xref: /petsc/src/ts/utils/dmplexlandau/plexland.c (revision 8917bc2f606a548f4cbffd48e64f20814df968a7)
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 #if defined(PETSC_USE_REAL_SINGLE)
9 #define SPEED_OF_LIGHT 2997924
10 #define C_0(v0) (SPEED_OF_LIGHT/v0) /* needed for relativistic tensor on all architectures */
11 #else
12 #define SPEED_OF_LIGHT 299792458
13 #define C_0(v0) (SPEED_OF_LIGHT/v0) /* needed for relativistic tensor on all architectures */
14 #endif
15 
16 #define PETSC_THREAD_SYNC
17 #include "land_tensors.h"
18 
19 /* vector padding not supported */
20 #define LANDAU_VL  1
21 
22 static PetscErrorCode LandauGPUMapsDestroy(void *ptr)
23 {
24   P4estVertexMaps *maps = (P4estVertexMaps *)ptr;
25   PetscErrorCode  ierr;
26   PetscFunctionBegin;
27   if (maps->deviceType != LANDAU_CPU) {
28 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
29     if (maps->deviceType == LANDAU_KOKKOS) {
30       ierr = LandauKokkosDestroyMatMaps(maps);CHKERRQ(ierr); // imples Kokkos does
31     } // else could be CUDA
32 #elif defined(PETSC_HAVE_CUDA)
33     if (maps->deviceType == LANDAU_CUDA) {
34       ierr = LandauCUDADestroyMatMaps(maps);CHKERRQ(ierr);
35     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps->deviceType %D ?????",maps->deviceType);
36 #endif
37   }
38   ierr = PetscFree(maps->c_maps);CHKERRQ(ierr);
39   ierr = PetscFree(maps->gIdx);CHKERRQ(ierr);
40   ierr = PetscFree(maps);CHKERRQ(ierr);
41   PetscFunctionReturn(0);
42 }
43 static PetscErrorCode energy_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
44 {
45   PetscReal     v2 = 0;
46   PetscFunctionBegin;
47   /* compute v^2 / 2 */
48   for (int i = 0; i < dim; ++i) v2 += x[i]*x[i];
49   /* evaluate the Maxwellian */
50   u[0] = v2/2;
51   PetscFunctionReturn(0);
52 }
53 
54 /* needs double */
55 static PetscErrorCode gamma_m1_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
56 {
57   PetscReal     *c2_0_arr = ((PetscReal*)actx);
58   double        u2 = 0, c02 = (double)*c2_0_arr, xx;
59 
60   PetscFunctionBegin;
61   /* compute u^2 / 2 */
62   for (int i = 0; i < dim; ++i) u2 += x[i]*x[i];
63   /* gamma - 1 = g_eps, for conditioning and we only take derivatives */
64   xx = u2/c02;
65 #if defined(PETSC_USE_DEBUG)
66   u[0] = PetscSqrtReal(1. + xx);
67 #else
68   u[0] = xx/(PetscSqrtReal(1. + xx) + 1.) - 1.; // better conditioned. -1 might help condition and only used for derivative
69 #endif
70   PetscFunctionReturn(0);
71 }
72 
73 /* ------------------------------------------------------------------- */
74 /*
75  LandauFormJacobian_Internal - Evaluates Jacobian matrix.
76 
77  Input Parameters:
78  .  globX - input vector
79  .  actx - optional user-defined context
80  .  dim - dimension
81 
82  Output Parameters:
83  .  J0acP - Jacobian matrix filled, not created
84  */
85 static PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, PetscReal shift, void *a_ctx)
86 {
87   LandauCtx         *ctx = (LandauCtx*)a_ctx;
88   PetscErrorCode    ierr;
89   PetscInt          cStart, cEnd, elemMatSize;
90   PetscDS           prob;
91   PetscSection      section,globsection;
92   PetscInt          numCells,totDim,ej,Nq,*Nbf,*Ncf,Nb,Ncx,Nf,d,f,fieldA,qj,N;
93   PetscQuadrature   quad;
94   const PetscReal   *quadWeights;
95   PetscTabulation   *Tf; // used for CPU and print info
96   PetscReal         Eq_m[LANDAU_MAX_SPECIES], m_0=ctx->m_0; /* normalize mass -- not needed! */
97   PetscScalar       *IPf=NULL;
98   const PetscScalar *xdata=NULL;
99   PetscLogDouble    flops;
100   PetscContainer    container;
101   P4estVertexMaps   *maps=NULL;
102 
103   PetscFunctionBegin;
104   PetscValidHeaderSpecific(a_X,VEC_CLASSID,1);
105   PetscValidHeaderSpecific(JacP,MAT_CLASSID,2);
106   PetscValidPointer(ctx,5);
107   /* check for matrix container for GPU assembly */
108   ierr = PetscLogEventBegin(ctx->events[10],0,0,0,0);CHKERRQ(ierr);
109   ierr = PetscObjectQuery((PetscObject) JacP, "assembly_maps", (PetscObject *) &container);CHKERRQ(ierr);
110   if (container /* && ctx->deviceType != LANDAU_CPU */) {
111     if (!ctx->gpu_assembly) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"GPU matrix container but no GPU assembly");
112     ierr = PetscContainerGetPointer(container, (void **) &maps);CHKERRQ(ierr);
113     if (!maps) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"empty GPU matrix container");
114   }
115   if (ctx->plex == NULL) {
116     ierr = DMConvert(ctx->dmv, DMPLEX, &ctx->plex);CHKERRQ(ierr);
117   }
118   ierr = DMPlexGetHeightStratum(ctx->plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
119   ierr = DMGetLocalSection(ctx->plex, &section);CHKERRQ(ierr);
120   ierr = DMGetGlobalSection(ctx->plex, &globsection);CHKERRQ(ierr);
121   ierr = DMGetDS(ctx->plex, &prob);CHKERRQ(ierr);
122   ierr = PetscDSGetTabulation(prob, &Tf);CHKERRQ(ierr); // Bf, &Df
123   ierr = PetscDSGetDimensions(prob, &Nbf);CHKERRQ(ierr); Nb = Nbf[0]; /* number of vertices*S */
124   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
125   if (Nf!=ctx->num_species) SETERRQ1(ctx->comm, PETSC_ERR_PLIB, "Nf %D != S",Nf);
126   ierr = PetscDSGetComponents(prob, &Ncf);CHKERRQ(ierr);
127   Ncx = Ncf[0];
128   if (Ncx!=1) SETERRQ1(ctx->comm, PETSC_ERR_PLIB, "Nc %D != 1",Ncx);
129   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
130   numCells = cEnd - cStart;
131   ierr = PetscFEGetQuadrature(ctx->fe[0], &quad);CHKERRQ(ierr);
132   ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, &quadWeights);CHKERRQ(ierr);
133   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);
134   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);
135   if (LANDAU_DIM != dim) SETERRQ2(ctx->comm, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim,LANDAU_DIM);
136   if (!ctx->SData_d) {
137     ierr = PetscNew(&ctx->SData_d);CHKERRQ(ierr);
138   }
139   elemMatSize = totDim*totDim; // used for CPU and print info
140   ierr = PetscLogEventEnd(ctx->events[10],0,0,0,0);CHKERRQ(ierr);
141   ierr = VecGetSize(a_X,&N);CHKERRQ(ierr);
142   if (!ctx->init) { /* create static point data, Jacobian called first */
143     PetscReal       *invJ,*ww,*xx,*yy,*zz=NULL,*mass_w,*invJ_a;
144     const PetscInt  nip = Nq*numCells;
145     Vec             v2_2 = NULL; // projected function: v^2/2 ofr non-relativistic, gamma... for relativistic
146     PetscSection    e_section;
147     DM              dmEnergy=NULL;
148     ierr = PetscLogEventBegin(ctx->events[7],0,0,0,0);CHKERRQ(ierr);
149     ctx->init = PETSC_TRUE;
150     ierr = PetscInfo(ctx->plex, "Initialize static data\n");CHKERRQ(ierr);
151     /* collect f data, first time is for Jacobian, but make mass now */
152     if (ctx->verbose > 1 || ctx->verbose > 0) {
153       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",
154                          0,"FormLandau",Nq*numCells,numCells, totDim, Nb, Nq, elemMatSize, dim, Tf[0]->Nb, Nf, Tf[0]->Np, Tf[0]->cdim, N, shift);CHKERRQ(ierr);
155     }
156     ierr = PetscMalloc5(nip,&mass_w,nip,&ww,nip,&xx,nip,&yy,nip*dim*dim,&invJ_a);CHKERRQ(ierr);
157     if (dim==3) {
158       ierr = PetscMalloc1(nip,&zz);CHKERRQ(ierr);
159     }
160     // prep energy trick, get v^2 / 2 vector
161     if (ctx->use_energy_tensor_trick) {
162       PetscErrorCode (*energyf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {ctx->use_relativistic_corrections ? gamma_m1_f : energy_f};
163       PetscFE        fe;
164       Vec            glob_v2;
165       PetscReal      *c2_0[1], data[1] = {PetscSqr(C_0(ctx->v_0))};
166 
167       ierr = DMClone(ctx->plex, &dmEnergy);CHKERRQ(ierr);
168       ierr = PetscObjectSetName((PetscObject) dmEnergy, "energy");CHKERRQ(ierr);
169       ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &fe);CHKERRQ(ierr);
170       ierr = PetscObjectSetName((PetscObject) fe, "energy");CHKERRQ(ierr);
171       ierr = DMSetField(dmEnergy, 0, NULL, (PetscObject)fe);CHKERRQ(ierr);
172       ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
173       ierr = DMCreateDS(dmEnergy);CHKERRQ(ierr);
174       ierr = DMGetSection(dmEnergy, &e_section);CHKERRQ(ierr);
175       ierr = DMGetGlobalVector(dmEnergy,&glob_v2);CHKERRQ(ierr);
176       ierr = PetscObjectSetName((PetscObject) glob_v2, "v^2/2");CHKERRQ(ierr);
177       c2_0[0] = &data[0];
178       ierr = DMProjectFunction(dmEnergy, 0., energyf, (void**)c2_0, INSERT_ALL_VALUES, glob_v2);CHKERRQ(ierr);
179       ierr = DMGetLocalVector(dmEnergy, &v2_2);CHKERRQ(ierr);
180       ierr = VecZeroEntries(v2_2);CHKERRQ(ierr); /* zero BCs so don't set */
181       ierr = DMGlobalToLocalBegin(dmEnergy, glob_v2, INSERT_VALUES, v2_2);CHKERRQ(ierr);
182       ierr = DMGlobalToLocalEnd  (dmEnergy, glob_v2, INSERT_VALUES, v2_2);CHKERRQ(ierr);
183       ierr = DMViewFromOptions(dmEnergy,NULL, "-energy_dm_view");CHKERRQ(ierr);
184       ierr = VecViewFromOptions(glob_v2,NULL, "-energy_vec_view");CHKERRQ(ierr);
185       ierr = DMRestoreGlobalVector(dmEnergy, &glob_v2);CHKERRQ(ierr);
186     }
187     for (ej = 0 ; ej < numCells; ++ej) {
188       PetscScalar *coefs = NULL;
189       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);
190       invJ = invJ_a ? invJ_a + ej * Nq*dim*dim : NULL;
191       ierr = DMPlexComputeCellGeometryFEM(ctx->plex, cStart+ej, quad, vj, Jdummy, invJ, detJj);CHKERRQ(ierr);
192       if (ctx->use_energy_tensor_trick) {
193         ierr = DMPlexVecGetClosure(dmEnergy, e_section, v2_2, cStart+ej, NULL, &coefs);CHKERRQ(ierr);
194       }
195       /* create dynamic point data */
196       for (qj = 0; qj < Nq; ++qj) {
197         PetscInt         gidx = (ej*Nq + qj);
198         mass_w[gidx] = detJj[qj] * quadWeights[qj];
199         if (dim==2) mass_w[gidx] *=  2.*PETSC_PI*vj[qj * dim + 0]; /* cylindrical coordinate, w/o 2pi */
200         // get xx, yy, zz
201         if (ctx->use_energy_tensor_trick) {
202           double                  refSpaceDer[3],eGradPhi[3];
203           const PetscReal * const DD = Tf[0]->T[1];
204           const PetscReal         *Dq = &DD[qj*Nb*dim];
205           for (int d = 0; d < 3; ++d) refSpaceDer[d] = eGradPhi[d] = 0.0;
206           for (int b = 0; b < Nb; ++b) {
207             for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[b*dim+d]*PetscRealPart(coefs[b]);
208             //PetscPrintf(ctx->comm,"%12.5e ", coefs[b]);
209           }
210           //PetscPrintf(ctx->comm,"\n");
211           xx[gidx] = 1e10;
212           if (ctx->use_relativistic_corrections) {
213             double dg2_c2 = 0;
214             //for (int d = 0; d < dim; ++d) refSpaceDer[d] *= c02;
215             for (int d = 0; d < dim; ++d) dg2_c2 += PetscSqr(refSpaceDer[d]);
216             dg2_c2 *= (double)c02;
217             if (dg2_c2 >= .999) {
218               xx[gidx] = vj[qj * dim + 0]; /* coordinate */
219               yy[gidx] = vj[qj * dim + 1];
220               if (dim==3) zz[gidx] = vj[qj * dim + 2];
221               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]);
222             } else {
223               PetscReal fact = c02/PetscSqrtReal(1. - dg2_c2);
224               for (int d = 0; d < dim; ++d) refSpaceDer[d] *= fact;
225               // could test with other point u' that (grad - grad') * U (refSpaceDer, refSpaceDer') == 0
226             }
227           }
228           if (xx[gidx] == 1e10) {
229             for (int d = 0; d < dim; ++d) {
230               for (int e = 0 ; e < dim; ++e) {
231                 eGradPhi[d] += invJ[qj * dim * dim + e*dim+d]*refSpaceDer[e];
232               }
233             }
234             xx[gidx] = eGradPhi[0];
235             yy[gidx] = eGradPhi[1];
236             if (dim==3) zz[gidx] = eGradPhi[2];
237           }
238         } else {
239           xx[gidx] = vj[qj * dim + 0]; /* coordinate */
240           yy[gidx] = vj[qj * dim + 1];
241           if (dim==3) zz[gidx] = vj[qj * dim + 2];
242         }
243         //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);
244         ww[gidx] = detJj[qj] * quadWeights[qj];
245         if (dim==2) ww[gidx] *= vj[qj * dim + 0];  /* cylindrical coordinate, w/o 2pi */
246       } /* q */
247       if (ctx->use_energy_tensor_trick) {
248         ierr = DMPlexVecRestoreClosure(dmEnergy, e_section, v2_2, cStart+ej, NULL, &coefs);CHKERRQ(ierr);
249       }
250     } /* ej */
251     if (ctx->use_energy_tensor_trick) {
252       ierr = DMRestoreLocalVector(dmEnergy, &v2_2);CHKERRQ(ierr);
253       ierr = DMDestroy(&dmEnergy);CHKERRQ(ierr);
254     }
255     /* cache static data */
256     if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
257 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_KOKKOS)
258       PetscReal invMass[LANDAU_MAX_SPECIES],nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
259       for (fieldA=0;fieldA<Nf;fieldA++) {
260         invMass[fieldA] = m_0/ctx->masses[fieldA];
261         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/m_0)*m_0/ctx->masses[fieldA];
262         nu_beta[fieldA] = PetscSqr(ctx->charges[fieldA]/ctx->epsilon0)*ctx->lnLam / (8*PETSC_PI) * ctx->t_0*ctx->n_0/PetscPowReal(ctx->v_0,3);
263       }
264       if (ctx->deviceType == LANDAU_CUDA) {
265 #if defined(PETSC_HAVE_CUDA)
266         ierr = LandauCUDAStaticDataSet(ctx->plex,Nq,nu_alpha,nu_beta,invMass,invJ_a,mass_w,xx,yy,zz,ww,ctx->SData_d);CHKERRQ(ierr);
267 #else
268         SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
269 #endif
270       } else if (ctx->deviceType == LANDAU_KOKKOS) {
271 #if defined(PETSC_HAVE_KOKKOS)
272         ierr = LandauKokkosStaticDataSet(ctx->plex,Nq,nu_alpha,nu_beta,invMass,invJ_a,mass_w,xx,yy,zz,ww,ctx->SData_d);CHKERRQ(ierr);
273 #else
274         SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
275 #endif
276       }
277 #endif
278       /* free */
279       ierr = PetscFree5(mass_w,ww,xx,yy,invJ_a);CHKERRQ(ierr);
280       if (dim==3) {
281         ierr = PetscFree(zz);CHKERRQ(ierr);
282       }
283     } else { /* CPU version, just copy in, only use part */
284       ctx->SData_d->w = (void*)ww;
285       ctx->SData_d->x = (void*)xx;
286       ctx->SData_d->y = (void*)yy;
287       ctx->SData_d->z = (void*)zz;
288       ctx->SData_d->invJ = (void*)invJ_a;
289       ctx->SData_d->mass_w = (void*)mass_w;
290     }
291     ierr = PetscLogEventEnd(ctx->events[7],0,0,0,0);CHKERRQ(ierr);
292   }
