xref: /petsc/src/ts/utils/dmplexlandau/plexland.c (revision d60b7d5cda9a3148fab971d2544cf20a2ffedfa6)
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 
6 /* Landau collision operator */
7 #define PETSC_THREAD_SYNC
8 #define PETSC_DEVICE_FUNC_DECL static
9 #include "land_tensors.h"
10 
11 #define LANDAU_VL  1
12 
13 int LandauGetIPDataSize(const LandauIPData *const d) {
14   return d->nip_*(1 + d->dim_ + d->ns_*(d->dim_ + 1));
15 }
16 
17 static PetscErrorCode LandauPointDataCreate(LandauIPData *IPData, PetscInt dim, PetscInt nip, PetscInt Ns)
18 {
19   PetscErrorCode  ierr;
20   PetscInt        s, jj, nip_pad = LANDAU_VL*(nip/LANDAU_VL + !!(nip%LANDAU_VL)), sz;
21   LandauIPReal    *pdata;
22   PetscFunctionBegin;
23   IPData->dim_ = dim;
24   IPData->nip_ = nip_pad;
25   IPData->ns_  = Ns;
26   sz = LandauGetIPDataSize(IPData);
27   ierr = PetscMalloc(sizeof(LandauIPReal)*sz,&pdata);CHKERRQ(ierr);
28   IPData->w_data = pdata + 0; /* w */
29   IPData->x    = pdata + 1*nip_pad;
30   IPData->y    = pdata + 2*nip_pad;
31   IPData->z    = pdata + 3*nip_pad;
32   IPData->f    = pdata + nip_pad*((dim+1) + 0);
33   IPData->dfx  = pdata + nip_pad*((dim+1) + 1*Ns);
34   IPData->dfy  = pdata + nip_pad*((dim+1) + 2*Ns);
35   IPData->dfz  = pdata + nip_pad*((dim+1) + 3*Ns);
36   if (dim==2) IPData->z = IPData->dfz = NULL;
37   /* pad with zeros in case we vectorize into this */
38   for (jj=nip ; jj < nip_pad; jj++){
39     IPData->w_data[jj] = 0;
40     IPData->x[jj] = -1;
41     IPData->y[jj] = -1;
42     if (IPData->z) IPData->z[jj] = -1;
43     for (s=0;s<Ns;s++) { // need to transpose
44       IPData->f  [jj*Ns+s] = 0;
45       IPData->dfx[jj*Ns+s] = 0;
46       IPData->dfy[jj*Ns+s] = 0;
47       if (IPData->dfz) IPData->dfz[jj*Ns+s] = 0;
48     }
49   }
50   PetscFunctionReturn(0);
51 }
52 
53 static PetscErrorCode LandauPointDataDestroy(LandauIPData *IPData)
54 {
55   PetscErrorCode   ierr;
56   PetscFunctionBegin;
57   ierr = PetscFree(IPData->w_data);CHKERRQ(ierr);
58   PetscFunctionReturn(0);
59 }
60 /* ------------------------------------------------------------------- */
61 /*
62   LandauFormJacobian_Internal - Evaluates Jacobian matrix.
63 
64   Input Parameters:
65   .  globX - input vector
66   .  actx - optional user-defined context
67   .  dim - dimension
68 
69   Output Parameters:
70   .  J0acP - Jacobian matrix filled, not created
71 */
72 PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, void *a_ctx)
73 {
74   LandauCtx         *ctx = (LandauCtx*)a_ctx;
75   PetscErrorCode    ierr;
76   PetscInt          cStart, cEnd, elemMatSize;
77   DM                plex = NULL;
78   PetscDS           prob;
79   PetscSection      section,globsection;
80   PetscScalar       *elemMat;
81   PetscInt          numCells,totDim,ej,Nq,*Nbf,*Ncf,Nb,Ncx,Nf,d,f,fieldA;
82   PetscQuadrature   quad;
83   PetscTabulation   *Tf;
84   PetscReal         nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
85   const PetscReal   *quadWeights;
86   PetscReal         *invJ,*invJ_a;
87   PetscReal         invMass[LANDAU_MAX_SPECIES],Eq_m[LANDAU_MAX_SPECIES],m_0=ctx->m_0; /* normalize mass -- not needed! */
88   PetscLogDouble    flops;
89   Vec               locX;
90   LandauIPData      IPData;
91 
92   PetscFunctionBegin;
93   PetscValidHeaderSpecific(a_X,VEC_CLASSID,1);
94   PetscValidHeaderSpecific(JacP,MAT_CLASSID,2);
95   PetscValidPointer(ctx,4);
96 
97   ierr = PetscLogEventBegin(ctx->events[1],0,0,0,0);CHKERRQ(ierr);
98   ierr = DMConvert(ctx->dmv, DMPLEX, &plex);CHKERRQ(ierr);
99   ierr = DMCreateLocalVector(plex, &locX);CHKERRQ(ierr);
100   ierr = VecZeroEntries(locX);CHKERRQ(ierr); /* zero BCs so don't set */
101   ierr = DMGlobalToLocalBegin(plex, a_X, INSERT_VALUES, locX);CHKERRQ(ierr);
102   ierr = DMGlobalToLocalEnd  (plex, a_X, INSERT_VALUES, locX);CHKERRQ(ierr);
103   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
104   ierr = DMGetLocalSection(plex, &section);CHKERRQ(ierr);
105   ierr = DMGetGlobalSection(plex, &globsection);CHKERRQ(ierr);
106   ierr = DMGetDS(plex, &prob);CHKERRQ(ierr);
107   ierr = PetscDSGetTabulation(prob, &Tf);CHKERRQ(ierr); // Bf, &Df
108   ierr = PetscDSGetDimensions(prob, &Nbf);CHKERRQ(ierr); Nb = Nbf[0]; /* number of vertices*S */
109   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);         if (Nf!=ctx->num_species) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Nf %D != S",Nf);
110   ierr = PetscDSGetComponents(prob, &Ncf);CHKERRQ(ierr); Ncx = Ncf[0]; if (Ncx!=1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Nc %D != 1",Ncx);
111   for (fieldA=0;fieldA<Nf;fieldA++) {
112     invMass[fieldA] = m_0/ctx->masses[fieldA];
113     Eq_m[fieldA] = -ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
114     if (dim==2) Eq_m[fieldA] *=  2 * PETSC_PI; /* add the 2pi term that is not in Landau */
115     nu_alpha[fieldA] = PetscSqr(ctx->charges[fieldA]/m_0)*m_0/ctx->masses[fieldA];
116     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);
117   }
