);CHKERRQ(ierr);
1990   }
1991   ierr = MatAssemblyBegin(Q, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1992   ierr = MatAssemblyEnd(Q, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1993   ierr = MatMatTransposeMult(Q,Q,MAT_INITIAL_MATRIX,4.0,&G);CHKERRQ(ierr);
1994   ierr = PetscObjectSetName((PetscObject) Q, "Q");CHKERRQ(ierr);
1995   ierr = PetscObjectSetName((PetscObject) G, "coloring graph");CHKERRQ(ierr);
1996   ierr = MatViewFromOptions(G,NULL,"-coloring_mat_view");CHKERRQ(ierr);
1997   ierr = MatViewFromOptions(Q,NULL,"-coloring_mat_view");CHKERRQ(ierr);
1998   ierr = MatDestroy(&Q);CHKERRQ(ierr);
1999   /* coloring */
2000   ierr = MatColoringCreate(G,&mc);CHKERRQ(ierr);
2001   ierr = MatColoringSetDistance(mc,1);CHKERRQ(ierr);
2002   ierr = MatColoringSetType(mc,MATCOLORINGJP);CHKERRQ(ierr);
2003   ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
2004   ierr = MatColoringApply(mc,&iscoloring);CHKERRQ(ierr);
2005   ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
2006   /* view */
2007   ierr = ISColoringViewFromOptions(iscoloring,NULL,"-coloring_is_view");CHKERRQ(ierr);
2008   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);CHKERRQ(ierr);
2009   if (ctx && ctx->verbose > 2) {
2010     PetscViewer    viewer;
2011     Vec            color_vec, eidx_vec;
2012     ierr = DMGetGlobalVector(colordm, &color_vec);CHKERRQ(ierr);
2013     ierr = DMGetGlobalVector(colordm, &eidx_vec);CHKERRQ(ierr);
2014     for (colour=0; colour<nc; colour++) {
2015       ierr = ISGetLocalSize(is[colour],&csize);CHKERRQ(ierr);
2016       ierr = ISGetIndices(is[colour],&indices);CHKERRQ(ierr);
2017       for (j=0; j<csize; j++) {
2018         PetscScalar v = (PetscScalar)colour;
2019         k = indices[j];
2020         ierr = VecSetValues(color_vec,1,&k,&v,INSERT_VALUES);CHKERRQ(ierr);
2021         v = (PetscScalar)k;
2022         ierr = VecSetValues(eidx_vec,1,&k,&v,INSERT_VALUES);CHKERRQ(ierr);
2023       }
2024       ierr = ISRestoreIndices(is[colour],&indices);CHKERRQ(ierr);
2025     }
2026     /* view */
2027     ierr = PetscViewerVTKOpen(ctx->comm, "color.vtu", FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
2028     ierr = PetscObjectSetName((PetscObject) color_vec, "color");CHKERRQ(ierr);
2029     ierr = VecView(color_vec, viewer);CHKERRQ(ierr);
2030     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2031     ierr = PetscViewerVTKOpen(ctx->comm, "eidx.vtu", FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
2032     ierr = PetscObjectSetName((PetscObject) eidx_vec, "element-idx");CHKERRQ(ierr);
2033     ierr = VecView(eidx_vec, viewer);CHKERRQ(ierr);
2034     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2035     ierr = DMRestoreGlobalVector(colordm, &color_vec);CHKERRQ(ierr);
2036     ierr = DMRestoreGlobalVector(colordm, &eidx_vec);CHKERRQ(ierr);
2037   }
2038   ierr = PetscSectionDestroy(&csection);CHKERRQ(ierr);
2039   ierr = DMDestroy(&colordm);CHKERRQ(ierr);
2040   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);CHKERRQ(ierr);
2041   ierr = MatDestroy(&G);CHKERRQ(ierr);
2042   /* stash coloring */
2043   ierr = PetscContainerCreate(PETSC_COMM_SELF, container);CHKERRQ(ierr);
2044   ierr = PetscContainerSetPointer(*container,(void*)iscoloring);CHKERRQ(ierr);
2045   ierr = PetscContainerSetUserDestroy(*container, destroy_coloring);CHKERRQ(ierr);
2046   ierr = PetscObjectCompose((PetscObject)JacP,"coloring",(PetscObject)*container);CHKERRQ(ierr);
2047   if (ctx && ctx->verbose > 0) {
2048     ierr = PetscPrintf(ctx->comm, "Made coloring with %D colors\n", nc);CHKERRQ(ierr);
2049   }
2050   PetscFunctionReturn(0);
2051 }
2052 
2053 PetscErrorCode LandauAssembleOpenMP(PetscInt cStart, PetscInt cEnd, PetscInt totDim, DM plex, PetscSection section, PetscSection globalSection, Mat JacP, PetscScalar elemMats[], PetscContainer container)
2054 {
2055   PetscErrorCode  ierr;
2056   IS             *is;
2057   PetscInt        nc,colour,j;