293   if (shift==0) { /* create dynamic point data */
294     ierr = PetscLogEventBegin(ctx->events[1],0,0,0,0);CHKERRQ(ierr);
295     ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
296     flops = (PetscLogDouble)numCells*(PetscLogDouble)Nq*(PetscLogDouble)(5*dim*dim*Nf*Nf + 165);
297     for (fieldA=0;fieldA<Nf;fieldA++) {
298       Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
299       if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
300     }
301     if (!ctx->gpu_assembly || !container) {
302       Vec locX;
303       ierr = DMGetLocalVector(ctx->plex, &locX);CHKERRQ(ierr);
304       ierr = VecZeroEntries(locX);CHKERRQ(ierr); /* zero BCs so don't set */
305       ierr = DMGlobalToLocalBegin(ctx->plex, a_X, INSERT_VALUES, locX);CHKERRQ(ierr);
306       ierr = DMGlobalToLocalEnd  (ctx->plex, a_X, INSERT_VALUES, locX);CHKERRQ(ierr);
307       ierr = PetscMalloc1(Nq*numCells*Nf,&IPf);CHKERRQ(ierr);
308       for (ej = 0 ; ej < numCells; ++ej) {
309         PetscScalar *coef = NULL;
310         ierr = DMPlexVecGetClosure(ctx->plex, section, locX, cStart+ej, NULL, &coef);CHKERRQ(ierr);
311         ierr = PetscMemcpy(&IPf[ej*Nb*Nf],coef,Nb*Nf*sizeof(PetscScalar));CHKERRQ(ierr); /* change if LandauIPReal != PetscScalar */
312         ierr = DMPlexVecRestoreClosure(ctx->plex, section, locX, cStart+ej, NULL, &coef);CHKERRQ(ierr);
313       } /* ej */
314       ierr = DMRestoreLocalVector(ctx->plex, &locX);CHKERRQ(ierr);
315     } else {
316       PetscMemType mtype;
317       ierr = VecGetArrayReadAndMemType(a_X,&xdata,&mtype);CHKERRQ(ierr);
318       if (mtype!=PETSC_MEMTYPE_HOST && ctx->deviceType == LANDAU_CPU) {
319         SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"CPU run with device data: use -mat_type aij");
320       }
321     }
322     ierr = PetscLogEventEnd(ctx->events[1],0,0,0,0);CHKERRQ(ierr);
323   } else {
324     flops = (PetscLogDouble)numCells*(PetscLogDouble)Nq*(PetscLogDouble)(5*dim*dim*Nf*Nf);
325   }
326   /* do it */
327   if (ctx->deviceType == LANDAU_CUDA || ctx->deviceType == LANDAU_KOKKOS) {
328     if (ctx->deviceType == LANDAU_CUDA) {
329 #if defined(PETSC_HAVE_CUDA)
330       ierr = LandauCUDAJacobian(ctx->plex,Nq,Eq_m,IPf,N,xdata,ctx->SData_d,ctx->subThreadBlockSize,shift,ctx->events,JacP);CHKERRQ(ierr);
331 #else
332       SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
333 #endif
334     } else if (ctx->deviceType == LANDAU_KOKKOS) {
335 #if defined(PETSC_HAVE_KOKKOS)
336       ierr = LandauKokkosJacobian(ctx->plex,Nq,Eq_m,IPf,N,xdata,ctx->SData_d,ctx->subThreadBlockSize,shift,ctx->events,JacP);CHKERRQ(ierr);
337 #else
338       SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
339 #endif
340     }
341   } else { /* CPU version */
342     PetscInt        ei, qi;
343     PetscScalar     *elemMat,coef_buff[LANDAU_MAX_SPECIES*LANDAU_MAX_NQ];
344     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;
345     const PetscInt  nip = Nq*numCells, mask_factor = (ctx->use_energy_tensor_trick && (Nq==8 || Nq==4)) ? Nq : 1; // 3D Q1
346     const PetscReal *const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
347     PetscReal       Eq_m[LANDAU_MAX_SPECIES], invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
348     if (shift!=0.0) { // mass
349       ierr = PetscMalloc1(elemMatSize, &elemMat);CHKERRQ(ierr);
350     } else {      /* compute f and df and init data for Jacobian */
351       ierr = PetscLogEventBegin(ctx->events[8],0,0,0,0);CHKERRQ(ierr);
352       for (fieldA=0;fieldA<Nf;fieldA++) {
353         invMass[fieldA] = m_0/ctx->masses[fieldA];
354         Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
355         if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
356         nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/m_0)*m_0/ctx->masses[fieldA];
357         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);
358       }
359       ierr = PetscMalloc5(elemMatSize, &elemMat, nip*Nf, &ff, nip*Nf, &dudx, nip*Nf, &dudy, dim==3 ? nip*Nf : 0, &dudz);CHKERRQ(ierr);
360       for (ei = cStart, invJ = invJ_a; ei < cEnd; ++ei, invJ += Nq*dim*dim) {
361         PetscScalar *coef;
362         PetscInt     b,f,idx,q;
363         PetscReal    u_x[LANDAU_MAX_SPECIES][LANDAU_DIM];
364         if (IPf) {
365           coef = &IPf[ei*Nb*Nf]; // this is const
366         } else {
367           if (!maps) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"!maps");
368           coef = coef_buff;
369           for (f = 0; f < Nf; ++f) {
370             LandauIdx *const Idxs = &maps->gIdx[ei-cStart][f][0];
371             for (b = 0; b < Nb; ++b) {
372               idx = Idxs[b];
373               if (idx >= 0) {
374                 coef[f*Nb+b] = xdata[idx];
375               } else {
376                 idx = -idx - 1;
377                 coef[f*Nb+b] = 0;
378                 for (q = 0; q < maps->num_face; q++) {
379                   PetscInt    id = maps->c_maps[idx][q].gid;
380                   PetscScalar scale = maps->c_maps[idx][q].scale;
381                   coef[f*Nb+b] += scale*xdata[id];
382                 }
383               }
384             }
385           }
386         }
387         /* get f and df */
388         for (qi = 0; qi < Nq; ++qi) {
389           const PetscReal  *Bq = &BB[qi*Nb];
390           const PetscReal  *Dq = &DD[qi*Nb*dim];
391           const PetscInt   gidx = ei*Nq + qi;
392           /* get f & df */
393           for (f = 0; f < Nf; ++f) {
394             PetscInt   b, e;
395             PetscReal  refSpaceDer[LANDAU_DIM];
396             ff[gidx + f*nip] = 0.0;
397             for (d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
398             for (b = 0; b < Nb; ++b) {
399               const PetscInt    cidx = b;
400               ff[gidx + f*nip] += Bq[cidx]*PetscRealPart(coef[f*Nb+cidx]);
401               for (d = 0; d < dim; ++d) refSpaceDer[d] += Dq[cidx*dim+d]*PetscRealPart(coef[f*Nb+cidx]);
402             }
403             for (d = 0; d < dim; ++d) {
404               for (e = 0, u_x[f][d] = 0.0; e < dim; ++e) {
405                 u_x[f][d] += invJ[qi * dim * dim + e*dim+d]*refSpaceDer[e];
406               }
407             }
408           }
409           for (f=0;f<Nf;f++) {
410             dudx[gidx + f*nip] = u_x[f][0];
411             dudy[gidx + f*nip] = u_x[f][1];
412 #if LANDAU_DIM==3
413             dudz[gidx + f*nip] = u_x[f][2];
414 #endif
415           }
416         }
417       }
418       ierr = PetscLogEventEnd(ctx->events[8],0,0,0,0);CHKERRQ(ierr);
419     }
420     for (ej = cStart, invJ = invJ_a; ej < cEnd; ++ej, invJ += Nq*dim*dim) {
421       ierr = PetscMemzero(elemMat, totDim *totDim * sizeof(PetscScalar));CHKERRQ(ierr);
422       ierr = PetscLogEventBegin(ctx->events[4],0,0,0,0);CHKERRQ(ierr);
423       ierr = PetscLogFlops((PetscLogDouble)Nq*flops);CHKERRQ(ierr);
424       //printf("\t:%d.%d) Invj[0] = %e (%d)\n",ej,qj,invJ[0],(int)(invJ-invJ_a));
425       for (qj = 0; qj < Nq; ++qj) {
426         const PetscReal * const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1];
427         PetscReal               g0[LANDAU_MAX_SPECIES], g2[LANDAU_MAX_SPECIES][LANDAU_DIM], g3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM];
428         PetscInt                d,d2,dp,d3,ipidx,fieldA;
429         const PetscInt          jpidx = Nq*(ej-cStart) + qj;
430         if (shift==0.0) {
431           const PetscReal * const invJj = &invJ[qj*dim*dim];
432           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];
433           const PetscReal         vj[3] = {xx[jpidx], yy[jpidx], zz ? zz[jpidx] : 0}, wj = ww[jpidx];
434 
435           // create g2 & g3
436           for (d=0;d<dim;d++) { // clear accumulation data D & K
437             gg2_temp[d] = 0;
438             for (d2=0;d2<dim;d2++) gg3_temp[d][d2] = 0;
439           }
440           for (ipidx = 0; ipidx < nip; ipidx++) {
441             const PetscReal wi = ww[ipidx], x = xx[ipidx], y = yy[ipidx];
442             PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
443 #if LANDAU_DIM==2
444             PetscReal       Ud[2][2], Uk[2][2];
445             LandauTensor2D(vj, x, y, Ud, Uk, (ipidx/mask_factor==jpidx/mask_factor) ? 0. : 1.);
446 #else
447             PetscReal U[3][3], z = zz[ipidx];
448             if (ctx->use_relativistic_corrections) {
449               PetscReal U2[3][3];
450               LandauTensor3DRelativistic(vj, x, y, z, U, (ipidx/mask_factor==jpidx/mask_factor) ? 0. : 1., C_0(ctx->v_0));
451             } else {
452               LandauTensor3D(vj, x, y, z, U, (ipidx==jpidx) ? 0. : 1.);
453             }
454 #endif
455             for (fieldA = 0; fieldA < Nf; ++fieldA) {
456               temp1[0] += dudx[ipidx + fieldA*nip]*nu_beta[fieldA]*invMass[fieldA];
457               temp1[1] += dudy[ipidx + fieldA*nip]*nu_beta[fieldA]*invMass[fieldA];
458 #if LANDAU_DIM==3
459               temp1[2] += dudz[ipidx + fieldA*nip]*nu_beta[fieldA]*invMass[fieldA];
460 #endif
461               temp2    += ff[ipidx + fieldA*nip]*nu_beta[fieldA];
462             }
463             temp1[0] *= wi;
464             temp1[1] *= wi;
465 #if LANDAU_DIM==3
466             temp1[2] *= wi;
467 #endif
468             temp2    *= wi;
469 #if LANDAU_DIM==2
470             for (d2 = 0; d2 < 2; d2++) {
471               for (d3 = 0; d3 < 2; ++d3) {
472                 /* K = U * grad(f): g2=e: i,A */
473                 gg2_temp[d2] += Uk[d2][d3]*temp1[d3];
474                 /* D = -U * (I \kron (fx)): g3=f: i,j,A */
475                 gg3_temp[d2][d3] += Ud[d2][d3]*temp2;
476               }
477             }
478 #else
479             for (d2 = 0; d2 < 3; ++d2) {
480               for (d3 = 0; d3 < 3; ++d3) {
481                 /* K = U * grad(f): g2 = e: i,A */
482                 gg2_temp[d2] += U[d2][d3]*temp1[d3];
483                 /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
484                 gg3_temp[d2][d3] += U[d2][d3]*temp2;
485               }
486             }
487 #endif
488           } /* IPs */
489           // add alpha and put in gg2/3
490           for (fieldA = 0; fieldA < Nf; ++fieldA) {
491             for (d2 = 0; d2 < dim; d2++) {
492               gg2[fieldA][d2] = gg2_temp[d2]*nu_alpha[fieldA];
493               for (d3 = 0; d3 < dim; d3++) {
494                 gg3[fieldA][d2][d3] = -gg3_temp[d2][d3]*nu_alpha[fieldA]*invMass[fieldA];
495               }
496             }
497           }
498           /* add electric field term once per IP */
499           for (fieldA = 0; fieldA < Nf; ++fieldA) {
500             gg2[fieldA][dim-1] += Eq_m[fieldA];
501           }
502           /* Jacobian transform - g2, g3 */
503           for (fieldA = 0; fieldA < Nf; ++fieldA) {
504             for (d = 0; d < dim; ++d) {
505               g2[fieldA][d] = 0.0;
506               for (d2 = 0; d2 < dim; ++d2) {
507                 g2[fieldA][d] += invJj[d*dim+d2]*gg2[fieldA][d2];
508                 g3[fieldA][d][d2] = 0.0;
509                 for (d3 = 0; d3 < dim; ++d3) {
510                   for (dp = 0; dp < dim; ++dp) {
511                     g3[fieldA][d][d2] += invJj[d*dim + d3]*gg3[fieldA][d3][dp]*invJj[d2*dim + dp];
512                   }
513                 }
514                 g3[fieldA][d][d2] *= wj;
515               }
516               g2[fieldA][d] *= wj;
517             }
518           }
519         } else { // mass
520           /* Jacobian transform - g0 */
521           for (fieldA = 0; fieldA < Nf; ++fieldA) {
522             g0[fieldA] = mass_w[jpidx] * shift; // move this to below and remove g0
523           }
524         }
525         /* FE matrix construction */
526         {
527           PetscInt  fieldA,d,f,d2,g;
528           const PetscReal *BJq = &BB[qj*Nb], *DIq = &DD[qj*Nb*dim];
529           /* assemble - on the diagonal (I,I) */
530           for (fieldA = 0; fieldA < Nf ; fieldA++) {
531             for (f = 0; f < Nb ; f++) {
532               const PetscInt i = fieldA*Nb + f; /* Element matrix row */
533               for (g = 0; g < Nb; ++g) {
534                 const PetscInt j    = fieldA*Nb + g; /* Element matrix column */
535                 const PetscInt fOff = i*totDim + j;
536                 if (shift==0.0) {
537                   for (d = 0; d < dim; ++d) {
538                     elemMat[fOff] += DIq[f*dim+d]*g2[fieldA][d]*BJq[g];
539                     //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]);
540                     for (d2 = 0; d2 < dim; ++d2) {
541                       elemMat[fOff] += DIq[f*dim + d]*g3[fieldA][d][d2]*DIq[g*dim + d2];
542                     }
543                   }
544                 } else { // mass
545                   elemMat[fOff] += BJq[f]*g0[fieldA]*BJq[g];
546                 }
547               }
548             }
549           }
550         }
551       } /* qj loop */
552       ierr = PetscLogEventEnd(ctx->events[4],0,0,0,0);CHKERRQ(ierr);
553       /* assemble matrix */
554       ierr = PetscLogEventBegin(ctx->events[6],0,0,0,0);CHKERRQ(ierr);
555       if (!maps) {
556         ierr = DMPlexMatSetClosure(ctx->plex, section, globsection, JacP, ej, elemMat, ADD_VALUES);CHKERRQ(ierr);
557       } else {  // GPU like assembly for debugging
558         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];
559         PetscScalar   vals[LANDAU_MAX_Q_FACE*LANDAU_MAX_Q_FACE],row_scale[LANDAU_MAX_Q_FACE],col_scale[LANDAU_MAX_Q_FACE]={0};
560         /* assemble - from the diagonal (I,I) in this format for DMPlexMatSetClosure */
561         for (fieldA = 0; fieldA < Nf ; fieldA++) {
562           LandauIdx *const Idxs = &maps->gIdx[ej-cStart][fieldA][0];
563           for (f = 0; f < Nb ; f++) {
564             idx = Idxs[f];
565             if (idx >= 0) {
566               nr = 1;
567               rows0[0] = idx;
568               row_scale[0] = 1.;
569             } else {
570               idx = -idx - 1;
571               nr = maps->num_face;
572               for (q = 0; q < maps->num_face; q++) {
573                 rows0[q]     = maps->c_maps[idx][q].gid;
574                 row_scale[q] = maps->c_maps[idx][q].scale;
575               }
576             }
577             for (g = 0; g < Nb; ++g) {
578               idx = Idxs[g];
579               if (idx >= 0) {
580                 nc = 1;
581                 cols0[0] = idx;