118   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
119   numCells = cEnd - cStart;
120   ierr = PetscFEGetQuadrature(ctx->fe[0], &quad);CHKERRQ(ierr);
121   ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, &quadWeights);CHKERRQ(ierr);
122   if (Nb!=Nq) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Nb!=Nq %D %D over integration or simplices? Tf[0]->Nb=%D dim=%D",Nb,Nq,Tf[0]->Nb,dim);
123   if (Nq >LANDAU_MAX_NQ) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"Order too high. Nq = %D > LANDAU_MAX_NQ (%D)",Nq,LANDAU_MAX_NQ);
124   if (LANDAU_DIM != dim) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim,LANDAU_DIM);
125   flops = (PetscLogDouble)numCells*(PetscLogDouble)Nq*(PetscLogDouble)(5*dim*dim*Nf*Nf + 165);
126   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
127   elemMatSize = totDim*totDim;
128   {
129     static int         cc = 0;
130     PetscScalar        uu[LANDAU_MAX_SPECIES],u_x[LANDAU_MAX_SPECIES*LANDAU_DIM];
131     /* collect f data */
132     if (ctx->verbose > 2 || (ctx->verbose > 0 && cc++ == 0)) {
133       PetscInt N,Nloc;
134       ierr = MatGetSize(JacP,&N,NULL);CHKERRQ(ierr);
135       ierr = VecGetSize(locX,&Nloc);CHKERRQ(ierr);
136       ierr = PetscPrintf(PETSC_COMM_WORLD,"[%D]%s: %D IPs, %D cells, %s elements, totDim=%D, Nb=%D, Nq=%D, elemMatSize=%D, dim=%D, Tab: Nb=%D Nf=%D Np=%D cdim=%D N=%D N_loc=%D\n",
137                          0,"FormLandau",Nq*numCells,numCells,ctx->simplex ? "SIMPLEX" : "TENSOR", totDim, Nb, Nq, elemMatSize, dim, Tf[0]->Nb, Nf, Tf[0]->Np, Tf[0]->cdim, N, Nloc);CHKERRQ(ierr);
138     }
139     ierr = LandauPointDataCreate(&IPData, dim, Nq*numCells, Nf);CHKERRQ(ierr);
140     ierr = PetscMalloc2(elemMatSize,&elemMat,IPData.nip_*dim*dim,&invJ_a);CHKERRQ(ierr);
141     /* cache geometry and x, f and df/dx at IPs */
142     for (ej = 0, invJ = invJ_a ; ej < numCells; ++ej, invJ += Nq*dim*dim) {
143       PetscReal    vj[LANDAU_MAX_NQ*LANDAU_DIM],detJj[LANDAU_MAX_NQ], Jdummy[LANDAU_MAX_NQ*LANDAU_DIM*LANDAU_DIM];
144       PetscInt     qj,f;
145       PetscScalar *coef = NULL;
146       ierr = DMPlexComputeCellGeometryFEM(plex, cStart+ej, quad, vj, Jdummy, invJ, detJj);CHKERRQ(ierr);
147       ierr = DMPlexVecGetClosure(plex, section, locX, cStart+ej, NULL, &coef);CHKERRQ(ierr);
148       /* create point data for cell i for Landau tensor: x, f(x), grad f(x) */
149       for (qj = 0; qj < Nq; ++qj) {
150         PetscInt         gidx = (ej*Nq + qj);
151         PetscScalar      refSpaceDer[LANDAU_DIM];
152         PetscInt         dOffset = 0, fOffset = 0;
153         IPData.x[gidx] = vj[qj * dim + 0]; /* coordinate */
154         IPData.y[gidx] = vj[qj * dim + 1];
155         if (dim==3) IPData.z[gidx] = vj[qj * dim + 2];
156         IPData.w_data[gidx] = detJj[qj] * quadWeights[qj];
157         if (dim==2) IPData.w_data[gidx] *= IPData.x[gidx];  /* cylindrical coordinate, w/o 2pi */
158         /* get u & du (EvaluateFieldJets) */
159         for (f = 0; f < Nf; ++f) {
160           const PetscReal *Bq = &Tf[f]->T[0][qj*Nb];
161           const PetscReal *Dq = &Tf[f]->T[1][qj*Nb*dim];
162           PetscInt         b, e;
163           uu[fOffset] = 0.0;
164           for (d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
165           for (b = 0; b < Nb; ++b) {
166             const PetscInt    cidx = b;
167             uu[fOffset] += Bq[cidx]*coef[dOffset+cidx];
168             for (d = 0; d < dim; ++d) refSpaceDer[d] += Dq[cidx*dim+d]*coef[dOffset+cidx];
169           }
170           for (d = 0; d < dim; ++d) {
171             for (e = 0, u_x[fOffset*dim+d] = 0.0; e < dim; ++e) {
172               u_x[fOffset*dim+d] += invJ[qj * dim * dim + e*dim+d]*refSpaceDer[e];
173             }
174           }
175           fOffset += 1;
176           dOffset += Nb;
177         }
178         /* copy to IPDataLocal */
179         for (f=0;f<Nf;f++) {
180           IPData.f[gidx + f*IPData.nip_] = PetscRealPart(uu[f]);
181           IPData.dfx[gidx + f*IPData.nip_] = PetscRealPart(u_x[f*dim+0]);
182           IPData.dfy[gidx + f*IPData.nip_] = PetscRealPart(u_x[f*dim+1]);
183           if (dim==3) IPData.dfz[gidx + f*IPData.nip_] = PetscRealPart(u_x[f*dim+2]);
184         }
185       } /* q */
186       ierr = DMPlexVecRestoreClosure(plex, section, locX, cStart+ej, NULL, &coef);CHKERRQ(ierr);
187     } /* e */
188   }
189   /* pad with zeros */
190   for (fieldA = numCells*Nq; fieldA < IPData.nip_; ++fieldA, invJ += dim*dim) {
191     for (d = 0; d < dim; ++d) {
192       int e;
193       for (e = 0; e < dim; ++e) {
194         invJ[e*dim+d] = 0;
195       }
196     }
197   }
198   ierr = DMRestoreLocalVector(plex, &locX);CHKERRQ(ierr);
199   ierr = PetscLogEventEnd(ctx->events[1],0,0,0,0);CHKERRQ(ierr);
200   /* outer element loop j is like a regular assembly loop */
201   if (ctx->deviceType == LANDAU_CUDA) {
202 #if defined(PETSC_HAVE_CUDA)
203     ierr = LandauCUDAJacobian(plex,Nq,nu_alpha,nu_beta,invMass,Eq_m,&IPData,invJ_a,ctx->subThreadBlockSize,ctx->events,JacP);CHKERRQ(ierr);