2058   const PetscInt *clr_idxs;
2059   ISColoring      iscoloring;
2060   PetscFunctionBegin;
2061   ierr = PetscContainerGetPointer(container,(void**)&iscoloring);CHKERRQ(ierr);
2062   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);CHKERRQ(ierr);
2063   for (colour=0; colour<nc; colour++) {
2064     PetscInt    *idx_arr[1024]; /* need to make dynamic for general use */
2065     PetscScalar *new_el_mats[1024];
2066     PetscInt     idx_size[1024],csize;
2067     ierr = ISGetLocalSize(is[colour],&csize);CHKERRQ(ierr);
2068     if (csize>1024) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many elements in color. %D > %D",csize,1024);
2069     ierr = ISGetIndices(is[colour],&clr_idxs);CHKERRQ(ierr);
2070     /* get indices and mats */
2071     for (j=0; j<csize; j++) {
2072       PetscInt    cell = cStart + clr_idxs[j];
2073       PetscInt    numindices,*indices;
2074       PetscScalar *elMat = &elemMats[clr_idxs[j]*totDim*totDim];
2075       PetscScalar *valuesOrig = elMat;
2076       ierr = DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
2077       idx_size[j] = numindices;
2078       ierr = PetscMalloc2(numindices,&idx_arr[j],numindices*numindices,&new_el_mats[j]);CHKERRQ(ierr);
2079       ierr = PetscMemcpy(idx_arr[j],indices,numindices*sizeof(PetscInt));CHKERRQ(ierr);
2080       ierr = PetscMemcpy(new_el_mats[j],elMat,numindices*numindices*sizeof(PetscScalar));CHKERRQ(ierr);
2081       ierr = DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
2082       if (elMat != valuesOrig) {ierr = DMRestoreWorkArray(plex, numindices*numindices, MPIU_SCALAR, &elMat);CHKERRQ(ierr);}
2083     }
2084     /* assemble matrix */
2085     for (j=0; j<csize; j++) {
2086       PetscInt    numindices = idx_size[j], *indices = idx_arr[j];
2087       PetscScalar *elMat = new_el_mats[j];
2088       MatSetValues(JacP,numindices,indices,numindices,indices,elMat,ADD_VALUES);
2089     }
2090     /* free */
2091     ierr = ISRestoreIndices(is[colour],&clr_idxs);CHKERRQ(ierr);
2092     for (j=0; j<csize; j++) {
2093       ierr = PetscFree2(idx_arr[j],new_el_mats[j]);CHKERRQ(ierr);
2094     }
2095   }
2096   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);CHKERRQ(ierr);
2097   PetscFunctionReturn(0);
2098 }
2099 
2100 /* < v, u > */
2101 static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux,
2102                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2103                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2104                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
2105 {
2106   g0[0] = 1.;
2107 }
2108 
2109 /* < v, u > */
2110 static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux,
2111                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2112                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2113                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
2114 {
2115   g0[0] = 2.*PETSC_PI*x[0];
2116 }
2117 
2118 /*@
2119  LandauCreateMassMatrix - Create mass matrix for Landau
2120 
2121  Collective on dm
2122 
2123  Input Parameters:
2124  . dm     - the DM object
2125 
2126  Output Parameters:
2127  . Amat - The mass matrix (optional), mass matrix is added to the DM context
2128 
2129  Level: beginner
2130 
2131  .keywords: mesh
2132  .seealso: LandauCreateVelocitySpace()
2133  @*/
2134 PetscErrorCode LandauCreateMassMatrix(DM dm, Mat *Amat)
2135 {
2136   DM             massDM;
2137   PetscDS        prob;
2138   PetscInt       ii,dim,N1=1,N2;
2139   PetscErrorCode ierr;
2140   LandauCtx      *ctx;
2141   Mat            M;
2142 
2143   PetscFunctionBegin;
2144   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
2145   if (Amat) PetscValidPointer(Amat,2);
2146   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
2147   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2148   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2149   ierr = DMClone(dm, &massDM);CHKERRQ(ierr);