582                 col_scale[0] = 1.;
583               } else {
584                 idx = -idx - 1;
585                 nc = maps->num_face;
586                 for (q = 0; q < maps->num_face; q++) {
587                   cols0[q]     = maps->c_maps[idx][q].gid;
588                   col_scale[q] = maps->c_maps[idx][q].scale;
589                 }
590               }
591               const PetscInt    i = fieldA*Nb + f; /* Element matrix row */
592               const PetscInt    j = fieldA*Nb + g; /* Element matrix column */
593               const PetscScalar Aij = elemMat[i*totDim + j];
594               for (q = 0; q < nr; q++) rows[q] = rows0[q];
595               for (q = 0; q < nc; q++) cols[q] = cols0[q];
596               for (q = 0; q < nr; q++) {
597                 for (d = 0; d < nc; d++) {
598                   vals[q*nc + d] = row_scale[q]*col_scale[d]*Aij;
599                 }
600               }
601               ierr = MatSetValues(JacP,nr,rows,nc,cols,vals,ADD_VALUES);CHKERRQ(ierr);
602             }
603           }
604         }
605       }
606       if (ej==-1) {
607         PetscErrorCode    ierr2;
608         ierr2 = PetscPrintf(ctx->comm,"CPU Element matrix\n");CHKERRQ(ierr2);
609         for (d = 0; d < totDim; ++d) {
610           for (f = 0; f < totDim; ++f) {ierr2 = PetscPrintf(ctx->comm," %12.5e",  PetscRealPart(elemMat[d*totDim + f]));CHKERRQ(ierr2);}
611           ierr2 = PetscPrintf(ctx->comm,"\n");CHKERRQ(ierr2);
612         }
613         exit(12);
614       }
615       ierr = PetscLogEventEnd(ctx->events[6],0,0,0,0);CHKERRQ(ierr);
616     } /* ej cells loop, not cuda */
617     if (shift!=0.0) { // mass
618       ierr = PetscFree(elemMat);CHKERRQ(ierr);
619     } else {
620       ierr = PetscFree5(elemMat, ff, dudx, dudy, dudz);CHKERRQ(ierr);
621     }
622   } /* CPU version */
623 
624   /* assemble matrix or vector */
625   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
626   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
627 #define MAP_BF_SIZE (64*LANDAU_DIM*LANDAU_DIM*LANDAU_MAX_Q_FACE*LANDAU_MAX_SPECIES)
628   if (ctx->gpu_assembly && !container) {
629     PetscScalar             elemMatrix[LANDAU_MAX_NQ*LANDAU_MAX_NQ*LANDAU_MAX_SPECIES*LANDAU_MAX_SPECIES], *elMat;
630     pointInterpolationP4est pointMaps[MAP_BF_SIZE][LANDAU_MAX_Q_FACE];
631     PetscInt                q,eidx,fieldA;
632     MatType                 type;
633     ierr = PetscInfo1(ctx->plex, "Make GPU maps %D\n",1);CHKERRQ(ierr);
634     ierr = MatGetType(JacP,&type);CHKERRQ(ierr);
635     ierr = PetscLogEventBegin(ctx->events[2],0,0,0,0);CHKERRQ(ierr);
636     ierr = PetscMalloc(sizeof(P4estVertexMaps), &maps);CHKERRQ(ierr);
637     ierr = PetscContainerCreate(PETSC_COMM_SELF, &container);CHKERRQ(ierr);
638     ierr = PetscContainerSetPointer(container, (void *)maps);CHKERRQ(ierr);
639     ierr = PetscContainerSetUserDestroy(container, LandauGPUMapsDestroy);CHKERRQ(ierr);
640     ierr = PetscObjectCompose((PetscObject) JacP, "assembly_maps", (PetscObject) container);CHKERRQ(ierr);
641     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
642     // make maps
643     maps->data = NULL;
644     maps->num_elements = numCells;
645     maps->num_face = (PetscInt)(pow(Nq,1./((double)dim))+.001); // Q
646     maps->num_face = (PetscInt)(pow(maps->num_face,(double)(dim-1))+.001); // Q^2
647     maps->num_reduced = 0;
648     maps->deviceType = ctx->deviceType;
649 
650     // count reduced and get
651     ierr = PetscMalloc(maps->num_elements * sizeof *maps->gIdx, &maps->gIdx);CHKERRQ(ierr);
652     for (fieldA=0;fieldA<Nf;fieldA++) {
653       for (ej = cStart, eidx = 0 ; ej < cEnd; ++ej, ++eidx) {
654         for (q = 0; q < Nb; ++q) {
655           PetscInt    numindices,*indices;
656           PetscScalar *valuesOrig = elMat = elemMatrix;
657           ierr = PetscMemzero(elMat, totDim*totDim*sizeof(PetscScalar));CHKERRQ(ierr);
658           elMat[ (fieldA*Nb + q)*totDim + fieldA*Nb + q] = 1;
659           ierr = DMPlexGetClosureIndices(ctx->plex, section, globsection, ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
660           for (f = 0 ; f < numindices ; ++f) { // look for a non-zero on the diagonal
661             if (PetscAbs(PetscRealPart(elMat[f*numindices + f])) > PETSC_MACHINE_EPSILON) {
662               // found it
663               if (PetscAbs(PetscRealPart(elMat[f*numindices + f] - 1.)) < PETSC_MACHINE_EPSILON) {
664                 maps->gIdx[eidx][fieldA][q] = (LandauIdx)indices[f]; // normal vertex 1.0
665               } else { //found a constraint
666                 int       jj = 0;
667                 PetscReal sum = 0;
668                 const PetscInt ff = f;
669                 maps->gIdx[eidx][fieldA][q] = -maps->num_reduced - 1; // gid = -(idx+1): idx = -gid - 1
670                 do {  // constraints are continous in Plex - exploit that here
671                   int ii;
672                   for (ii = 0, pointMaps[maps->num_reduced][jj].scale = 0; ii < maps->num_face; ii++) { // DMPlex puts them all together
673                     if (ff + ii < numindices) {
674                       pointMaps[maps->num_reduced][jj].scale += PetscRealPart(elMat[f*numindices + ff + ii]);
675                     }
676                   }
677                   sum += pointMaps[maps->num_reduced][jj].scale;
678                   if (pointMaps[maps->num_reduced][jj].scale == 0) pointMaps[maps->num_reduced][jj].gid = -1; // 3D has Q and Q^2 interps -- all contiguous???
679                   else                                             pointMaps[maps->num_reduced][jj].gid = indices[f];
680                 } while (++jj < maps->num_face && ++f < numindices); // jj is incremented if we hit the end
681                 while (jj++ < maps->num_face) {
682                   pointMaps[maps->num_reduced][jj].scale = 0;
683                   pointMaps[maps->num_reduced][jj].gid = -1;
684                 }
685                 if (PetscAbs(sum-1.0) > 10*PETSC_MACHINE_EPSILON) { // debug
686                   int       d,f;
687                   PetscReal tmp = 0;
688                   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);
689                   for (d = 0, tmp = 0; d < numindices; ++d) {
690                     if (tmp!=0 && PetscAbs(tmp-1.0) > 10*PETSC_MACHINE_EPSILON) ierr = PetscPrintf(PETSC_COMM_WORLD,"%3D) %3D: ",d,indices[d]);CHKERRQ(ierr);
691                     for (f = 0; f < numindices; ++f) {
692                       tmp += PetscRealPart(elMat[d*numindices + f]);
693                     }
694                     if (tmp!=0) ierr = PetscPrintf(ctx->comm," | %22.16e\n",tmp);CHKERRQ(ierr);
695                   }
696                 }
697                 maps->num_reduced++;
698                 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);
699               }
700               break;
701             }
702           }
703           // cleanup
704           ierr = DMPlexRestoreClosureIndices(ctx->plex, section, globsection, ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
705           if (elMat != valuesOrig) {ierr = DMRestoreWorkArray(ctx->plex, numindices*numindices, MPIU_SCALAR, &elMat);CHKERRQ(ierr);}
706         }
707       }
708     }
709     // allocate and copy point datamaps->gIdx[eidx][field][q] -- for CPU version of this code, for debugging
710     ierr = PetscMalloc(maps->num_reduced * sizeof *maps->c_maps, &maps->c_maps);CHKERRQ(ierr);
711     for (ej = 0; ej < maps->num_reduced; ++ej) {
712       for (q = 0; q < maps->num_face; ++q) {
713         maps->c_maps[ej][q].scale = pointMaps[ej][q].scale;
714         maps->c_maps[ej][q].gid = pointMaps[ej][q].gid;
715       }
716     }
717 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
718     if (ctx->deviceType == LANDAU_KOKKOS) {
719       ierr = LandauKokkosCreateMatMaps(maps, pointMaps,Nf,Nq);CHKERRQ(ierr); // imples Kokkos does
720     } // else could be CUDA
721 #endif
722 #if defined(PETSC_HAVE_CUDA)
723     if (ctx->deviceType == LANDAU_CUDA) {
724       ierr = LandauCUDACreateMatMaps(maps, pointMaps,Nf,Nq);CHKERRQ(ierr);
725     }
726 #endif
727 
728     ierr = PetscLogEventEnd(ctx->events[2],0,0,0,0);CHKERRQ(ierr);
729   }
730   /* clean up */
731   if (IPf) {
732     ierr = PetscFree(IPf);CHKERRQ(ierr);
733   }
734   if (xdata) {
735     ierr = VecRestoreArrayReadAndMemType(a_X,&xdata);CHKERRQ(ierr);
736   }
737 
738   PetscFunctionReturn(0);
739 }
740 
741 #if defined(LANDAU_ADD_BCS)
742 static void zero_bc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
743                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
744                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
745                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
746 {
747   uexact[0] = 0;
748 }
749 #endif
750 
751 #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]; }}
752 static void CircleInflate(PetscReal r1, PetscReal r2, PetscReal r0, PetscInt num_sections, PetscReal x, PetscReal y,
753                           PetscReal *outX, PetscReal *outY)
754 {
755   PetscReal rr = PetscSqrtReal(x*x + y*y), outfact, efact;
756   if (rr < r1 + PETSC_SQRT_MACHINE_EPSILON) {
757     *outX = x; *outY = y;
758   } else {
759     const PetscReal xy[2] = {x,y}, sinphi=y/rr, cosphi=x/rr;
760     PetscReal       cth,sth,xyprime[2],Rth[2][2],rotcos,newrr;
761     if (num_sections==2) {
762       rotcos = 0.70710678118654;
763       outfact = 1.5; efact = 2.5;
764       /* rotate normalized vector into [-pi/4,pi/4) */
765       if (sinphi >= 0.) {         /* top cell, -pi/2 */
766         cth = 0.707106781186548; sth = -0.707106781186548;
767       } else {                    /* bottom cell -pi/8 */
768         cth = 0.707106781186548; sth = .707106781186548;
769       }
770     } else if (num_sections==3) {
771       rotcos = 0.86602540378443;
772       outfact = 1.5; efact = 2.5;
773       /* rotate normalized vector into [-pi/6,pi/6) */
774       if (sinphi >= 0.5) {         /* top cell, -pi/3 */
775         cth = 0.5; sth = -0.866025403784439;
776       } else if (sinphi >= -.5) {  /* mid cell 0 */
777         cth = 1.; sth = .0;
778       } else { /* bottom cell +pi/3 */
779         cth = 0.5; sth = 0.866025403784439;
780       }
781     } else if (num_sections==4) {
782       rotcos = 0.9238795325112;
783       outfact = 1.5; efact = 3;
784       /* rotate normalized vector into [-pi/8,pi/8) */
785       if (sinphi >= 0.707106781186548) {         /* top cell, -3pi/8 */
786         cth = 0.38268343236509; sth = -0.923879532511287;
787       } else if (sinphi >= 0.) {                 /* mid top cell -pi/8 */
788         cth = 0.923879532511287; sth = -.38268343236509;
789       } else if (sinphi >= -0.707106781186548) { /* mid bottom cell + pi/8 */
790         cth = 0.923879532511287; sth = 0.38268343236509;
791       } else {                                   /* bottom cell + 3pi/8 */
792         cth = 0.38268343236509; sth = .923879532511287;
793       }
794     } else {
795       cth = 0.; sth = 0.; rotcos = 0; efact = 0;
796     }
797     Rth[0][0] = cth; Rth[0][1] =-sth;
798     Rth[1][0] = sth; Rth[1][1] = cth;
799     MATVEC2(Rth,xy,xyprime);
800     if (num_sections==2) {
801       newrr = xyprime[0]/rotcos;
802     } else {
803       PetscReal newcosphi=xyprime[0]/rr, rin = r1, rout = rr - rin;
804       PetscReal routmax = r0*rotcos/newcosphi - rin, nroutmax = r0 - rin, routfrac = rout/routmax;
805       newrr = rin + routfrac*nroutmax;
806     }
807     *outX = cosphi*newrr; *outY = sinphi*newrr;
808     /* grade */
809     PetscReal fact,tt,rs,re, rr = PetscSqrtReal(PetscSqr(*outX) + PetscSqr(*outY));
810     if (rr > r2) { rs = r2; re = r0; fact = outfact;} /* outer zone */
811     else {         rs = r1; re = r2; fact = efact;} /* electron zone */
812     tt = (rs + PetscPowReal((rr - rs)/(re - rs),fact) * (re-rs)) / rr;
813     *outX *= tt;
814     *outY *= tt;
815   }
816 }
817 
818 static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
819 {
820   LandauCtx   *ctx = (LandauCtx*)a_ctx;
821   PetscReal   r = abc[0], z = abc[1];
822   if (ctx->inflate) {
823     PetscReal absR, absZ;
824     absR = PetscAbs(r);
825     absZ = PetscAbs(z);
826     CircleInflate(ctx->i_radius,ctx->e_radius,ctx->radius,ctx->num_sections,absR,absZ,&absR,&absZ);
827     r = (r > 0) ? absR : -absR;
828     z = (z > 0) ? absZ : -absZ;
829   }
830   xyz[0] = r;
831   xyz[1] = z;
832   if (dim==3) xyz[2] = abc[2];
833 
834   PetscFunctionReturn(0);
835 }
836 
837 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)
838 {
839   PetscReal err = 0.0;
840   PetscInt  f = *(PetscInt*)actx, j;
841   PetscFunctionBegin;
842   for (j = 0; j < dim; ++j) {
843     err += PetscSqr(PetscRealPart(u_x[f*dim+j]));
844   }
845   err = PetscRealPart(u[f]); /* just use rho */
846   *error = volume * err; /* * (ctx->axisymmetric ? 2.*PETSC_PI * r : 1); */
847   PetscFunctionReturn(0);
848 }
849 
850 static PetscErrorCode LandauDMCreateVMesh(MPI_Comm comm, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM *dm)
851 {
852   PetscErrorCode ierr;
853   PetscReal      radius = ctx->radius;
854   size_t         len;
855   char           fname[128] = ""; /* we can add a file if we want */
856 
857   PetscFunctionBegin;
858   /* create DM */
859   ierr = PetscStrlen(fname, &len);CHKERRQ(ierr);
860   if (len) {
861     PetscInt dim2;
862     ierr = DMPlexCreateFromFile(comm, fname, ctx->interpolate, dm);CHKERRQ(ierr);
863     ierr = DMGetDimension(*dm, &dim2);CHKERRQ(ierr);
864     if (LANDAU_DIM != dim2) SETERRQ2(comm, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim2,LANDAU_DIM);
865   } else {    /* p4est, quads */
866     /* Create plex mesh of Landau domain */
867     if (!ctx->sphere) {
868       PetscInt       cells[] = {2,2,2};
869       PetscReal      lo[] = {-radius,-radius,-radius}, hi[] = {radius,radius,radius};
870       DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim==2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
871       for (int i=0;i<ctx->preAMRRefine;i++) for (int j=0;j<3;j++) cells[j] *= 2;
872       if (dim==2) { lo[0] = 0; cells[0] /= 2; }
873       ierr = DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, cells, lo, hi, periodicity, PETSC_TRUE, dm);CHKERRQ(ierr);