204 #else
205     SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","cuda");
206 #endif
207   } else if (ctx->deviceType == LANDAU_KOKKOS) {
208 #if defined(PETSC_HAVE_KOKKOS)
209     ierr = LandauKokkosJacobian(plex,Nq,nu_alpha,nu_beta,invMass,Eq_m,&IPData,invJ_a,ctx->subThreadBlockSize,ctx->events,JacP);CHKERRQ(ierr);
210 #else
211     SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"-landau_device_type %s not built","kokkos");
212 #endif
213   } else { /* CPU version */
214     for (ej = cStart, invJ = invJ_a; ej < cEnd; ++ej, invJ += Nq*dim*dim) {
215       PetscInt     qj;
216       ierr = PetscLogEventBegin(ctx->events[3],0,0,0,0);CHKERRQ(ierr);
217       ierr = PetscMemzero(elemMat, totDim *totDim * sizeof(PetscScalar));CHKERRQ(ierr);
218       ierr = PetscLogEventEnd(ctx->events[3],0,0,0,0);CHKERRQ(ierr);
219       ierr = PetscLogEventBegin(ctx->events[4],0,0,0,0);CHKERRQ(ierr);
220       ierr = PetscLogFlops((PetscLogDouble)Nq*flops);CHKERRQ(ierr);
221       for (qj = 0; qj < Nq; ++qj) {
222         PetscReal               g2[LANDAU_MAX_SPECIES][LANDAU_DIM], g3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM], gg2_temp[LANDAU_DIM], gg3_temp[LANDAU_DIM][LANDAU_DIM];
223         const PetscInt          jpidx = Nq*(ej-cStart) + qj;
224         const PetscReal * const BB = Tf[0]->T[0], * const DD = Tf[0]->T[1], * const invJj = &invJ[qj*dim*dim];
225         PetscReal               gg2[LANDAU_MAX_SPECIES][LANDAU_DIM],gg3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM];
226         PetscInt                d,d2,dp,d3,ipidx,fieldA;
227         const PetscReal         vj[3] = {IPData.x[jpidx], IPData.y[jpidx], IPData.z ? IPData.z[jpidx] : 0}, wj = IPData.w_data[jpidx];
228         // create g2 & g3
229         for (d=0;d<dim;d++) { // clear accumulation data D & K
230           gg2_temp[d] = 0;
231           for (d2=0;d2<dim;d2++) gg3_temp[d][d2] = 0;
232         }
233         for (ipidx = 0; ipidx < IPData.nip_; ipidx++) {
234           const PetscReal wi = IPData.w_data[ipidx], x = IPData.x[ipidx], y = IPData.y[ipidx];
235           PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
236 #if LANDAU_DIM==2
237           PetscReal       Ud[2][2], Uk[2][2];
238           LandauTensor2D(vj, x, y, Ud, Uk, (ipidx==jpidx) ? 0. : 1.);
239 #else
240           PetscReal U[3][3], z = IPData.z[ipidx];
241           LandauTensor3D(vj, x, y, z, U, (ipidx==jpidx) ? 0. : 1.);
242 #endif
243           for (fieldA = 0; fieldA < Nf; ++fieldA) {
244             temp1[0] += IPData.dfx[ipidx + fieldA*IPData.nip_]*nu_beta[fieldA]*invMass[fieldA];
245             temp1[1] += IPData.dfy[ipidx + fieldA*IPData.nip_]*nu_beta[fieldA]*invMass[fieldA];
246 #if LANDAU_DIM==3
247             temp1[2] += IPData.dfz[ipidx + fieldA*IPData.nip_]*nu_beta[fieldA]*invMass[fieldA];
248 #endif
249             temp2    += IPData.f[ipidx + fieldA*IPData.nip_]*nu_beta[fieldA];
250           }
251           temp1[0] *= wi;
252           temp1[1] *= wi;
253 #if LANDAU_DIM==3
254           temp1[2] *= wi;
255 #endif
256           temp2    *= wi;
257 #if LANDAU_DIM==2
258           for (d2 = 0; d2 < 2; d2++) {
259             for (d3 = 0; d3 < 2; ++d3) {
260               /* K = U * grad(f): g2=e: i,A */
261               gg2_temp[d2] += Uk[d2][d3]*temp1[d3];
262               /* D = -U * (I \kron (fx)): g3=f: i,j,A */
263               gg3_temp[d2][d3] += Ud[d2][d3]*temp2;
264             }
265           }
266 #else
267           for (d2 = 0; d2 < 3; ++d2) {
268             for (d3 = 0; d3 < 3; ++d3) {
269               /* K = U * grad(f): g2 = e: i,A */
270               gg2_temp[d2] += U[d2][d3]*temp1[d3];
271               /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
272               gg3_temp[d2][d3] += U[d2][d3]*temp2;
273             }
274           }
275 #endif
276         } /* IPs */
277         //if (ej==0) printf("\t:%d.%d) temp gg3=%e %e %e %e\n",ej,qj,gg3_temp[0][0],gg3_temp[1][0],gg3_temp[0][1],gg3_temp[1][1]);
278         // add alpha and put in gg2/3
279         for (fieldA = 0; fieldA < Nf; ++fieldA) {
280           for (d2 = 0; d2 < dim; d2++) {
281             gg2[fieldA][d2] = gg2_temp[d2]*nu_alpha[fieldA];
282             for (d3 = 0; d3 < dim; d3++) {
283               gg3[fieldA][d2][d3] = -gg3_temp[d2][d3]*nu_alpha[fieldA]*invMass[fieldA];
284             }
285           }
286         }
287         /* add electric field term once per IP */
288         for (fieldA = 0; fieldA < Nf; ++fieldA) {
289           gg2[fieldA][dim-1] += Eq_m[fieldA];
290         }
291         //intf("%d %d gg2[1][1]=%g\n",myelem,qj,gg2[1][dim-1]);
292         /* Jacobian transform - g2 */
293         for (fieldA = 0; fieldA < Nf; ++fieldA) {
294           for (d = 0; d < dim; ++d) {
295             g2[fieldA][d] = 0.0;
296             for (d2 = 0; d2 < dim; ++d2) {
297               g2[fieldA][d] += invJj[d*dim+d2]*gg2[fieldA][d2];
298               g3[fieldA][d][d2] = 0.0;