2150   ierr = DMCopyFields(dm, massDM);CHKERRQ(ierr);
2151   ierr = DMCreateDS(massDM);CHKERRQ(ierr);
2152   ierr = DMGetDS(massDM, &prob);CHKERRQ(ierr);
2153   for (ii=0;ii<ctx->num_species;ii++) {
2154     if (dim==3) {ierr = PetscDSSetJacobian(prob, ii, ii, g0_1, NULL, NULL, NULL);CHKERRQ(ierr);}
2155     else        {ierr = PetscDSSetJacobian(prob, ii, ii, g0_r, NULL, NULL, NULL);CHKERRQ(ierr);}
2156   }
2157   ierr = DMViewFromOptions(massDM,NULL,"-dm_landau_mass_dm_view");CHKERRQ(ierr);
2158   ierr = DMCreateMatrix(massDM, &M);CHKERRQ(ierr);
2159   ierr = MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2160   {
2161     Vec locX;
2162     DM  plex;
2163     ierr = DMConvert(massDM, DMPLEX, &plex);CHKERRQ(ierr);
2164     ierr = DMGetLocalVector(massDM, &locX);CHKERRQ(ierr);
2165     /* Mass matrix is independent of the input, so no need to fill locX */
2166     if (plex->prealloc_only != dm->prealloc_only) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "plex->prealloc_only = massDM->prealloc_only %D, =%D",plex->prealloc_only,massDM->prealloc_only);
2167     ierr = DMPlexSNESComputeJacobianFEM(plex, locX, M, M, ctx);CHKERRQ(ierr);
2168     ierr = DMRestoreLocalVector(massDM, &locX);CHKERRQ(ierr);
2169     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2170   }
2171   ierr = DMDestroy(&massDM);CHKERRQ(ierr);
2172   ierr = MatGetSize(ctx->J, &N1, NULL);CHKERRQ(ierr);
2173   ierr = MatGetSize(M, &N2, NULL);CHKERRQ(ierr);
2174   if (N1 != N2) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Incorrect matrix sizes: |Jacobian| = %D, |Mass|=%D",N1,N2);
2175   ierr = PetscObjectSetName((PetscObject)M, "mass");CHKERRQ(ierr);
2176   ierr = MatViewFromOptions(M,NULL,"-dm_landau_mass_mat_view");CHKERRQ(ierr);
2177   ctx->M = M; /* this could be a noop, a = a */
2178   if (Amat) *Amat = M;
2179   PetscFunctionReturn(0);
2180 }
2181 
2182 /*@
2183  LandauIFunction - TS residual calculation
2184 
2185  Collective on ts
2186 
2187  Input Parameters:
2188  +   TS  - The time stepping context
2189  .   time_dummy - current time (not used)
2190  -   X - Current state
2191  +   X_t - Time derivative of current state
2192  .   actx - Landau context
2193 
2194  Output Parameter:
2195  .   F  - The residual
2196 
2197  Level: beginner
2198 
2199  .keywords: mesh
2200  .seealso: LandauCreateVelocitySpace(), LandauIJacobian()
2201  @*/
2202 PetscErrorCode LandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
2203 {
2204   PetscErrorCode ierr;
2205   LandauCtx      *ctx=(LandauCtx*)actx;
2206   PetscInt       dim;
2207   DM             dm;
2208 #if defined(PETSC_HAVE_THREADSAFETY)
2209   double         starttime, endtime;
2210 #endif
2211 
2212   PetscFunctionBegin;
2213   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2214   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
2215   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2216   //ierr = MPI_Barrier(MPI_COMM_WORLD);CHKERRMPI(ierr);
2217   ierr = PetscLogEventBegin(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2218   ierr = PetscLogEventBegin(ctx->events[0],0,0,0,0);CHKERRQ(ierr);
2219 #if defined(PETSC_HAVE_THREADSAFETY)
2220   starttime = MPI_Wtime();
2221 #endif
2222   ierr = DMGetDimension(ctx->dmv, &dim);CHKERRQ(ierr);
2223   if (!ctx->aux_bool) {
2224     ierr = PetscInfo3(ts, "Create Landau Jacobian t=%g X=%p %s\n",time_dummy,X_t,ctx->aux_bool ? " -- seems to be in line search" : "");CHKERRQ(ierr);
2225     ierr = LandauFormJacobian_Internal(X,ctx->J,dim,0.0,(void*)ctx);CHKERRQ(ierr);
2226     ctx->aux_bool = PETSC_TRUE;
2227   } else {
2228     ierr = PetscInfo(ts, "Skip forming Jacobian, has not changed (should check norm)\n");CHKERRQ(ierr);
2229   }
2230   ierr = MatViewFromOptions(ctx->J,NULL,"-landau_jacobian_mat_view");CHKERRQ(ierr);
2231   /* mat vec for op */
2232   ierr = MatMult(ctx->J,X,F);CHKERRQ(ierr);CHKERRQ(ierr); /* C*f */
2233   /* add time term */
2234   if (X_t) {
2235     ierr = MatMultAdd(ctx->M,X_t,F,F);CHKERRQ(ierr);