874       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr); /* needed for periodic */
875       if (dim==3) {ierr = PetscObjectSetName((PetscObject) *dm, "cube");CHKERRQ(ierr);}
876       else {ierr = PetscObjectSetName((PetscObject) *dm, "half-plane");CHKERRQ(ierr);}
877     } else if (dim==2) {
878       PetscInt       numCells,cells[16][4],i,j;
879       PetscInt       numVerts;
880       PetscReal      inner_radius1 = ctx->i_radius, inner_radius2 = ctx->e_radius;
881       PetscReal      *flatCoords = NULL;
882       PetscInt       *flatCells = NULL, *pcell;
883       if (ctx->num_sections==2) {
884 #if 1
885         numCells = 5;
886         numVerts = 10;
887         int cells2[][4] = { {0,1,4,3},
888                             {1,2,5,4},
889                             {3,4,7,6},
890                             {4,5,8,7},
891                             {6,7,8,9} };
892         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
893         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
894         {
895           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
896           for (j = 0; j < numVerts-1; j++) {
897             PetscReal z, r, theta = -PETSC_PI/2 + (j%3) * PETSC_PI/2;
898             PetscReal rad = (j >= 6) ? inner_radius1 : (j >= 3) ? inner_radius2 : ctx->radius;
899             z = rad * PetscSinReal(theta);
900             coords[j][1] = z;
901             r = rad * PetscCosReal(theta);
902             coords[j][0] = r;
903           }
904           coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
905         }
906 #else
907         numCells = 4;
908         numVerts = 8;
909         static int     cells2[][4] = {{0,1,2,3},
910                                       {4,5,1,0},
911                                       {5,6,2,1},
912                                       {6,7,3,2}};
913         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
914         ierr = loc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
915         {
916           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
917           PetscInt j;
918           for (j = 0; j < 8; j++) {
919             PetscReal z, r;
920             PetscReal theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3.;
921             PetscReal rad = ctx->radius * ((j < 4) ? 0.5 : 1.0);
922             z = rad * PetscSinReal(theta);
923             coords[j][1] = z;
924             r = rad * PetscCosReal(theta);
925             coords[j][0] = r;
926           }
927         }
928 #endif
929       } else if (ctx->num_sections==3) {
930         numCells = 7;
931         numVerts = 12;
932         int cells2[][4] = { {0,1,5,4},
933                             {1,2,6,5},
934                             {2,3,7,6},
935                             {4,5,9,8},
936                             {5,6,10,9},
937                             {6,7,11,10},
938                             {8,9,10,11} };
939         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
940         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
941         {
942           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
943           for (j = 0; j < numVerts; j++) {
944             PetscReal z, r, theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3;
945             PetscReal rad = (j >= 8) ? inner_radius1 : (j >= 4) ? inner_radius2 : ctx->radius;
946             z = rad * PetscSinReal(theta);
947             coords[j][1] = z;
948             r = rad * PetscCosReal(theta);
949             coords[j][0] = r;
950           }
951         }
952       } else if (ctx->num_sections==4) {
953         numCells = 10;
954         numVerts = 16;
955         int cells2[][4] = { {0,1,6,5},
956                             {1,2,7,6},
957                             {2,3,8,7},
958                             {3,4,9,8},
959                             {5,6,11,10},
960                             {6,7,12,11},
961                             {7,8,13,12},
962                             {8,9,14,13},
963                             {10,11,12,15},
964                             {12,13,14,15}};
965         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
966         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
967         {
968           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
969           for (j = 0; j < numVerts-1; j++) {
970             PetscReal z, r, theta = -PETSC_PI/2 + (j%5) * PETSC_PI/4;
971             PetscReal rad = (j >= 10) ? inner_radius1 : (j >= 5) ? inner_radius2 : ctx->radius;
972             z = rad * PetscSinReal(theta);
973             coords[j][1] = z;
974             r = rad * PetscCosReal(theta);
975             coords[j][0] = r;
976           }
977           coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
978         }
979       } else {
980         numCells = 0;
981         numVerts = 0;
982       }
983       for (j = 0, pcell = flatCells; j < numCells; j++, pcell += 4) {
984         pcell[0] = cells[j][0]; pcell[1] = cells[j][1];
985         pcell[2] = cells[j][2]; pcell[3] = cells[j][3];
986       }
987       ierr = DMPlexCreateFromCellListPetsc(comm,2,numCells,numVerts,4,ctx->interpolate,flatCells,2,flatCoords,dm);CHKERRQ(ierr);
988       ierr = PetscFree2(flatCoords,flatCells);CHKERRQ(ierr);
989       ierr = PetscObjectSetName((PetscObject) *dm, "semi-circle");CHKERRQ(ierr);
990     } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Velocity space meshes does not support cubed sphere");
991   }
992   ierr = PetscObjectSetOptionsPrefix((PetscObject)*dm,prefix);CHKERRQ(ierr);
993 
994   ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); /* Plex refine */
995 
996   { /* p4est? */
997     char      convType[256];
998     PetscBool flg;
999     ierr = PetscOptionsBegin(ctx->comm, prefix, "Mesh conversion options", "DMPLEX");CHKERRQ(ierr);
1000     ierr = PetscOptionsFList("-dm_landau_type","Convert DMPlex to another format (should not be Plex!)","plexland.c",DMList,DMPLEX,convType,256,&flg);CHKERRQ(ierr);
1001     ierr = PetscOptionsEnd();CHKERRQ(ierr);
1002     if (flg) {
1003       DM dmforest;
1004       ierr = DMConvert(*dm,convType,&dmforest);CHKERRQ(ierr);
1005       if (dmforest) {
1006         PetscBool isForest;
1007         if (dmforest->prealloc_only != (*dm)->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"plex->prealloc_only != dm->prealloc_only");
1008         ierr = PetscObjectSetOptionsPrefix((PetscObject)dmforest,prefix);CHKERRQ(ierr);
1009         ierr = DMIsForest(dmforest,&isForest);CHKERRQ(ierr);
1010         if (isForest) {
1011           if (ctx->sphere && ctx->inflate) {
1012             ierr = DMForestSetBaseCoordinateMapping(dmforest,GeometryDMLandau,ctx);CHKERRQ(ierr);
1013           }
1014           if (dmforest->prealloc_only != (*dm)->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"plex->prealloc_only != dm->prealloc_only");
1015           ierr = DMDestroy(dm);CHKERRQ(ierr);
1016           *dm = dmforest;
1017           ctx->errorIndicator = ErrorIndicator_Simple; /* flag for Forest */
1018         } else SETERRQ(ctx->comm, PETSC_ERR_USER, "Converted to non Forest?");
1019       } else SETERRQ(ctx->comm, PETSC_ERR_USER, "Convert failed?");
1020     }
1021   }
1022   ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr);
1023   PetscFunctionReturn(0);
1024 }
1025 
1026 static PetscErrorCode SetupDS(DM dm, PetscInt dim, LandauCtx *ctx)
1027 {
1028   PetscErrorCode  ierr;
1029   PetscInt        ii;
1030   PetscFunctionBegin;
1031   for (ii=0;ii<ctx->num_species;ii++) {
1032     char     buf[256];
1033     if (ii==0) ierr = PetscSNPrintf(buf, 256, "e");
1034     else {ierr = PetscSNPrintf(buf, 256, "i%D", ii);CHKERRQ(ierr);}
1035     /* Setup Discretization - FEM */
1036     ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, NULL, PETSC_DECIDE, &ctx->fe[ii]);CHKERRQ(ierr);
1037     ierr = PetscObjectSetName((PetscObject) ctx->fe[ii], buf);CHKERRQ(ierr);
1038     ierr = DMSetField(dm, ii, NULL, (PetscObject) ctx->fe[ii]);CHKERRQ(ierr);
1039   }
1040   ierr = DMCreateDS(dm);CHKERRQ(ierr);
1041   if (1) {
1042     PetscInt        ii;
1043     PetscSection    section;
1044     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1045     for (ii=0;ii<ctx->num_species;ii++) {
1046       char buf[256];
1047       if (ii==0) ierr = PetscSNPrintf(buf, 256, "se");
1048       else ierr = PetscSNPrintf(buf, 256, "si%D", ii);
1049       ierr = PetscSectionSetComponentName(section, ii, 0, buf);CHKERRQ(ierr);
1050     }
1051   }
1052   PetscFunctionReturn(0);
1053 }
1054 
1055 /* Define a Maxwellian function for testing out the operator. */
1056 
1057 /* Using cartesian velocity space coordinates, the particle */
1058 /* density, [1/m^3], is defined according to */
1059 
1060 /* $$ n=\int_{R^3} dv^3 \left(\frac{m}{2\pi T}\right)^{3/2}\exp [- mv^2/(2T)] $$ */
1061 
1062 /* Using some constant, c, we normalize the velocity vector into a */
1063 /* dimensionless variable according to v=c*x. Thus the density, $n$, becomes */
1064 
1065 /* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */
1066 
1067 /* Defining $\theta=2T/mc^2$, we thus find that the probability density */
1068 /* for finding the particle within the interval in a box dx^3 around x is */
1069 
1070 /* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */
1071 
1072 typedef struct {
1073   LandauCtx   *ctx;
1074   PetscReal kT_m;
1075   PetscReal n;
1076   PetscReal shift;
1077 } MaxwellianCtx;
1078 
1079 static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
1080 {
1081   MaxwellianCtx *mctx = (MaxwellianCtx*)actx;
1082   LandauCtx     *ctx = mctx->ctx;
1083   PetscInt      i;
1084   PetscReal     v2 = 0, theta = 2*mctx->kT_m/(ctx->v_0*ctx->v_0); /* theta = 2kT/mc^2 */
1085   PetscFunctionBegin;
1086   /* compute the exponents, v^2 */
1087   for (i = 0; i < dim; ++i) v2 += x[i]*x[i];
1088   /* evaluate the Maxwellian */
1089   u[0] = mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
1090   if (mctx->shift!=0.) {
1091     v2 = 0;
1092     for (i = 0; i < dim-1; ++i) v2 += x[i]*x[i];
1093     v2 += (x[dim-1]-mctx->shift)*(x[dim-1]-mctx->shift);
1094     /* evaluate the shifted Maxwellian */
1095     u[0] += mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
1096   }
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 /*@
1101  LandauAddMaxwellians - Add a Maxwellian distribution to a state
1102 
1103  Collective on X
1104 
1105  Input Parameters:
1106  .   dm - The mesh
1107  +   time - Current time
1108  -   temps - Temperatures of each species
1109  .   ns - Number density of each species
1110  +   actx - Landau context
1111 
1112  Output Parameter:
1113  .   X  - The state
1114 
1115  Level: beginner
1116 
1117  .keywords: mesh
1118  .seealso: LandauCreateVelocitySpace()
1119  @*/
1120 PetscErrorCode LandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], void *actx)
1121 {
1122   LandauCtx      *ctx = (LandauCtx*)actx;
1123   PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *);
1124   PetscErrorCode ierr,ii;
1125   PetscInt       dim;
1126   MaxwellianCtx  *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];
1127 
1128   PetscFunctionBegin;
1129   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1130   if (!ctx) { ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr); }
1131   for (ii=0;ii<ctx->num_species;ii++) {
1132     mctxs[ii] = &data[ii];
1133     data[ii].ctx = ctx;
1134     data[ii].kT_m = ctx->k*temps[ii]/ctx->masses[ii]; /* kT/m */
1135     data[ii].n = ns[ii];
1136     initu[ii] = maxwellian;
1137     data[ii].shift = 0;
1138   }
1139   data[0].shift = ctx->electronShift;
1140   /* need to make ADD_ALL_VALUES work - TODO */
1141   ierr = DMProjectFunction(dm, time, initu, (void**)mctxs, INSERT_ALL_VALUES, X);CHKERRQ(ierr);
1142   PetscFunctionReturn(0);
1143 }
1144 
1145 /*
1146  LandauSetInitialCondition - Addes Maxwellians with context
1147 
1148  Collective on X
1149 
1150  Input Parameters:
1151  .   dm - The mesh
1152  +   actx - Landau context with T and n
1153 
1154  Output Parameter:
1155  .   X  - The state
1156 
1157  Level: beginner
1158 
1159  .keywords: mesh
1160  .seealso: LandauCreateVelocitySpace(), LandauAddMaxwellians()
1161  */
1162 static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, void *actx)
1163 {
1164   LandauCtx        *ctx = (LandauCtx*)actx;
1165   PetscErrorCode ierr;
1166   PetscFunctionBegin;
1167   if (!ctx) { ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr); }
1168   ierr = VecZeroEntries(X);CHKERRQ(ierr);
1169   ierr = LandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, ctx);CHKERRQ(ierr);
1170   PetscFunctionReturn(0);
1171 }
1172 
1173 static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscReal refineTol[], PetscReal coarsenTol[], PetscInt type, LandauCtx *ctx, DM *newDM)
1174 {
1175   DM               dm, plex, adaptedDM = NULL;
1176   PetscDS          prob;
1177   PetscBool        isForest;
1178   PetscQuadrature  quad;
1179   PetscInt         Nq, *Nb, cStart, cEnd, c, dim, qj, k;
1180   DMLabel          adaptLabel = NULL;
1181   PetscErrorCode   ierr;
1182 
1183   PetscFunctionBegin;
1184   ierr = VecGetDM(sol, &dm);CHKERRQ(ierr);
1185   ierr = DMCreateDS(dm);CHKERRQ(ierr);
1186   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1187   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1188   ierr = DMIsForest(dm, &isForest);CHKERRQ(ierr);
1189   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1190   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1191   ierr = DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);CHKERRQ(ierr);
1192   ierr = PetscFEGetQuadrature(fem, &quad);CHKERRQ(ierr);
1193   ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1194   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);
1195   ierr = PetscDSGetDimensions(prob, &Nb);CHKERRQ(ierr);
1196   if (type==4) {
1197     for (c = cStart; c < cEnd; c++) {
1198       ierr = DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);CHKERRQ(ierr);
1199     }
1200     ierr = PetscInfo1(sol, "Phase:%s: Uniform refinement\n","adaptToleranceFEM");CHKERRQ(ierr);
1201   } else if (type==2) {
1202     PetscInt  rCellIdx[8], eCellIdx[64], iCellIdx[64], eMaxIdx = -1, iMaxIdx = -1, nr = 0, nrmax = (dim==3) ? 8 : 2;