299               for (d3 = 0; d3 < dim; ++d3) {
300                 for (dp = 0; dp < dim; ++dp) {
301                   g3[fieldA][d][d2] += invJj[d*dim + d3]*gg3[fieldA][d3][dp]*invJj[d2*dim + dp];
302                 }
303               }
304               g3[fieldA][d][d2] *= wj;
305             }
306             g2[fieldA][d] *= wj;
307           }
308         }
309         /* FE matrix construction */
310         PETSC_THREAD_SYNC;   // Synchronize (ensure all the data is available) and sum IP matrices
311         {
312           PetscInt  fieldA,d,f,d2,g,totDim=Nb*Nf;
313           const PetscReal *BJq = &BB[qj*Nb], *DIq = &DD[qj*Nb*dim];
314           /* assemble - on the diagonal (I,I) */
315           for (fieldA = 0; fieldA < Nf ; fieldA++) {
316             for (f = 0; f < Nb ; f++) { /* vectorizing here, maybe */
317               const PetscInt i = fieldA*Nb + f; /* Element matrix row */
318               for (g = 0; g < Nb; ++g) {
319                 const PetscInt j    = fieldA*Nb + g; /* Element matrix column */
320                 const PetscInt fOff = i*totDim + j;
321                 for (d = 0; d < dim; ++d) {
322                   elemMat[fOff] += DIq[f*dim+d]*g2[fieldA][d]*BJq[g];
323                   for (d2 = 0; d2 < dim; ++d2) {
324                     elemMat[fOff] += DIq[f*dim + d]*g3[fieldA][d][d2]*DIq[g*dim + d2];
325                   }
326                 }
327               }
328             }
329           }
330         }
331       } /* qj loop */
332       ierr = PetscLogEventEnd(ctx->events[4],0,0,0,0);CHKERRQ(ierr);
333 
334       /* assemble matrix */
335       ierr = PetscLogEventBegin(ctx->events[6],0,0,0,0);CHKERRQ(ierr);
336       ierr = DMPlexMatSetClosure(plex, section, globsection, JacP, ej, elemMat, ADD_VALUES);
337       if (ej==-1 || ierr) {
338         PetscErrorCode    ierr2;
339         ierr2 = PetscErrorPrintf("CPU Element matrix\n");CHKERRQ(ierr2);
340         for (d = 0; d < totDim; ++d){
341           for (f = 0; f < totDim; ++f) {ierr2 = PetscErrorPrintf(" %12.5e",  PetscRealPart(elemMat[d*totDim + f]));CHKERRQ(ierr2);}
342            ierr2 = PetscErrorPrintf("\n");CHKERRQ(ierr2);
343         }
344       }
345       CHKERRQ(ierr);
346       ierr = PetscLogEventEnd(ctx->events[6],0,0,0,0);CHKERRQ(ierr);
347     } /* ej cells loop, not cuda */
348   }
349 
350   /* assemble matrix or vector */
351   ierr = PetscLogEventBegin(ctx->events[7],0,0,0,0);CHKERRQ(ierr);
352   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
353   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
354   ierr = MatScale(JacP, -1.0);CHKERRQ(ierr); /* The code reflect the papers: du/dt = C, whereas PETSc use the form G(u) = du/dt - C(u) = 0 */
355   ierr = PetscLogEventEnd(ctx->events[7],0,0,0,0);CHKERRQ(ierr);
356 
357   /* clean up */
358   ierr = PetscFree2(elemMat,invJ_a);CHKERRQ(ierr);
359   ierr = DMDestroy(&plex);CHKERRQ(ierr);
360   ierr = LandauPointDataDestroy(&IPData);CHKERRQ(ierr);
361   PetscFunctionReturn(0);
362 }
363 
364 #if defined(LANDAU_ADD_BCS)
365 static void zero_bc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
366                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
367                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
368                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
369 {
370   uexact[0] = 0;
371 }
372 #endif
373 
374 #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]; }}
375 static void CircleInflate(PetscReal r1, PetscReal r2, PetscReal r0, PetscInt num_sections, PetscReal x, PetscReal y,
376                           PetscReal *outX, PetscReal *outY)
377 {
378   PetscReal rr = PetscSqrtReal(x*x + y*y), outfact, efact;
379   if (rr < r1 + PETSC_SQRT_MACHINE_EPSILON) {
380     *outX = x; *outY = y;
381   } else {
382     const PetscReal xy[2] = {x,y}, sinphi=y/rr, cosphi=x/rr;
383     PetscReal       cth,sth,xyprime[2],Rth[2][2],rotcos,newrr;
384     if (num_sections==2) {
385       rotcos = 0.70710678118654;
386       outfact = 1.5; efact = 2.5;
387       /* rotate normalized vector into [-pi/4,pi/4) */
388       if (sinphi >= 0.) {         /* top cell, -pi/2 */
389         cth = 0.707106781186548; sth = -0.707106781186548;
390       } else {                    /* bottom cell -pi/8 */
391         cth = 0.707106781186548; sth = .707106781186548;
392       }
393     } else if (num_sections==3) {
394       rotcos = 0.86602540378443;
395       outfact = 1.5; efact = 2.5;
396       /* rotate normalized vector into [-pi/6,pi/6) */
397       if (sinphi >= 0.5) {         /* top cell, -pi/3 */
398         cth = 0.5; sth = -0.866025403784439;
399       } else if (sinphi >= -.5) {  /* mid cell 0 */
400         cth = 1.; sth = .0;
401       } else { /* bottom cell +pi/3 */
402         cth = 0.5; sth = 0.866025403784439;
403       }
404     } else if (num_sections==4) {
405       rotcos = 0.9238795325112;
406       outfact = 1.5; efact = 3;
407       /* rotate normalized vector into [-pi/8,pi/8) */