2236   }
2237 #if defined(PETSC_HAVE_THREADSAFETY)
2238   endtime = MPI_Wtime();
2239   ctx->times[0] += (endtime - starttime);
2240 #endif
2241   ierr = PetscLogEventEnd(ctx->events[0],0,0,0,0);CHKERRQ(ierr);
2242   ierr = PetscLogEventEnd(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2243   PetscFunctionReturn(0);
2244 }
2245 static PetscErrorCode MatrixNfDestroy(void *ptr)
2246 {
2247   PetscInt *nf = (PetscInt *)ptr;
2248   PetscErrorCode  ierr;
2249   PetscFunctionBegin;
2250   ierr = PetscFree(nf);CHKERRQ(ierr);
2251   PetscFunctionReturn(0);
2252 }
2253 /*@
2254  LandauIJacobian - TS Jacobian construction
2255 
2256  Collective on ts
2257 
2258  Input Parameters:
2259  +   TS  - The time stepping context
2260  .   time_dummy - current time (not used)
2261  -   X - Current state
2262  +   U_tdummy - Time derivative of current state (not used)
2263  .   shift - shift for du/dt term
2264  -   actx - Landau context
2265 
2266  Output Parameter:
2267  .   Amat  - Jacobian
2268  +   Pmat  - same as Amat
2269 
2270  Level: beginner
2271 
2272  .keywords: mesh
2273  .seealso: LandauCreateVelocitySpace(), LandauIFunction()
2274  @*/
2275 PetscErrorCode LandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
2276 {
2277   PetscErrorCode ierr;
2278   LandauCtx      *ctx=(LandauCtx*)actx;
2279   PetscInt       dim;
2280   DM             dm;
2281   PetscContainer container;
2282 #if defined(PETSC_HAVE_THREADSAFETY)
2283   double         starttime, endtime;
2284 #endif
2285 
2286   PetscFunctionBegin;
2287   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2288   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
2289   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2290   if (Amat!=Pmat || Amat!=ctx->J) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Amat!=Pmat || Amat!=ctx->J");
2291   ierr = DMGetDimension(ctx->dmv, &dim);CHKERRQ(ierr);
2292   /* get collision Jacobian into A */
2293   ierr = PetscLogEventBegin(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2294   ierr = PetscLogEventBegin(ctx->events[9],0,0,0,0);CHKERRQ(ierr);
2295 #if defined(PETSC_HAVE_THREADSAFETY)
2296   starttime = MPI_Wtime();
2297 #endif
2298   ierr = PetscInfo2(ts, "Adding just mass to Jacobian t=%g, shift=%g\n",(double)time_dummy,(double)shift);CHKERRQ(ierr);
2299   if (shift==0.0) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "zero shift");
2300   if (!ctx->aux_bool) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "wrong state");
2301   if (!ctx->use_matrix_mass) {
2302     ierr = LandauFormJacobian_Internal(X,ctx->J,dim,shift,(void*)ctx);CHKERRQ(ierr);
2303   } else { /* add mass */
2304     ierr = MatAXPY(Pmat,shift,ctx->M,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2305   }
2306   ctx->aux_bool = PETSC_FALSE;
2307   ierr = MatViewFromOptions(Pmat,NULL,"-landau_mat_view");CHKERRQ(ierr);
2308   /* set number species in Jacobian */
2309   ierr = PetscObjectQuery((PetscObject) ctx->J, "Nf", (PetscObject *) &container);CHKERRQ(ierr);
2310   if (!container) {
2311     PetscInt *pNf;
2312     ierr = PetscContainerCreate(PETSC_COMM_SELF, &container);CHKERRQ(ierr);
2313     ierr = PetscMalloc(sizeof(PetscInt), &pNf);CHKERRQ(ierr);
2314     *pNf = ctx->num_species + 1000*ctx->numConcurrency;
2315     ierr = PetscContainerSetPointer(container, (void *)pNf);CHKERRQ(ierr);
2316     ierr = PetscContainerSetUserDestroy(container, MatrixNfDestroy);CHKERRQ(ierr);
2317     ierr = PetscObjectCompose((PetscObject)ctx->J, "Nf", (PetscObject) container);CHKERRQ(ierr);
2318     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
2319   }
2320 #if defined(PETSC_HAVE_THREADSAFETY)
2321   endtime = MPI_Wtime();
2322   ctx->times[0] += (endtime - starttime);
2323 #endif
2324   ierr = PetscLogEventEnd(ctx->events[9],0,0,0,0);CHKERRQ(ierr);
2325   ierr = PetscLogEventEnd(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2326   PetscFunctionReturn(0);
2327 }
2328