1203     PetscReal minRad = PETSC_INFINITY, r, eMinRad = PETSC_INFINITY, iMinRad = PETSC_INFINITY;
1204     for (c = 0; c < 64; c++) { eCellIdx[c] = iCellIdx[c] = -1; }
1205     for (c = cStart; c < cEnd; c++) {
1206       PetscReal    tt, v0[LANDAU_MAX_NQ*3], detJ[LANDAU_MAX_NQ];
1207       ierr = DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ);CHKERRQ(ierr);
1208       for (qj = 0; qj < Nq; ++qj) {
1209         tt = PetscSqr(v0[dim*qj+0]) + PetscSqr(v0[dim*qj+1]) + PetscSqr(((dim==3) ? v0[dim*qj+2] : 0));
1210         r = PetscSqrtReal(tt);
1211         if (r < minRad - PETSC_SQRT_MACHINE_EPSILON*10.) {
1212           minRad = r;
1213           nr = 0;
1214           rCellIdx[nr++]= c;
1215           ierr = PetscInfo4(sol, "\t\tPhase: adaptToleranceFEM Found first inner r=%e, cell %D, qp %D/%D\n", r, c, qj+1, Nq);CHKERRQ(ierr);
1216         } else if ((r-minRad) < PETSC_SQRT_MACHINE_EPSILON*100. && nr < nrmax) {
1217           for (k=0;k<nr;k++) if (c == rCellIdx[k]) break;
1218           if (k==nr) {
1219             rCellIdx[nr++]= c;
1220             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);
1221           }
1222         }
1223         if (ctx->sphere) {
1224           if ((tt=r-ctx->e_radius) > 0) {
1225             PetscInfo2(sol, "\t\t\t %D cell r=%g\n",c,tt);
1226             if (tt < eMinRad - PETSC_SQRT_MACHINE_EPSILON*100.) {
1227               eMinRad = tt;
1228               eMaxIdx = 0;
1229               eCellIdx[eMaxIdx++] = c;
1230             } else if (eMaxIdx > 0 && (tt-eMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != eCellIdx[eMaxIdx-1]) {
1231               eCellIdx[eMaxIdx++] = c;
1232             }
1233           }
1234           if ((tt=r-ctx->i_radius) > 0) {
1235             if (tt < iMinRad - 1.e-5) {
1236               iMinRad = tt;
1237               iMaxIdx = 0;
1238               iCellIdx[iMaxIdx++] = c;
1239             } else if (iMaxIdx > 0 && (tt-iMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != iCellIdx[iMaxIdx-1]) {
1240               iCellIdx[iMaxIdx++] = c;
1241             }
1242           }
1243         }
1244       }
1245     }
1246     for (k=0;k<nr;k++) {
1247       ierr = DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE);CHKERRQ(ierr);
1248     }
1249     if (ctx->sphere) {
1250       for (c = 0; c < eMaxIdx; c++) {
1251         ierr = DMLabelSetValue(adaptLabel, eCellIdx[c], DM_ADAPT_REFINE);CHKERRQ(ierr);
1252         ierr = PetscInfo3(sol, "\t\tPhase:%s: refine sphere e cell %D r=%g\n","adaptToleranceFEM",eCellIdx[c],eMinRad);CHKERRQ(ierr);
1253       }
1254       for (c = 0; c < iMaxIdx; c++) {
1255         ierr = DMLabelSetValue(adaptLabel, iCellIdx[c], DM_ADAPT_REFINE);CHKERRQ(ierr);
1256         ierr = PetscInfo3(sol, "\t\tPhase:%s: refine sphere i cell %D r=%g\n","adaptToleranceFEM",iCellIdx[c],iMinRad);CHKERRQ(ierr);
1257       }
1258     }
1259     ierr = PetscInfo4(sol, "Phase:%s: Adaptive refine origin cells %D,%D r=%g\n","adaptToleranceFEM",rCellIdx[0],rCellIdx[1],minRad);CHKERRQ(ierr);
1260   } else if (type==0 || type==1 || type==3) { /* refine along r=0 axis */
1261     PetscScalar  *coef = NULL;
1262     Vec          coords;
1263     PetscInt     csize,Nv,d,nz;
1264     DM           cdm;
1265     PetscSection cs;
1266     ierr = DMGetCoordinatesLocal(dm, &coords);CHKERRQ(ierr);
1267     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
1268     ierr = DMGetLocalSection(cdm, &cs);CHKERRQ(ierr);
1269     for (c = cStart; c < cEnd; c++) {
1270       PetscInt doit = 0, outside = 0;
1271       ierr = DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef);CHKERRQ(ierr);
1272       Nv = csize/dim;
1273       for (nz = d = 0; d < Nv; d++) {
1274         PetscReal z = PetscRealPart(coef[d*dim + (dim-1)]), x = PetscSqr(PetscRealPart(coef[d*dim + 0])) + ((dim==3) ? PetscSqr(PetscRealPart(coef[d*dim + 1])) : 0);
1275         x = PetscSqrtReal(x);
1276         if (x < PETSC_MACHINE_EPSILON*10. && PetscAbs(z)<PETSC_MACHINE_EPSILON*10.) doit = 1;             /* refine origin */
1277         else if (type==0 && (z < -PETSC_MACHINE_EPSILON*10. || z > ctx->re_radius+PETSC_MACHINE_EPSILON*10.)) outside++;   /* first pass don't refine bottom */
1278         else if (type==1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) outside++; /* don't refine outside electron refine radius */
1279         else if (type==3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) outside++; /* don't refine outside ion refine radius */
1280         if (x < PETSC_MACHINE_EPSILON*10.) nz++;
1281       }
1282       ierr = DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef);CHKERRQ(ierr);
1283       if (doit || (outside<Nv && nz)) {
1284         ierr = DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);CHKERRQ(ierr);
1285       }
1286     }
1287     ierr = PetscInfo1(sol, "Phase:%s: RE refinement\n","adaptToleranceFEM");CHKERRQ(ierr);
1288   }
1289   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1290   ierr = DMAdaptLabel(dm, adaptLabel, &adaptedDM);CHKERRQ(ierr);
1291   ierr = DMLabelDestroy(&adaptLabel);CHKERRQ(ierr);
1292   *newDM = adaptedDM;
1293   if (adaptedDM) {
1294     if (isForest) {
1295       ierr = DMForestSetAdaptivityForest(adaptedDM,NULL);CHKERRQ(ierr);
1296     }
1297     ierr = DMConvert(adaptedDM, DMPLEX, &plex);CHKERRQ(ierr);
1298     ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1299     ierr = PetscInfo2(sol, "\tPhase: adaptToleranceFEM: %D cells, %d total quadrature points\n",cEnd-cStart,Nq*(cEnd-cStart));CHKERRQ(ierr);
1300     ierr = DMDestroy(&plex);CHKERRQ(ierr);
1301   }
1302   PetscFunctionReturn(0);
1303 }
1304 
1305 static PetscErrorCode adapt(DM *dm, LandauCtx *ctx, Vec *uu)
1306 {
1307   PetscErrorCode  ierr;
1308   PetscInt        type, limits[5] = {ctx->numRERefine,ctx->nZRefine1,ctx->maxRefIts,ctx->nZRefine2,ctx->postAMRRefine};
1309   PetscInt        adaptIter;
1310 
1311   PetscFunctionBegin;
1312   for (type=0;type<5;type++) {
1313     for (adaptIter = 0; adaptIter<limits[type];adaptIter++) {
1314       DM  dmNew = NULL;
1315       ierr = adaptToleranceFEM(ctx->fe[0], *uu, ctx->refineTol, ctx->coarsenTol, type, ctx, &dmNew);CHKERRQ(ierr);
1316       if (dmNew)  { // can happen with no AMR and post refinement
1317         ierr = DMDestroy(dm);CHKERRQ(ierr);
1318         ierr = VecDestroy(uu);CHKERRQ(ierr);
1319         ierr = DMCreateGlobalVector(dmNew,uu);CHKERRQ(ierr);
1320         ierr = PetscObjectSetName((PetscObject) *uu, "u");CHKERRQ(ierr);
1321         ierr = LandauSetInitialCondition(dmNew, *uu, ctx);CHKERRQ(ierr);
1322         *dm = dmNew;
1323       }
1324     }
1325   }
1326   PetscFunctionReturn(0);
1327 }
1328 
1329 static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
1330 {
1331   PetscErrorCode    ierr;
1332   PetscBool         flg, sph_flg;
1333   PetscInt          ii,nt,nm,nc;
1334   DM                dummy;
1335 
1336   PetscFunctionBegin;
1337   ierr = DMCreate(ctx->comm,&dummy);CHKERRQ(ierr);
1338   /* get options - initialize context */
1339   ctx->verbose = 1;
1340   ctx->interpolate = PETSC_TRUE;
1341   ctx->gpu_assembly = PETSC_TRUE;
1342   ctx->sphere = PETSC_FALSE;
1343   ctx->inflate = PETSC_FALSE;
1344   ctx->electronShift = 0;
1345   ctx->errorIndicator = NULL;
1346   ctx->radius = 5.; /* electron thermal radius (velocity) */
1347   ctx->re_radius = 0.;
1348   ctx->vperp0_radius1 = 0;
1349   ctx->vperp0_radius2 = 0;
1350   ctx->e_radius = .1;
1351   ctx->i_radius = .01;
1352   ctx->maxRefIts = 5;
1353   ctx->postAMRRefine = 0;
1354   ctx->preAMRRefine = 0;
1355   ctx->nZRefine1 = 0;
1356   ctx->nZRefine2 = 0;
1357   ctx->numRERefine = 0;
1358   ctx->aux_bool = PETSC_FALSE;
1359   ctx->num_sections = 3; /* 2, 3 or 4 */
1360   /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
1361   ctx->charges[0] = -1;  /* electron charge (MKS) */
1362   ctx->masses[0] = 1/1835.5; /* temporary value in proton mass */
1363   ctx->n[0] = 1;
1364   ctx->thermal_temps[0] = 1;
1365   /* constants, etc. */
1366   ctx->epsilon0 = 8.8542e-12; /* permittivity of free space (MKS) F/m */
1367   ctx->k = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
1368   ctx->lnLam = 10;         /* cross section ratio large - small angle collisions */
1369   ctx->n_0 = 1.e20;        /* typical plasma n, but could set it to 1 */
1370   ctx->Ez = 0;
1371   ctx->v_0 = 1; /* in electron thermal velocity */
1372   ctx->subThreadBlockSize = 1; /* for device and maybe OMP */
1373   ctx->numConcurrency = 1; /* for device */
1374   ctx->SData_d = NULL;     /* for device */
1375   ctx->times[0] = 0;
1376   ctx->init = PETSC_FALSE; // doit first time
1377   ctx->use_matrix_mass = PETSC_FALSE; /* fast but slightly fragile */
1378   ctx->plex = NULL;     /* cache as expensive to Convert */
1379   ctx->use_relativistic_corrections = PETSC_FALSE;
1380   ctx->use_energy_tensor_trick = PETSC_FALSE; /* Use Eero's trick for energy conservation v --> grad(v^2/2) */
1381   ierr = PetscOptionsBegin(ctx->comm, prefix, "Options for Fokker-Plank-Landau collision operator", "none");CHKERRQ(ierr);
1382   {
1383     char opstring[256];
1384 #if defined(PETSC_HAVE_KOKKOS)
1385     ctx->deviceType = LANDAU_KOKKOS;
1386     ierr = PetscStrcpy(opstring,"kokkos");CHKERRQ(ierr);
1387 #if defined(PETSC_HAVE_CUDA)
1388     ctx->subThreadBlockSize = 16;
1389 #endif
1390 #elif defined(PETSC_HAVE_CUDA)
1391     ctx->deviceType = LANDAU_CUDA;
1392     ierr = PetscStrcpy(opstring,"cuda");CHKERRQ(ierr);
1393 #else
1394     ctx->deviceType = LANDAU_CPU;
1395     ierr = PetscStrcpy(opstring,"cpu");CHKERRQ(ierr);
1396     ctx->subThreadBlockSize = 0;
1397 #endif
1398     ierr = PetscOptionsString("-dm_landau_device_type","Use kernels on 'cpu', 'cuda', or 'kokkos'","plexland.c",opstring,opstring,256,NULL);CHKERRQ(ierr);
1399     ierr = PetscStrcmp("cpu",opstring,&flg);CHKERRQ(ierr);
1400     if (flg) {
1401       ctx->deviceType = LANDAU_CPU;
1402       ctx->subThreadBlockSize = 0;
1403     } else {
1404       ierr = PetscStrcmp("cuda",opstring,&flg);CHKERRQ(ierr);
1405       if (flg) {
1406         ctx->deviceType = LANDAU_CUDA;
1407         ctx->subThreadBlockSize = 0;
1408       } else {
1409         ierr = PetscStrcmp("kokkos",opstring,&flg);CHKERRQ(ierr);
1410         if (flg) ctx->deviceType = LANDAU_KOKKOS;
1411         else SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_device_type %s",opstring);
1412       }
1413     }
1414   }
1415   ierr = PetscOptionsBool("-dm_landau_gpu_assembly", "Assemble Jacobian on GPU", "plexland.c", ctx->gpu_assembly, &ctx->gpu_assembly, NULL);CHKERRQ(ierr);
1416   ierr = PetscOptionsReal("-dm_landau_electron_shift","Shift in thermal velocity of electrons","none",ctx->electronShift,&ctx->electronShift, NULL);CHKERRQ(ierr);
1417   ierr = PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, &sph_flg);CHKERRQ(ierr);
1418   ierr = PetscOptionsBool("-dm_landau_inflate", "With sphere, inflate for curved edges (no AMR)", "plexland.c", ctx->inflate, &ctx->inflate, NULL);CHKERRQ(ierr);
1419   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);
1420   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);
1421   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);
1422   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);
1423   ierr = PetscOptionsInt("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &ctx->postAMRRefine, NULL);CHKERRQ(ierr);
1424   ierr = PetscOptionsInt("-dm_landau_amr_pre_refine", "Number of levels to uniformly refine before AMR", "plexland.c", ctx->preAMRRefine, &ctx->preAMRRefine, NULL);CHKERRQ(ierr);
1425   ierr = PetscOptionsInt("-dm_landau_verbose", "", "plexland.c", ctx->verbose, &ctx->verbose, NULL);CHKERRQ(ierr);
1426   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);
1427   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);
1428   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);
1429   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);
1430   ierr = PetscOptionsReal("-dm_landau_n_0","Normalization constant for number density","plexland.c",ctx->n_0,&ctx->n_0, NULL);CHKERRQ(ierr);
1431   ierr = PetscOptionsReal("-dm_landau_ln_lambda","Cross section parameter","plexland.c",ctx->lnLam,&ctx->lnLam, NULL);CHKERRQ(ierr);
1432   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);
1433   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);
1434   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);
1435   ierr = PetscOptionsBool("-dm_landau_use_relativistic_corrections", "Use relativistic corrections", "plexland.c", ctx->use_relativistic_corrections, &ctx->use_relativistic_corrections, NULL);CHKERRQ(ierr);
1436   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);
1437 
1438   /* get num species with temperature*/
1439   {
1440     PetscReal arr[100];
1441     nt = 100;
1442     ierr = PetscOptionsRealArray("-dm_landau_thermal_temps", "Temperature of each species [e,i_0,i_1,...] in keV", "plexland.c", arr, &nt, &flg);CHKERRQ(ierr);
1443     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);
1444   }
1445   nt = LANDAU_MAX_SPECIES;
1446   for (ii=1;ii<LANDAU_MAX_SPECIES;ii++) {
1447     ctx->thermal_temps[ii] = 1.;
1448     ctx->charges[ii] = 1;
1449     ctx->masses[ii] = 1;
1450     ctx->n[ii] = (ii==1) ? 1 : 0;
1451   }
1452   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);
1453   if (flg) {
1454     PetscInfo1(dummy, "num_species set to number of thermal temps provided (%D)\n",nt);
1455     ctx->num_species = nt;
1456   } else SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
1457   for (ii=0;ii<ctx->num_species;ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
1458   nm = LANDAU_MAX_SPECIES-1;
1459   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);
1460   if (flg && nm != ctx->num_species-1) {
1461     SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"num ion masses %D != num species %D",nm,ctx->num_species-1);
1462   }
1463   nm = LANDAU_MAX_SPECIES;
1464   ierr = PetscOptionsRealArray("-dm_landau_n", "Normalized (by -n_0) number density of each species", "plexland.c", ctx->n, &nm, &flg);CHKERRQ(ierr);
1465   if (flg && nm != ctx->num_species) SETERRQ2(ctx->comm,PETSC_ERR_ARG_WRONG,"wrong num n: %D != num species %D",nm,ctx->num_species);
1466   ctx->n_0 *= ctx->n[0]; /* normalized number density */