408       if (sinphi >= 0.707106781186548) {         /* top cell, -3pi/8 */
409         cth = 0.38268343236509; sth = -0.923879532511287;
410       } else if (sinphi >= 0.) {                 /* mid top cell -pi/8 */
411         cth = 0.923879532511287; sth = -.38268343236509;
412       } else if (sinphi >= -0.707106781186548) { /* mid bottom cell + pi/8 */
413         cth = 0.923879532511287; sth = 0.38268343236509;
414       } else {                                   /* bottom cell + 3pi/8 */
415         cth = 0.38268343236509; sth = .923879532511287;
416       }
417     } else {
418       cth = 0.; sth = 0.; rotcos = 0; efact = 0;
419     }
420     Rth[0][0] = cth; Rth[0][1] =-sth;
421     Rth[1][0] = sth; Rth[1][1] = cth;
422     MATVEC2(Rth,xy,xyprime);
423     if (num_sections==2) {
424       newrr = xyprime[0]/rotcos;
425     } else {
426       PetscReal newcosphi=xyprime[0]/rr, rin = r1, rout = rr - rin;
427       PetscReal routmax = r0*rotcos/newcosphi - rin, nroutmax = r0 - rin, routfrac = rout/routmax;
428       newrr = rin + routfrac*nroutmax;
429     }
430     *outX = cosphi*newrr; *outY = sinphi*newrr;
431     /* grade */
432     PetscReal fact,tt,rs,re, rr = PetscSqrtReal(PetscSqr(*outX) + PetscSqr(*outY));
433     if (rr > r2) { rs = r2; re = r0; fact = outfact;} /* outer zone */
434     else {         rs = r1; re = r2; fact = efact;} /* electron zone */
435     tt = (rs + PetscPowReal((rr - rs)/(re - rs),fact) * (re-rs)) / rr;
436     *outX *= tt;
437     *outY *= tt;
438   }
439 }
440 
441 static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
442 {
443   LandauCtx   *ctx = (LandauCtx*)a_ctx;
444   PetscReal   r = abc[0], z = abc[1];
445   if (ctx->inflate) {
446     PetscReal absR, absZ;
447     absR = PetscAbsReal(r);
448     absZ = PetscAbsReal(z);
449     CircleInflate(ctx->i_radius,ctx->e_radius,ctx->radius,ctx->num_sections,absR,absZ,&absR,&absZ);
450     r = (r > 0) ? absR : -absR;
451     z = (z > 0) ? absZ : -absZ;
452   }
453   xyz[0] = r;
454   xyz[1] = z;
455   if (dim==3) xyz[2] = abc[2];
456 
457   PetscFunctionReturn(0);
458 }
459 
460 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)
461 {
462   PetscReal err = 0.0;
463   PetscInt  f = *(PetscInt*)actx, j;
464   PetscFunctionBegin;
465   for (j = 0; j < dim; ++j) {
466     err += PetscSqr(PetscRealPart(u_x[f*dim+j]));
467   }
468   err = PetscRealPart(u[f]); /* just use rho */
469   *error = volume * err; /* * (ctx->axisymmetric ? 2.*PETSC_PI * r : 1); */
470   PetscFunctionReturn(0);
471 }
472 
473 static PetscErrorCode LandauDMCreateVMesh(MPI_Comm comm, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM *dm)
474 {
475   PetscErrorCode ierr;
476   PetscReal      radius = ctx->radius;
477   size_t         len;
478   char           fname[128] = ""; /* we can add a file if we want */
479 
480   PetscFunctionBegin;
481   /* create DM */
482   ierr = PetscStrlen(fname, &len);CHKERRQ(ierr);
483   if (len) {
484     PetscInt dim2;
485     ierr = DMPlexCreateFromFile(comm, fname, ctx->interpolate, dm);CHKERRQ(ierr);
486     ierr = DMGetDimension(*dm, &dim2);CHKERRQ(ierr);
487     if (LANDAU_DIM != dim2) SETERRQ2(comm, PETSC_ERR_PLIB, "dim %D != LANDAU_DIM %d",dim2,LANDAU_DIM);
488   } else {    /* p4est, quads */
489     /* Create plex mesh of Landau domain */
490     if (!ctx->sphere) {
491       PetscInt       cells[] = {2,2,2};
492       PetscReal      lo[] = {-radius,-radius,-radius}, hi[] = {radius,radius,radius};
493       DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim==2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
494       if (dim==2) { lo[0] = 0; cells[0] = 1; }
495       ierr = DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, cells, lo, hi, periodicity, PETSC_TRUE, dm);CHKERRQ(ierr);
496       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr); /* needed for periodic */
497       if (dim==3) {ierr = PetscObjectSetName((PetscObject) *dm, "cube");CHKERRQ(ierr);}
498       else {ierr = PetscObjectSetName((PetscObject) *dm, "half-plane");CHKERRQ(ierr);}
499     } else if (dim==2) {
500       PetscInt       numCells,cells[16][4],i,j;
501       PetscInt       numVerts;
502       PetscReal      inner_radius1 = ctx->i_radius, inner_radius2 = ctx->e_radius;
503       PetscReal      *flatCoords = NULL;
504       PetscInt       *flatCells = NULL, *pcell;
505       if (ctx->num_sections==2) {
506 #if 1
507         numCells = 5;
508         numVerts = 10;
509         int cells2[][4] = { {0,1,4,3},
510                             {1,2,5,4},
511                             {3,4,7,6},
512                             {4,5,8,7},
513                             {6,7,8,9} };
514         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
515         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
516         {
517           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
518           for (j = 0; j < numVerts-1; j++) {
519             PetscReal z, r, theta = -PETSC_PI/2 + (j%3) * PETSC_PI/2;