1467   for (ii=1;ii<ctx->num_species;ii++) ctx->n[ii] = ctx->n[ii]/ctx->n[0];
1468   ctx->n[0] = 1;
1469   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
1470   ctx->masses[0] = 9.10938356e-31; /* electron mass kg (should be about right already) */
1471   ctx->m_0 = ctx->masses[0]; /* arbitrary reference mass, electrons */
1472   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);
1473   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) */
1474   nc = LANDAU_MAX_SPECIES-1;
1475   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);
1476   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);
1477   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
1478   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 */
1479   /* geometry */
1480   for (ii=0;ii<ctx->num_species;ii++) ctx->refineTol[ii]  = PETSC_MAX_REAL;
1481   for (ii=0;ii<ctx->num_species;ii++) ctx->coarsenTol[ii] = 0.;
1482   ii = LANDAU_MAX_SPECIES;
1483   ierr = PetscOptionsRealArray("-dm_landau_refine_tol","tolerance for refining cells in AMR","plexland.c",ctx->refineTol, &ii, &flg);CHKERRQ(ierr);
1484   if (flg && ii != ctx->num_species) ierr = PetscInfo2(dummy, "Phase: Warning, #refine_tol %D != num_species %D\n",ii,ctx->num_species);CHKERRQ(ierr);
1485   ii = LANDAU_MAX_SPECIES;
1486   ierr = PetscOptionsRealArray("-dm_landau_coarsen_tol","tolerance for coarsening cells in AMR","plexland.c",ctx->coarsenTol, &ii, &flg);CHKERRQ(ierr);
1487   if (flg && ii != ctx->num_species) ierr = PetscInfo2(dummy, "Phase: Warning, #coarsen_tol %D != num_species %D\n",ii,ctx->num_species);CHKERRQ(ierr);
1488   ierr = PetscOptionsReal("-dm_landau_domain_radius","Phase space size in units of electron thermal velocity","plexland.c",ctx->radius,&ctx->radius, &flg);CHKERRQ(ierr);
1489   if (flg && ctx->radius <= 0) { /* negative is ratio of c */
1490     if (ctx->radius == 0) ctx->radius = 0.75;
1491     else ctx->radius = -ctx->radius;
1492     ctx->radius = ctx->radius*C_0(ctx->v_0);
1493     ierr = PetscInfo1(dummy, "Change domain radius to %e\n",ctx->radius);CHKERRQ(ierr);
1494   }
1495   ierr = PetscOptionsReal("-dm_landau_i_radius","Ion thermal velocity, used for circular meshes","plexland.c",ctx->i_radius,&ctx->i_radius, &flg);CHKERRQ(ierr);
1496   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an ion radius but did not set sphere, user error really */
1497   if (!flg) {
1498     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 */
1499   }
1500   ierr = PetscOptionsReal("-dm_landau_e_radius","Electron thermal velocity, used for circular meshes","plexland.c",ctx->e_radius,&ctx->e_radius, &flg);CHKERRQ(ierr);
1501   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an e radius but did not set sphere, user error really */
1502   if (!flg) {
1503     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 */
1504   }
1505   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);
1506   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);
1507   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1508   for (ii=ctx->num_species;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] = ctx->thermal_temps[ii]  = ctx->charges[ii] = 0;
1509   if (ctx->verbose > 0) {
1510     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);
1511     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);
1512     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);
1513   }
1514   ierr = DMDestroy(&dummy);CHKERRQ(ierr);
1515   {
1516     PetscMPIInt    rank;
1517     ierr = MPI_Comm_rank(ctx->comm, &rank);CHKERRMPI(ierr);
1518     /* PetscLogStage  setup_stage; */
1519     ierr = PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[11]);CHKERRQ(ierr); /* 11 */
1520     ierr = PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[0]);CHKERRQ(ierr); /* 0 */
1521     ierr = PetscLogEventRegister("Landau Mass", DM_CLASSID, &ctx->events[9]);CHKERRQ(ierr); /* 9 */
1522     ierr = PetscLogEventRegister(" Preamble", DM_CLASSID, &ctx->events[10]);CHKERRQ(ierr); /* 10 */
1523     ierr = PetscLogEventRegister(" static IP Data", DM_CLASSID, &ctx->events[7]);CHKERRQ(ierr); /* 7 */
1524     ierr = PetscLogEventRegister(" dynamic IP-Jac", DM_CLASSID, &ctx->events[1]);CHKERRQ(ierr); /* 1 */
1525     ierr = PetscLogEventRegister(" Kernel-init", DM_CLASSID, &ctx->events[3]);CHKERRQ(ierr); /* 3 */
1526     ierr = PetscLogEventRegister(" Jac-f-df (GPU)", DM_CLASSID, &ctx->events[8]);CHKERRQ(ierr); /* 8 */
1527     ierr = PetscLogEventRegister(" Kernel (GPU)", DM_CLASSID, &ctx->events[4]);CHKERRQ(ierr); /* 4 */
1528     ierr = PetscLogEventRegister(" Copy to CPU", DM_CLASSID, &ctx->events[5]);CHKERRQ(ierr); /* 5 */
1529     ierr = PetscLogEventRegister(" Jac-assemble", DM_CLASSID, &ctx->events[6]);CHKERRQ(ierr); /* 6 */
1530     ierr = PetscLogEventRegister(" Jac asmbl setup", DM_CLASSID, &ctx->events[2]);CHKERRQ(ierr); /* 2 */
1531     ierr = PetscLogEventRegister(" Other", DM_CLASSID, &ctx->events[13]);CHKERRQ(ierr); /* 13 */
1532 
1533     if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
1534       ierr = PetscOptionsClearValue(NULL,"-snes_converged_reason");CHKERRQ(ierr);
1535       ierr = PetscOptionsClearValue(NULL,"-ksp_converged_reason");CHKERRQ(ierr);
1536       ierr = PetscOptionsClearValue(NULL,"-snes_monitor");CHKERRQ(ierr);
1537       ierr = PetscOptionsClearValue(NULL,"-ksp_monitor");CHKERRQ(ierr);
1538       ierr = PetscOptionsClearValue(NULL,"-ts_monitor");CHKERRQ(ierr);
1539       ierr = PetscOptionsClearValue(NULL,"-ts_adapt_monitor");CHKERRQ(ierr);
1540       ierr = PetscOptionsClearValue(NULL,"-dm_landau_amr_dm_view");CHKERRQ(ierr);
1541       ierr = PetscOptionsClearValue(NULL,"-dm_landau_amr_vec_view");CHKERRQ(ierr);
1542       ierr = PetscOptionsClearValue(NULL,"-dm_landau_pre_dm_view");CHKERRQ(ierr);
1543       ierr = PetscOptionsClearValue(NULL,"-dm_landau_pre_vec_view");CHKERRQ(ierr);
1544       ierr = PetscOptionsClearValue(NULL,"-info");CHKERRQ(ierr);
1545     }
1546   }
1547   PetscFunctionReturn(0);
1548 }
1549 
1550 /*@C
1551  LandauCreateVelocitySpace - Create a DMPlex velocity space mesh
1552 
1553  Collective on comm
1554 
1555  Input Parameters:
1556  +   comm  - The MPI communicator
1557  .   dim - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
1558  -   prefix - prefix for options
1559 
1560  Output Parameter:
1561  .   dm  - The DM object representing the mesh
1562  +   X - A vector (user destroys)
1563  -   J - Optional matrix (object destroys)
1564 
1565  Level: beginner
1566 
1567  .keywords: mesh
1568  .seealso: DMPlexCreate(), LandauDestroyVelocitySpace()
1569  @*/
1570 PetscErrorCode LandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *dm)
1571 {
1572   PetscErrorCode ierr;
1573   LandauCtx      *ctx;
1574   PetscBool      prealloc_only,flg;
1575 
1576   PetscFunctionBegin;
1577   if (dim!=2 && dim!=3) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Only 2D and 3D supported");
1578   ierr = PetscNew(&ctx);CHKERRQ(ierr);
1579   ctx->comm = comm; /* used for diagnostics and global errors */
1580   /* process options */
1581   ierr = ProcessOptions(ctx,prefix);CHKERRQ(ierr);
1582   if (dim==2) ctx->use_relativistic_corrections = PETSC_FALSE;
1583   /* Create Mesh */
1584   ierr = LandauDMCreateVMesh(PETSC_COMM_SELF, dim, prefix, ctx, dm);CHKERRQ(ierr);
1585   prealloc_only = (*dm)->prealloc_only;
1586   ierr = DMViewFromOptions(*dm,NULL,"-dm_landau_pre_dm_view");CHKERRQ(ierr);
1587   ierr = DMSetApplicationContext(*dm, ctx);CHKERRQ(ierr);
1588   /* create FEM */
1589   ierr = SetupDS(*dm,dim,ctx);CHKERRQ(ierr);
1590   /* set initial state */
1591   ierr = DMCreateGlobalVector(*dm,X);CHKERRQ(ierr);
1592   ierr = PetscObjectSetName((PetscObject) *X, "u");CHKERRQ(ierr);
1593   /* initial static refinement, no solve */
1594   ierr = LandauSetInitialCondition(*dm, *X, ctx);CHKERRQ(ierr);
1595   ierr = VecViewFromOptions(*X, NULL, "-dm_landau_pre_vec_view");CHKERRQ(ierr);
1596   /* forest refinement */
1597   if (ctx->errorIndicator) {
1598     /* AMR */
1599     ierr = adapt(dm,ctx,X);CHKERRQ(ierr);
1600     if ((*dm)->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"(*dm)->prealloc_only != prealloc_only");
1601     ierr = DMViewFromOptions(*dm,NULL,"-dm_landau_amr_dm_view");CHKERRQ(ierr);
1602     ierr = VecViewFromOptions(*X, NULL, "-dm_landau_amr_vec_view");CHKERRQ(ierr);
1603   }
1604   ierr = DMSetApplicationContext(*dm, ctx);CHKERRQ(ierr);
1605   ctx->dmv = *dm;
1606   if (ctx->dmv->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"ctx->dmv->prealloc_only != prealloc_only");
1607   ierr = DMCreateMatrix(ctx->dmv, &ctx->J);CHKERRQ(ierr);
1608   ierr = MatSetOption(ctx->J, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
1609   ierr = MatSetOption(ctx->J, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE);CHKERRQ(ierr);
1610   if (J) *J = ctx->J;
1611   /* check for types that we need */
1612 #if defined(PETSC_HAVE_KOKKOS)
1613   if (ctx->deviceType == LANDAU_CPU) {
1614     ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,MATAIJKOKKOS,"");CHKERRQ(ierr);
1615   }
1616 #elif defined(PETSC_HAVE_CUDA)
1617   if (ctx->deviceType == LANDAU_CPU) {
1618     ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");CHKERRQ(ierr);
1619   }
1620 #endif
1621   if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
1622     if (ctx->deviceType == LANDAU_CUDA) {
1623       ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");CHKERRQ(ierr);
1624       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must use '-dm_mat_type aijcusparse -dm_vec_type cuda' for GPU assembly and Cuda");
1625     } else if (ctx->deviceType == LANDAU_KOKKOS) {
1626       ierr = PetscObjectTypeCompareAny((PetscObject)ctx->J,&flg,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,MATAIJKOKKOS,"");CHKERRQ(ierr);
1627 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1628       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for GPU assembly and Kokkos");
1629 #else
1630       if (!flg) SETERRQ(ctx->comm,PETSC_ERR_ARG_WRONG,"must configure with '--download-kokkos-kernels=1' for GPU assembly and Kokkos");
1631 #endif
1632     }
1633   }
1634   PetscFunctionReturn(0);
1635 }
1636 
1637 /*@
1638  LandauDestroyVelocitySpace - Destroy a DMPlex velocity space mesh
1639 
1640  Collective on dm
1641 
1642  Input/Output Parameters:
1643  .   dm - the dm to destroy
1644 
1645  Level: beginner
1646 
1647  .keywords: mesh
1648  .seealso: LandauCreateVelocitySpace()
1649  @*/
1650 PetscErrorCode LandauDestroyVelocitySpace(DM *dm)
1651 {
1652   PetscErrorCode ierr,ii;
1653   LandauCtx      *ctx;
1654   PetscContainer container = NULL;
1655   PetscFunctionBegin;
1656   ierr = DMGetApplicationContext(*dm, &ctx);CHKERRQ(ierr);
1657   ierr = PetscObjectQuery((PetscObject)ctx->J,"coloring", (PetscObject*)&container);CHKERRQ(ierr);
1658   if (container) {
1659     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
1660   }
1661   ierr = MatDestroy(&ctx->M);CHKERRQ(ierr);
1662   ierr = MatDestroy(&ctx->J);CHKERRQ(ierr);
1663   for (ii=0;ii<ctx->num_species;ii++) {
1664     ierr = PetscFEDestroy(&ctx->fe[ii]);CHKERRQ(ierr);
1665   }
1666   if (ctx->deviceType == LANDAU_CUDA) {
1667 #if defined(PETSC_HAVE_CUDA)
1668     ierr = LandauCUDAStaticDataClear(ctx->SData_d);CHKERRQ(ierr);
1669 #else
1670     SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
1671 #endif
1672   } else if (ctx->deviceType == LANDAU_KOKKOS) {
1673 #if defined(PETSC_HAVE_KOKKOS)
1674     ierr = LandauKokkosStaticDataClear(ctx->SData_d);CHKERRQ(ierr);
1675 #else
1676     SETERRQ1(ctx->comm,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
1677 #endif
1678   } else {
1679     if (ctx->SData_d) { /* in a CPU run */
1680       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;
1681       ierr = PetscFree5(mass_w,ww,xx,yy,invJ);CHKERRQ(ierr);
1682       if (zz) {
1683         ierr = PetscFree(zz);CHKERRQ(ierr);
1684       }
1685     }
1686   }
1687   ierr = PetscFree(ctx->SData_d);CHKERRQ(ierr);
1688   if (ctx->times[0] > 0) {
1689     ierr = PetscPrintf(ctx->comm, "Landau Operator       %d 1.0 %10.3e ....\n",10000,ctx->times[0]);CHKERRQ(ierr);
1690   }
1691   if (ctx->plex != NULL) {
1692     ierr = DMDestroy(&ctx->plex);CHKERRQ(ierr);
1693   }
1694   PetscFree(ctx);
1695   ierr = DMDestroy(dm);CHKERRQ(ierr);
1696   PetscFunctionReturn(0);
1697 }
1698 
1699 /* < v, ru > */
1700 static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1701                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1702                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1703                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1704 {
1705   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1706   f0[0] = u[ii];
1707 }
1708 
1709 /* < v, ru > */
1710 static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1711                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1712                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1713                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1714 {
1715   PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
1716   f0[0] = x[jj]*u[ii]; /* x momentum */
1717 }
1718 
1719 static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1720                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1721                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1722                     PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1723 {
1724   PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
1725   double tmp1 = 0.;
1726   for (i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1727   f0[0] = tmp1*u[ii];
1728 }
1729 
1730 static PetscErrorCode gamma_n_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *actx)
1731 {
1732   const PetscReal *c2_0_arr = ((PetscReal*)actx);
1733   const PetscReal c02 = c2_0_arr[0];
1734 
1735   PetscFunctionBegin;
1736   for (int s = 0 ; s < Nf ; s++) {
1737     PetscReal tmp1 = 0.;
1738     for (int i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1739 #if defined(PETSC_USE_DEBUG)
1740     u[s] = PetscSqrtReal(1. + tmp1/c02);//  u[0] = PetscSqrtReal(1. + xx);
1741 #else
1742     {
1743       PetscReal xx = tmp1/c02;
1744       u[s] = xx/(PetscSqrtReal(1. + xx) + 1.); // better conditioned = xx/(PetscSqrtReal(1. + xx) + 1.)
1745     }
1746 #endif
1747   }
1748   PetscFunctionReturn(0);
1749 }
1750 
1751 /* < v, ru > */
1752 static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1753                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1754                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1755                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1756 {
1757   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1758   f0[0] = 2.*PETSC_PI*x[0]*u[ii];
1759 }
1760 
1761 /* < v, ru > */
1762 static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1763                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1764                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1765                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1766 {
1767   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1768   f0[0] = 2.*PETSC_PI*x[0]*x[1]*u[ii];
1769 }
1770 
1771 static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1772                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1773                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1774                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1775 {
1776   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1777   f0[0] =  2.*PETSC_PI*x[0]*(x[0]*x[0] + x[1]*x[1])*u[ii];
1778 }
1779 
1780 /*@
1781  LandauPrintNorms - collects moments and prints them
1782 
1783  Collective on dm
1784 
1785  Input Parameters:
1786  +   X  - the state
1787  -   stepi - current step to print
1788 
1789  Level: beginner
1790 
1791  .keywords: mesh
1792  .seealso: LandauCreateVelocitySpace()
1793  @*/
1794 PetscErrorCode LandauPrintNorms(Vec X, PetscInt stepi)
1795 {
1796   PetscErrorCode ierr;
1797   LandauCtx      *ctx;
1798   PetscDS        prob;
1799   DM             dm;
1800   PetscInt       cStart, cEnd, dim, ii;
1801   PetscScalar    xmomentumtot=0, ymomentumtot=0, zmomentumtot=0, energytot=0, densitytot=0, tt[LANDAU_MAX_SPECIES];
1802   PetscScalar    xmomentum[LANDAU_MAX_SPECIES],  ymomentum[LANDAU_MAX_SPECIES],  zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
1803 
1804   PetscFunctionBegin;
1805   ierr = VecGetDM(X, &dm);CHKERRQ(ierr);
1806   if (!dm) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no DM");
1807   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1808   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
1809   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1810   if (!ctx->plex) {
1811     ierr = DMConvert(ctx->dmv, DMPLEX, &ctx->plex);CHKERRQ(ierr);
1812   }
1813   ierr = DMCreateDS(ctx->plex);CHKERRQ(ierr);
1814   ierr = DMGetDS(ctx->plex, &prob);CHKERRQ(ierr);
1815   /* print momentum and energy */
1816   for (ii=0;ii<ctx->num_species;ii++) {
1817     PetscScalar user[2] = { (PetscScalar)ii, (PetscScalar)ctx->charges[ii]};
1818     ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1819     if (dim==2) { /* 2/3X + 3V (cylindrical coordinates) */
1820       ierr = PetscDSSetObjective(prob, 0, &f0_s_rden);CHKERRQ(ierr);
1821       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1822       density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1823       ierr = PetscDSSetObjective(prob, 0, &f0_s_rmom);CHKERRQ(ierr);
1824       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1825       zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1826       ierr = PetscDSSetObjective(prob, 0, &f0_s_rv2);CHKERRQ(ierr);
1827       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1828       energy[ii] = tt[0]*0.5*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1829       zmomentumtot += zmomentum[ii];
1830       energytot  += energy[ii];
1831       densitytot += density[ii];
1832       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);
1833     } else { /* 2/3X + 3V */
1834       ierr = PetscDSSetObjective(prob, 0, &f0_s_den);CHKERRQ(ierr);
1835       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1836       density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1837       ierr = PetscDSSetObjective(prob, 0, &f0_s_mom);CHKERRQ(ierr);
1838       user[1] = 0;
1839       ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1840       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1841       xmomentum[ii]  = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1842       user[1] = 1;
1843       ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1844       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1845       ymomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1846       user[1] = 2;
1847       ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1848       ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1849       zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1850       if (ctx->use_relativistic_corrections) {
1851         if (ii==0) {
1852           Vec            gamma_glob,Mf,v1,v2;
1853           PetscErrorCode (*gammaf[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {gamma_n_f};
1854           PetscReal      *c2_0[1], data[1];
1855           PetscInt       N;
1856 
1857           data[0] = PetscSqr(C_0(ctx->v_0));
1858           ierr = DMGetGlobalVector(dm,&gamma_glob);CHKERRQ(ierr);
1859           ierr = DMGetGlobalVector(dm,&Mf);CHKERRQ(ierr);
1860           c2_0[0] = &data[0];
1861           ierr = DMProjectFunction(dm, 0., gammaf, (void**)c2_0, INSERT_ALL_VALUES, gamma_glob);CHKERRQ(ierr);
1862           ierr = MatMult(ctx->M,X,Mf);CHKERRQ(ierr);
1863           // get each component
1864           ierr = VecGetSize(X,&N);CHKERRQ(ierr);
1865           ierr = VecCreate(ctx->comm,&v1);CHKERRQ(ierr);
1866           ierr = VecSetSizes(v1,PETSC_DECIDE,N/ctx->num_species);CHKERRQ(ierr);
1867           ierr = VecCreate(ctx->comm,&v2);CHKERRQ(ierr);
1868           ierr = VecSetSizes(v2,PETSC_DECIDE,N/ctx->num_species);CHKERRQ(ierr);
1869           ierr = VecGetBlockSize(gamma_glob,&N);CHKERRQ(ierr);
1870           ierr = VecSetFromOptions(v1);CHKERRQ(ierr);
1871           ierr = VecSetFromOptions(v2);CHKERRQ(ierr);
1872           for (int i=0;i<ctx->num_species;i++) {
1873             PetscScalar val;
1874             ierr = VecStrideGather(gamma_glob,i,v1,INSERT_VALUES);CHKERRQ(ierr);
1875             ierr = VecStrideGather(Mf,i,v2,INSERT_VALUES);CHKERRQ(ierr);
1876             ierr = VecDot(v1,v2,&val);CHKERRQ(ierr);
1877             energy[i] = PetscRealPart(val)*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[i];
1878           }
1879           ierr = DMRestoreGlobalVector(dm, &gamma_glob);CHKERRQ(ierr);
1880           ierr = DMRestoreGlobalVector(dm, &Mf);CHKERRQ(ierr);
1881           ierr = VecDestroy(&v1);CHKERRQ(ierr);
1882           ierr = VecDestroy(&v2);CHKERRQ(ierr);
1883          }
1884       } else {
1885         ierr = PetscDSSetObjective(prob, 0, &f0_s_v2);CHKERRQ(ierr);
1886         ierr = DMPlexComputeIntegralFEM(ctx->plex,X,tt,ctx);CHKERRQ(ierr);
1887         energy[ii]    = 0.5*tt[0]*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1888       }
1889       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",
1890                          stepi,ii,PetscRealPart(density[ii]),PetscRealPart(xmomentum[ii]),PetscRealPart(ymomentum[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));CHKERRQ(ierr);
1891       xmomentumtot += xmomentum[ii];
1892       ymomentumtot += ymomentum[ii];
1893       zmomentumtot += zmomentum[ii];
1894       energytot  += energy[ii];
1895       densitytot += density[ii];
1896     }
1897     if (ctx->num_species>1) PetscPrintf(ctx->comm, "\n");
1898   }
1899   /* totals */
1900   ierr = DMPlexGetHeightStratum(ctx->plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1901   if (ctx->num_species>1) {
1902     if (dim==2) {
1903       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)",
1904                          stepi,(double)PetscRealPart(densitytot),(double)PetscRealPart(zmomentumtot),(double)PetscRealPart(energytot),(double)(ctx->masses[1]/ctx->masses[0]),cEnd-cStart);CHKERRQ(ierr);
1905     } else {
1906       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)",
1907                          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);
1908     }
1909   } else {
1910     ierr = PetscPrintf(ctx->comm, " -- %D cells",cEnd-cStart);CHKERRQ(ierr);
1911   }
1912   if (ctx->verbose > 1) {ierr = PetscPrintf(ctx->comm,", %D sub (vector) threads\n",ctx->subThreadBlockSize);CHKERRQ(ierr);}
1913   else {ierr = PetscPrintf(ctx->comm,"\n");CHKERRQ(ierr);}
1914   PetscFunctionReturn(0);
1915 }
1916 
1917 static PetscErrorCode destroy_coloring (void *is)
1918 {
1919   ISColoring tmp = (ISColoring)is;
1920   return ISColoringDestroy(&tmp);
1921 }
1922 
1923 /*@
1924  LandauCreateColoring - create a coloring and add to matrix (Landau context used just for 'print' flag, should be in DMPlex)
1925 
1926  Collective on JacP
1927 
1928  Input Parameters:
1929  +   JacP  - matrix to add coloring to
1930  -   plex - The DM
1931 
1932  Output Parameter:
1933  .   container  - Container with coloring
1934 
1935  Level: beginner
1936 
1937  .keywords: mesh
1938  .seealso: LandauCreateVelocitySpace()
1939  @*/
1940 PetscErrorCode LandauCreateColoring(Mat JacP, DM plex, PetscContainer *container)
1941 {
1942   PetscErrorCode  ierr;
1943   PetscInt        dim,cell,i,ej,nc,Nv,totDim,numGCells,cStart,cEnd;
1944   ISColoring      iscoloring = NULL;
1945   Mat             G,Q;
1946   PetscScalar     ones[128];
1947   MatColoring     mc;
1948   IS             *is;
1949   PetscInt        csize,colour,j,k;
1950   const PetscInt *indices;
1951   PetscInt       numComp[1];
1952   PetscInt       numDof[4];
1953   PetscFE        fe;
1954   DM             colordm;
1955   PetscSection   csection, section, globalSection;
1956   PetscDS        prob;
1957   LandauCtx      *ctx;
1958 
1959   PetscFunctionBegin;
1960   ierr = DMGetApplicationContext(plex, &ctx);CHKERRQ(ierr);
1961   ierr = DMGetLocalSection(plex, &section);CHKERRQ(ierr);
1962   ierr = DMGetGlobalSection(plex, &globalSection);CHKERRQ(ierr);
1963   ierr = DMGetDimension(plex, &dim);CHKERRQ(ierr);
1964   ierr = DMGetDS(plex, &prob);CHKERRQ(ierr);
1965   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1966   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1967   numGCells = cEnd - cStart;
1968   /* create cell centered DM */
1969   ierr = DMClone(plex, &colordm);CHKERRQ(ierr);
1970   ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, "color_", PETSC_DECIDE, &fe);CHKERRQ(ierr);
1971   ierr = PetscObjectSetName((PetscObject) fe, "color");CHKERRQ(ierr);
1972   ierr = DMSetField(colordm, 0, NULL, (PetscObject)fe);CHKERRQ(ierr);
1973   ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
1974   for (i = 0; i < (dim+1); ++i) numDof[i] = 0;
1975   numDof[dim] = 1;
1976   numComp[0] = 1;
1977   ierr = DMPlexCreateSection(colordm, NULL, numComp, numDof, 0, NULL, NULL, NULL, NULL, &csection);CHKERRQ(ierr);
1978   ierr = PetscSectionSetFieldName(csection, 0, "color");CHKERRQ(ierr);
1979   ierr = DMSetLocalSection(colordm, csection);CHKERRQ(ierr);
1980   ierr = DMViewFromOptions(colordm,NULL,"-color_dm_view");CHKERRQ(ierr);
1981   /* get vertex to element map Q and colroing graph G */
1982   ierr = MatGetSize(JacP,NULL,&Nv);CHKERRQ(ierr);
1983   ierr = MatCreateAIJ(PETSC_COMM_SELF,PETSC_DECIDE,PETSC_DECIDE,numGCells,Nv,totDim,NULL,0,NULL,&Q);CHKERRQ(ierr);
1984   for (i=0;i<128;i++) ones[i] = 1.0;
1985   for (cell = cStart, ej = 0 ; cell < cEnd; ++cell, ++ej) {
1986     PetscInt numindices,*indices;
1987     ierr = DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);CHKERRQ(ierr);
1988     if (numindices>128) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many indices. %D > %D",numindices,128);
1989     ierr = MatSetValues(Q,1,&ej,numindices,indices,ones,ADD_VALUES);CHKERRQ(ierr);
1990     ierr = DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);CHKERRQ(ierr);
1991   }
1992   ierr = MatAssemblyBegin(Q, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1993   ierr = MatAssemblyEnd(Q, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1994   ierr = MatMatTransposeMult(Q,Q,MAT_INITIAL_MATRIX,4.0,&G);CHKERRQ(ierr);
1995   ierr = PetscObjectSetName((PetscObject) Q, "Q");CHKERRQ(ierr);
1996   ierr = PetscObjectSetName((PetscObject) G, "coloring graph");CHKERRQ(ierr);
1997   ierr = MatViewFromOptions(G,NULL,"-coloring_mat_view");CHKERRQ(ierr);
1998   ierr = MatViewFromOptions(Q,NULL,"-coloring_mat_view");CHKERRQ(ierr);
1999   ierr = MatDestroy(&Q);CHKERRQ(ierr);
2000   /* coloring */
2001   ierr = MatColoringCreate(G,&mc);CHKERRQ(ierr);
2002   ierr = MatColoringSetDistance(mc,1);CHKERRQ(ierr);
2003   ierr = MatColoringSetType(mc,MATCOLORINGJP);CHKERRQ(ierr);
2004   ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
2005   ierr = MatColoringApply(mc,&iscoloring);CHKERRQ(ierr);
2006   ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
2007   /* view */
2008   ierr = ISColoringViewFromOptions(iscoloring,NULL,"-coloring_is_view");CHKERRQ(ierr);
2009   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);CHKERRQ(ierr);
2010   if (ctx && ctx->verbose > 2) {
2011     PetscViewer    viewer;
2012     Vec            color_vec, eidx_vec;
2013     ierr = DMGetGlobalVector(colordm, &color_vec);CHKERRQ(ierr);
2014     ierr = DMGetGlobalVector(colordm, &eidx_vec);CHKERRQ(ierr);
2015     for (colour=0; colour<nc; colour++) {
2016       ierr = ISGetLocalSize(is[colour],&csize);CHKERRQ(ierr);
2017       ierr = ISGetIndices(is[colour],&indices);CHKERRQ(ierr);
2018       for (j=0; j<csize; j++) {
2019         PetscScalar v = (PetscScalar)colour;
2020         k = indices[j];
2021         ierr = VecSetValues(color_vec,1,&k,&v,INSERT_VALUES);CHKERRQ(ierr);