520             PetscReal rad = (j >= 6) ? inner_radius1 : (j >= 3) ? inner_radius2 : ctx->radius;
521             z = rad * PetscSinReal(theta);
522             coords[j][1] = z;
523             r = rad * PetscCosReal(theta);
524             coords[j][0] = r;
525           }
526           coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
527         }
528 #else
529         numCells = 4;
530         numVerts = 8;
531         static int     cells2[][4] = {{0,1,2,3},
532                                      {4,5,1,0},
533                                      {5,6,2,1},
534                                      {6,7,3,2}};
535         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
536         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
537         {
538           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
539           PetscInt j;
540           for (j = 0; j < 8; j++) {
541             PetscReal z, r;
542             PetscReal theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3.;
543             PetscReal rad = ctx->radius * ((j < 4) ? 0.5 : 1.0);
544             z = rad * PetscSinReal(theta);
545             coords[j][1] = z;
546             r = rad * PetscCosReal(theta);
547             coords[j][0] = r;
548           }
549         }
550 #endif
551       } else if (ctx->num_sections==3) {
552         numCells = 7;
553         numVerts = 12;
554         int cells2[][4] = { {0,1,5,4},
555                             {1,2,6,5},
556                             {2,3,7,6},
557                             {4,5,9,8},
558                             {5,6,10,9},
559                             {6,7,11,10},
560                             {8,9,10,11} };
561         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
562         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
563         {
564           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
565           for (j = 0; j < numVerts; j++) {
566             PetscReal z, r, theta = -PETSC_PI/2 + (j%4) * PETSC_PI/3;
567             PetscReal rad = (j >= 8) ? inner_radius1 : (j >= 4) ? inner_radius2 : ctx->radius;
568             z = rad * PetscSinReal(theta);
569             coords[j][1] = z;
570             r = rad * PetscCosReal(theta);
571             coords[j][0] = r;
572           }
573         }
574       } else if (ctx->num_sections==4) {
575         numCells = 10;
576         numVerts = 16;
577         int cells2[][4] = { {0,1,6,5},
578                             {1,2,7,6},
579                             {2,3,8,7},
580                             {3,4,9,8},
581                             {5,6,11,10},
582                             {6,7,12,11},
583                             {7,8,13,12},
584                             {8,9,14,13},
585                             {10,11,12,15},
586                             {12,13,14,15}};
587         for (i = 0; i < numCells; i++) for (j = 0; j < 4; j++) cells[i][j] = cells2[i][j];
588         ierr = PetscMalloc2(numVerts * 2, &flatCoords, numCells * 4, &flatCells);CHKERRQ(ierr);
589         {
590           PetscReal (*coords)[2] = (PetscReal (*) [2]) flatCoords;
591           for (j = 0; j < numVerts-1; j++) {
592             PetscReal z, r, theta = -PETSC_PI/2 + (j%5) * PETSC_PI/4;
593             PetscReal rad = (j >= 10) ? inner_radius1 : (j >= 5) ? inner_radius2 : ctx->radius;
594             z = rad * PetscSinReal(theta);
595             coords[j][1] = z;
596             r = rad * PetscCosReal(theta);
597             coords[j][0] = r;
598           }
599           coords[numVerts-1][0] = coords[numVerts-1][1] = 0;
600         }
601       } else {
602         numCells = 0;
603         numVerts = 0;
604       }
605       for (j = 0, pcell = flatCells; j < numCells; j++, pcell += 4) {
606         pcell[0] = cells[j][0]; pcell[1] = cells[j][1];
607         pcell[2] = cells[j][2]; pcell[3] = cells[j][3];
608       }
609       ierr = DMPlexCreateFromCellListPetsc(comm,2,numCells,numVerts,4,ctx->interpolate,flatCells,2,flatCoords,dm);CHKERRQ(ierr);
610       ierr = PetscFree2(flatCoords,flatCells);CHKERRQ(ierr);
611       ierr = PetscObjectSetName((PetscObject) *dm, "semi-circle");CHKERRQ(ierr);
612     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Velocity space meshes does not support cubed sphere");
613   }
614   ierr = PetscObjectSetOptionsPrefix((PetscObject)*dm,prefix);CHKERRQ(ierr);
615 
616   ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); /* Plex refine */
617 
618   { /* p4est? */
619     char      convType[256];
620     PetscBool flg;
621     ierr = PetscOptionsBegin(PETSC_COMM_WORLD, prefix, "Mesh conversion options", "DMPLEX");CHKERRQ(ierr);
622     ierr = PetscOptionsFList("-dm_landau_type","Convert DMPlex to another format (should not be Plex!)","ex6f.c",DMList,DMPLEX,convType,256,&flg);CHKERRQ(ierr);
623     ierr = PetscOptionsEnd();
624     if (flg) {
625       DM dmforest;