2022         v = (PetscScalar)k;
2023         ierr = VecSetValues(eidx_vec,1,&k,&v,INSERT_VALUES);CHKERRQ(ierr);
2024       }
2025       ierr = ISRestoreIndices(is[colour],&indices);CHKERRQ(ierr);
2026     }
2027     /* view */
2028     ierr = PetscViewerVTKOpen(ctx->comm, "color.vtu", FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
2029     ierr = PetscObjectSetName((PetscObject) color_vec, "color");CHKERRQ(ierr);
2030     ierr = VecView(color_vec, viewer);CHKERRQ(ierr);
2031     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2032     ierr = PetscViewerVTKOpen(ctx->comm, "eidx.vtu", FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
2033     ierr = PetscObjectSetName((PetscObject) eidx_vec, "element-idx");CHKERRQ(ierr);
2034     ierr = VecView(eidx_vec, viewer);CHKERRQ(ierr);
2035     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2036     ierr = DMRestoreGlobalVector(colordm, &color_vec);CHKERRQ(ierr);
2037     ierr = DMRestoreGlobalVector(colordm, &eidx_vec);CHKERRQ(ierr);
2038   }
2039   ierr = PetscSectionDestroy(&csection);CHKERRQ(ierr);
2040   ierr = DMDestroy(&colordm);CHKERRQ(ierr);
2041   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);CHKERRQ(ierr);
2042   ierr = MatDestroy(&G);CHKERRQ(ierr);
2043   /* stash coloring */
2044   ierr = PetscContainerCreate(PETSC_COMM_SELF, container);CHKERRQ(ierr);
2045   ierr = PetscContainerSetPointer(*container,(void*)iscoloring);CHKERRQ(ierr);
2046   ierr = PetscContainerSetUserDestroy(*container, destroy_coloring);CHKERRQ(ierr);
2047   ierr = PetscObjectCompose((PetscObject)JacP,"coloring",(PetscObject)*container);CHKERRQ(ierr);
2048   if (ctx && ctx->verbose > 0) {
2049     ierr = PetscPrintf(ctx->comm, "Made coloring with %D colors\n", nc);CHKERRQ(ierr);
2050   }
2051   PetscFunctionReturn(0);
2052 }
2053 
2054 PetscErrorCode LandauAssembleOpenMP(PetscInt cStart, PetscInt cEnd, PetscInt totDim, DM plex, PetscSection section, PetscSection globalSection, Mat JacP, PetscScalar elemMats[], PetscContainer container)
2055 {
2056   PetscErrorCode  ierr;
2057   IS             *is;
2058   PetscInt        nc,colour,j;
2059   const PetscInt *clr_idxs;
2060   ISColoring      iscoloring;
2061   PetscFunctionBegin;
2062   ierr = PetscContainerGetPointer(container,(void**)&iscoloring);CHKERRQ(ierr);
2063   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);CHKERRQ(ierr);
2064   for (colour=0; colour<nc; colour++) {
2065     PetscInt    *idx_arr[1024]; /* need to make dynamic for general use */
2066     PetscScalar *new_el_mats[1024];
2067     PetscInt     idx_size[1024],csize;
2068     ierr = ISGetLocalSize(is[colour],&csize);CHKERRQ(ierr);
2069     if (csize>1024) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many elements in color. %D > %D",csize,1024);
2070     ierr = ISGetIndices(is[colour],&clr_idxs);CHKERRQ(ierr);
2071     /* get indices and mats */
2072     for (j=0; j<csize; j++) {
2073       PetscInt    cell = cStart + clr_idxs[j];
2074       PetscInt    numindices,*indices;
2075       PetscScalar *elMat = &elemMats[clr_idxs[j]*totDim*totDim];
2076       PetscScalar *valuesOrig = elMat;
2077       ierr = DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
2078       idx_size[j] = numindices;
2079       ierr = PetscMalloc2(numindices,&idx_arr[j],numindices*numindices,&new_el_mats[j]);CHKERRQ(ierr);
2080       ierr = PetscMemcpy(idx_arr[j],indices,numindices*sizeof(PetscInt));CHKERRQ(ierr);
2081       ierr = PetscMemcpy(new_el_mats[j],elMat,numindices*numindices*sizeof(PetscScalar));CHKERRQ(ierr);
2082       ierr = DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
2083       if (elMat != valuesOrig) {ierr = DMRestoreWorkArray(plex, numindices*numindices, MPIU_SCALAR, &elMat);CHKERRQ(ierr);}
2084     }
2085     /* assemble matrix */
2086     for (j=0; j<csize; j++) {
2087       PetscInt    numindices = idx_size[j], *indices = idx_arr[j];
2088       PetscScalar *elMat = new_el_mats[j];
2089       MatSetValues(JacP,numindices,indices,numindices,indices,elMat,ADD_VALUES);
2090     }
2091     /* free */
2092     ierr = ISRestoreIndices(is[colour],&clr_idxs);CHKERRQ(ierr);
2093     for (j=0; j<csize; j++) {
2094       ierr = PetscFree2(idx_arr[j],new_el_mats[j]);CHKERRQ(ierr);
2095     }
2096   }
2097   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);CHKERRQ(ierr);
2098   PetscFunctionReturn(0);
2099 }
2100 
2101 /* < v, u > */
2102 static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux,
2103                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2104                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2105                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
2106 {
2107   g0[0] = 1.;
2108 }
2109 
2110 /* < v, u > */
2111 static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux,
2112                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2113                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2114                  PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
2115 {
2116   g0[0] = 2.*PETSC_PI*x[0];
2117 }
2118 
2119 /*@
2120  LandauCreateMassMatrix - Create mass matrix for Landau
2121 
2122  Collective on dm
2123 
2124  Input Parameters:
2125  . dm     - the DM object
2126 
2127  Output Parameters:
2128  . Amat - The mass matrix (optional), mass matrix is added to the DM context
2129 
2130  Level: beginner
2131 
2132  .keywords: mesh
2133  .seealso: LandauCreateVelocitySpace()
2134  @*/
2135 PetscErrorCode LandauCreateMassMatrix(DM dm, Mat *Amat)
2136 {
2137   DM             massDM;
2138   PetscDS        prob;
2139   PetscInt       ii,dim,N1=1,N2;
2140   PetscErrorCode ierr;
2141   LandauCtx      *ctx;
2142   Mat            M;
2143 
2144   PetscFunctionBegin;
2145   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
2146   if (Amat) PetscValidPointer(Amat,2);
2147   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
2148   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2149   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2150   ierr = DMClone(dm, &massDM);CHKERRQ(ierr);
2151   ierr = DMCopyFields(dm, massDM);CHKERRQ(ierr);
2152   ierr = DMCreateDS(massDM);CHKERRQ(ierr);
2153   ierr = DMGetDS(massDM, &prob);CHKERRQ(ierr);
2154   for (ii=0;ii<ctx->num_species;ii++) {
2155     if (dim==3) {ierr = PetscDSSetJacobian(prob, ii, ii, g0_1, NULL, NULL, NULL);CHKERRQ(ierr);}
2156     else        {ierr = PetscDSSetJacobian(prob, ii, ii, g0_r, NULL, NULL, NULL);CHKERRQ(ierr);}
2157   }
2158   ierr = DMViewFromOptions(massDM,NULL,"-dm_landau_mass_dm_view");CHKERRQ(ierr);
2159   ierr = DMCreateMatrix(massDM, &M);CHKERRQ(ierr);
2160   ierr = MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2161   {
2162     Vec locX;
2163     DM  plex;
2164     ierr = DMConvert(massDM, DMPLEX, &plex);CHKERRQ(ierr);
2165     ierr = DMGetLocalVector(massDM, &locX);CHKERRQ(ierr);
2166     /* Mass matrix is independent of the input, so no need to fill locX */
2167     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);
2168     ierr = DMPlexSNESComputeJacobianFEM(plex, locX, M, M, ctx);CHKERRQ(ierr);
2169     ierr = DMRestoreLocalVector(massDM, &locX);CHKERRQ(ierr);
2170     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2171   }
2172   ierr = DMDestroy(&massDM);CHKERRQ(ierr);
2173   ierr = MatGetSize(ctx->J, &N1, NULL);CHKERRQ(ierr);
2174   ierr = MatGetSize(M, &N2, NULL);CHKERRQ(ierr);
2175   if (N1 != N2) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Incorrect matrix sizes: |Jacobian| = %D, |Mass|=%D",N1,N2);
2176   ierr = PetscObjectSetName((PetscObject)M, "mass");CHKERRQ(ierr);
2177   ierr = MatViewFromOptions(M,NULL,"-dm_landau_mass_mat_view");CHKERRQ(ierr);
2178   ctx->M = M; /* this could be a noop, a = a */
2179   if (Amat) *Amat = M;
2180   PetscFunctionReturn(0);
2181 }
2182 
2183 /*@
2184  LandauIFunction - TS residual calculation
2185 
2186  Collective on ts
2187 
2188  Input Parameters:
2189  +   TS  - The time stepping context
2190  .   time_dummy - current time (not used)
2191  -   X - Current state
2192  +   X_t - Time derivative of current state
2193  .   actx - Landau context
2194 
2195  Output Parameter:
2196  .   F  - The residual
2197 
2198  Level: beginner
2199 
2200  .keywords: mesh
2201  .seealso: LandauCreateVelocitySpace(), LandauIJacobian()
2202  @*/
2203 PetscErrorCode LandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
2204 {
2205   PetscErrorCode ierr;
2206   LandauCtx      *ctx=(LandauCtx*)actx;
2207   PetscInt       dim;
2208   DM             dm;
2209 #if defined(PETSC_HAVE_THREADSAFETY)
2210   double         starttime, endtime;
2211 #endif
2212 
2213   PetscFunctionBegin;
2214   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2215   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
2216   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2217   //ierr = MPI_Barrier(MPI_COMM_WORLD);CHKERRMPI(ierr);
2218   ierr = PetscLogEventBegin(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2219   ierr = PetscLogEventBegin(ctx->events[0],0,0,0,0);CHKERRQ(ierr);
2220 #if defined(PETSC_HAVE_THREADSAFETY)
2221   starttime = MPI_Wtime();
2222 #endif
2223   ierr = DMGetDimension(ctx->dmv, &dim);CHKERRQ(ierr);
2224   if (!ctx->aux_bool) {
2225     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);
2226     ierr = LandauFormJacobian_Internal(X,ctx->J,dim,0.0,(void*)ctx);CHKERRQ(ierr);
2227     ctx->aux_bool = PETSC_TRUE;
2228   } else {
2229     ierr = PetscInfo(ts, "Skip forming Jacobian, has not changed (should check norm)\n");CHKERRQ(ierr);
2230   }
2231   ierr = MatViewFromOptions(ctx->J,NULL,"-landau_jacobian_mat_view");CHKERRQ(ierr);
2232   /* mat vec for op */
2233   ierr = MatMult(ctx->J,X,F);CHKERRQ(ierr);CHKERRQ(ierr); /* C*f */
2234   /* add time term */
2235   if (X_t) {
2236     ierr = MatMultAdd(ctx->M,X_t,F,F);CHKERRQ(ierr);
2237   }
2238 #if defined(PETSC_HAVE_THREADSAFETY)
2239   endtime = MPI_Wtime();
2240   ctx->times[0] += (endtime - starttime);
2241 #endif
2242   ierr = PetscLogEventEnd(ctx->events[0],0,0,0,0);CHKERRQ(ierr);
2243   ierr = PetscLogEventEnd(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2244   PetscFunctionReturn(0);
2245 }
2246 static PetscErrorCode MatrixNfDestroy(void *ptr)
2247 {
2248   PetscInt *nf = (PetscInt *)ptr;
2249   PetscErrorCode  ierr;
2250   PetscFunctionBegin;
2251   ierr = PetscFree(nf);CHKERRQ(ierr);
2252   PetscFunctionReturn(0);
2253 }
2254 /*@
2255  LandauIJacobian - TS Jacobian construction
2256 
2257  Collective on ts
2258 
2259  Input Parameters:
2260  +   TS  - The time stepping context
2261  .   time_dummy - current time (not used)
2262  -   X - Current state
2263  +   U_tdummy - Time derivative of current state (not used)
2264  .   shift - shift for du/dt term
2265  -   actx - Landau context
2266 
2267  Output Parameter:
2268  .   Amat  - Jacobian
2269  +   Pmat  - same as Amat
2270 
2271  Level: beginner
2272 
2273  .keywords: mesh
2274  .seealso: LandauCreateVelocitySpace(), LandauIFunction()
2275  @*/
2276 PetscErrorCode LandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
2277 {
2278   PetscErrorCode ierr;
2279   LandauCtx      *ctx=(LandauCtx*)actx;
2280   PetscInt       dim;
2281   DM             dm;
2282   PetscContainer container;
2283 #if defined(PETSC_HAVE_THREADSAFETY)
2284   double         starttime, endtime;
2285 #endif
2286 
2287   PetscFunctionBegin;
2288   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2289   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
2290   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
2291   if (Amat!=Pmat || Amat!=ctx->J) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Amat!=Pmat || Amat!=ctx->J");
2292   ierr = DMGetDimension(ctx->dmv, &dim);CHKERRQ(ierr);
2293   /* get collision Jacobian into A */
2294   ierr = PetscLogEventBegin(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2295   ierr = PetscLogEventBegin(ctx->events[9],0,0,0,0);CHKERRQ(ierr);
2296 #if defined(PETSC_HAVE_THREADSAFETY)
2297   starttime = MPI_Wtime();
2298 #endif
2299   ierr = PetscInfo2(ts, "Adding just mass to Jacobian t=%g, shift=%g\n",(double)time_dummy,(double)shift);CHKERRQ(ierr);
2300   if (shift==0.0) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "zero shift");
2301   if (!ctx->aux_bool) SETERRQ(ctx->comm, PETSC_ERR_PLIB, "wrong state");
2302   if (!ctx->use_matrix_mass) {
2303     ierr = LandauFormJacobian_Internal(X,ctx->J,dim,shift,(void*)ctx);CHKERRQ(ierr);
2304   } else { /* add mass */
2305     ierr = MatAXPY(Pmat,shift,ctx->M,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2306   }
2307   ctx->aux_bool = PETSC_FALSE;
2308   ierr = MatViewFromOptions(Pmat,NULL,"-landau_mat_view");CHKERRQ(ierr);
2309   /* set number species in Jacobian */
2310   ierr = PetscObjectQuery((PetscObject) ctx->J, "Nf", (PetscObject *) &container);CHKERRQ(ierr);
2311   if (!container) {
2312     PetscInt *pNf;
2313     ierr = PetscContainerCreate(PETSC_COMM_SELF, &container);CHKERRQ(ierr);
2314     ierr = PetscMalloc(sizeof(PetscInt), &pNf);CHKERRQ(ierr);
2315     *pNf = ctx->num_species + 1000*ctx->numConcurrency;
2316     ierr = PetscContainerSetPointer(container, (void *)pNf);CHKERRQ(ierr);
2317     ierr = PetscContainerSetUserDestroy(container, MatrixNfDestroy);CHKERRQ(ierr);
2318     ierr = PetscObjectCompose((PetscObject)ctx->J, "Nf", (PetscObject) container);CHKERRQ(ierr);
2319     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
2320   }
2321 #if defined(PETSC_HAVE_THREADSAFETY)
2322   endtime = MPI_Wtime();
2323   ctx->times[0] += (endtime - starttime);
2324 #endif
2325   ierr = PetscLogEventEnd(ctx->events[9],0,0,0,0);CHKERRQ(ierr);
2326   ierr = PetscLogEventEnd(ctx->events[11],0,0,0,0);CHKERRQ(ierr);
2327   PetscFunctionReturn(0);
2328 }
2329