626       ierr = DMConvert(*dm,convType,&dmforest);CHKERRQ(ierr);
627       if (dmforest) {
628         PetscBool isForest;
629         if (dmforest->prealloc_only != (*dm)->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"plex->prealloc_only != dm->prealloc_only");
630         ierr = PetscObjectSetOptionsPrefix((PetscObject)dmforest,prefix);CHKERRQ(ierr);
631         ierr = DMIsForest(dmforest,&isForest);CHKERRQ(ierr);
632         if (isForest) {
633           if (ctx->sphere && ctx->inflate) {
634             ierr = DMForestSetBaseCoordinateMapping(dmforest,GeometryDMLandau,ctx);CHKERRQ(ierr);
635           }
636           if (dmforest->prealloc_only != (*dm)->prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"plex->prealloc_only != dm->prealloc_only");
637           ierr = DMDestroy(dm);CHKERRQ(ierr);
638           *dm = dmforest;
639           ctx->errorIndicator = ErrorIndicator_Simple; /* flag for Forest */
640         } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Converted to non Forest?");
641       } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Convert failed?");
642     }
643   }
644   ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr);
645   PetscFunctionReturn(0);
646 }
647 
648 static PetscErrorCode SetupDS(DM dm, PetscInt dim, LandauCtx *ctx)
649 {
650   PetscErrorCode  ierr;
651   PetscInt        ii;
652   PetscFunctionBegin;
653   for (ii=0;ii<ctx->num_species;ii++) {
654     char     buf[256];
655     if (ii==0) ierr = PetscSNPrintf(buf, 256, "e");
656     else {ierr = PetscSNPrintf(buf, 256, "i%D", ii);CHKERRQ(ierr);}
657     /* Setup Discretization - FEM */
658     ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, 1, ctx->simplex, NULL, PETSC_DECIDE, &ctx->fe[ii]);CHKERRQ(ierr);
659     ierr = PetscObjectSetName((PetscObject) ctx->fe[ii], buf);CHKERRQ(ierr);
660     ierr = DMSetField(dm, ii, NULL, (PetscObject) ctx->fe[ii]);CHKERRQ(ierr);
661   }
662   ierr = DMCreateDS(dm);CHKERRQ(ierr);
663   if (1) {
664     PetscInt        ii;
665     PetscSection    section;
666     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
667     for (ii=0;ii<ctx->num_species;ii++){
668       char buf[256];
669       if (ii==0) ierr = PetscSNPrintf(buf, 256, "se");
670       else ierr = PetscSNPrintf(buf, 256, "si%D", ii);
671       ierr = PetscSectionSetComponentName(section, ii, 0, buf);CHKERRQ(ierr);
672     }
673   }
674   PetscFunctionReturn(0);
675 }
676 
677 /* Define a Maxwellian function for testing out the operator. */
678 
679  /* Using cartesian velocity space coordinates, the particle */
680  /* density, [1/m^3], is defined according to */
681 
682  /* $$ n=\int_{R^3} dv^3 \left(\frac{m}{2\pi T}\right)^{3/2}\exp [- mv^2/(2T)] $$ */
683 
684  /* Using some constant, c, we normalize the velocity vector into a */
685  /* dimensionless variable according to v=c*x. Thus the density, $n$, becomes */
686 
687  /* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */
688 
689  /* Defining $\theta=2T/mc^2$, we thus find that the probability density */
690  /* for finding the particle within the interval in a box dx^3 around x is */
691 
692  /* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */
693 
694 typedef struct {
695   LandauCtx   *ctx;
696   PetscReal kT_m;
697   PetscReal n;
698   PetscReal shift;
699 } MaxwellianCtx;
700 
701 static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
702 {
703   MaxwellianCtx *mctx = (MaxwellianCtx*)actx;
704   LandauCtx     *ctx = mctx->ctx;
705   PetscInt      i;
706   PetscReal     v2 = 0, theta = 2*mctx->kT_m/(ctx->v_0*ctx->v_0); /* theta = 2kT/mc^2 */
707   PetscFunctionBegin;
708   /* compute the exponents, v^2 */
709   for (i = 0; i < dim; ++i) v2 += x[i]*x[i];
710   /* evaluate the Maxwellian */
711   u[0] = mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
712   if (mctx->shift!=0.) {
713     v2 = 0;
714     for (i = 0; i < dim-1; ++i) v2 += x[i]*x[i];
715     v2 += (x[dim-1]-mctx->shift)*(x[dim-1]-mctx->shift);
716     /* evaluate the shifted Maxwellian */
717     u[0] += mctx->n*PetscPowReal(PETSC_PI*theta,-1.5)*(PetscExpReal(-v2/theta));
718   }
719   PetscFunctionReturn(0);
720 }
721 
722 /*@
723  LandauAddMaxwellians - Add a Maxwellian distribution to a state
724 
725  Collective on X
726 
727  Input Parameters:
728  .   dm - The mesh
729  +   time - Current time
730  -   temps - Temperatures of each species
731  .   ns - Number density of each species
732  +   actx - Landau context
733 
734  Output Parameter:
735  .   X  - The state
736 
737  Level: beginner
738 
739 .keywords: mesh
740 .seealso: LandauCreateVelocitySpace()
741 @*/
742 PetscErrorCode LandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], void *actx)
743 {
744   LandauCtx      *ctx = (LandauCtx*)actx;
745   PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *);
746   PetscErrorCode ierr,ii;
747   PetscInt       dim;
748   MaxwellianCtx  *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];
749 
750   PetscFunctionBegin;
751   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
752   if (!ctx) { ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr); }
753   for (ii=0;ii<ctx->num_species;ii++) {
754     mctxs[ii] = &data[ii];
755     data[ii].ctx = ctx;
756     data[ii].kT_m = ctx->k*temps[ii]/ctx->masses[ii]; /* kT/m */
757     data[ii].n = ns[ii];
758     initu[ii] = maxwellian;
759     data[ii].shift = 0;
760   }
761   data[0].shift = ctx->electronShift;
762   /* need to make ADD_ALL_VALUES work - TODO */
763   ierr = DMProjectFunction(dm, time, initu, (void**)mctxs, INSERT_ALL_VALUES, X);CHKERRQ(ierr);
764   PetscFunctionReturn(0);
765 }
766 
767 /*
768  LandauSetInitialCondition - Addes Maxwellians with context
769 
770 Collective on X
771 
772  Input Parameters:
773  .   dm - The mesh
774  +   actx - Landau context with T and n
775 
776  Output Parameter:
777  .   X  - The state
778 
779  Level: beginner
780 
781 .keywords: mesh
782 .seealso: LandauCreateVelocitySpace(), LandauAddMaxwellians()
783 */
784 static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, void *actx)
785 {
786   LandauCtx        *ctx = (LandauCtx*)actx;
787   PetscErrorCode ierr;
788   PetscFunctionBegin;
789   if (!ctx) { ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr); }
790   ierr = VecZeroEntries(X);CHKERRQ(ierr);
791   ierr = LandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, ctx);CHKERRQ(ierr);
792   PetscFunctionReturn(0);
793 }
794 
795 static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscReal refineTol[], PetscReal coarsenTol[], PetscInt type, LandauCtx *ctx, DM *newDM)
796 {
797   DM               dm, plex, adaptedDM = NULL;
798   PetscDS          prob;
799   PetscBool        isForest;
800   PetscQuadrature  quad;
801   PetscInt         Nq, *Nb, cStart, cEnd, c, dim, qj, k;
802   DMLabel          adaptLabel = NULL;
803   PetscErrorCode   ierr;
804 
805   PetscFunctionBegin;
806   ierr = VecGetDM(sol, &dm);CHKERRQ(ierr);
807   ierr = DMCreateDS(dm);CHKERRQ(ierr);
808   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
809   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
810   ierr = DMIsForest(dm, &isForest);CHKERRQ(ierr);
811   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
812   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
813   ierr = DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);CHKERRQ(ierr);
814   ierr = PetscFEGetQuadrature(fem, &quad);CHKERRQ(ierr);
815   ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
816   if (Nq >LANDAU_MAX_NQ) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"Order too high. Nq = %D > LANDAU_MAX_NQ (%D)",Nq,LANDAU_MAX_NQ);
817   ierr = PetscDSGetDimensions(prob, &Nb);CHKERRQ(ierr);
818   if (type==4) {
819     for (c = cStart; c < cEnd; c++) {
820       ierr = DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);CHKERRQ(ierr);
821     }
822     ierr = PetscInfo1(sol, "Phase:%s: Uniform refinement\n","adaptToleranceFEM");CHKERRQ(ierr);
823   } else if (type==2) {
824     PetscInt  rCellIdx[8], eCellIdx[64], iCellIdx[64], eMaxIdx = -1, iMaxIdx = -1, nr = 0, nrmax = (dim==3) ? 8 : 2;
825     PetscReal minRad = PETSC_INFINITY, r, eMinRad = PETSC_INFINITY, iMinRad = PETSC_INFINITY;
826     for (c = 0; c < 64; c++) { eCellIdx[c] = iCellIdx[c] = -1; }
827     for (c = cStart; c < cEnd; c++) {
828       PetscReal    tt, v0[LANDAU_MAX_NQ*3], detJ[LANDAU_MAX_NQ];
829       ierr = DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ);CHKERRQ(ierr);
830       for (qj = 0; qj < Nq; ++qj) {
831         tt = PetscSqr(v0[dim*qj+0]) + PetscSqr(v0[dim*qj+1]) + PetscSqr(((dim==3) ? v0[dim*qj+2] : 0));
832         r = PetscSqrtReal(tt);
833         if (r < minRad - PETSC_SQRT_MACHINE_EPSILON*10.) {
834           minRad = r;
835           nr = 0;
836           rCellIdx[nr++]= c;
837           ierr = PetscInfo4(sol, "\t\tPhase: adaptToleranceFEM Found first inner r=%e, cell %D, qp %D/%D\n", r, c, qj+1, Nq);CHKERRQ(ierr);
838         } else if ((r-minRad) < PETSC_SQRT_MACHINE_EPSILON*100. && nr < nrmax) {
839           for (k=0;k<nr;k++) if (c == rCellIdx[k]) break;
840           if (k==nr) {
841             rCellIdx[nr++]= c;
842             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);
843           }
844         }
845         if (ctx->sphere) {
846           if ((tt=r-ctx->e_radius) > 0) {
847             PetscInfo2(sol, "\t\t\t %D cell r=%g\n",c,tt);
848             if (tt < eMinRad - PETSC_SQRT_MACHINE_EPSILON*100.) {
849               eMinRad = tt;
850               eMaxIdx = 0;
851               eCellIdx[eMaxIdx++] = c;
852             } else if (eMaxIdx > 0 && (tt-eMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != eCellIdx[eMaxIdx-1]) {
853               eCellIdx[eMaxIdx++] = c;
854             }
855           }
856           if ((tt=r-ctx->i_radius) > 0) {
857             if (tt < iMinRad - 1.e-5) {
858               iMinRad = tt;
859               iMaxIdx = 0;
860               iCellIdx[iMaxIdx++] = c;
861             } else if (iMaxIdx > 0 && (tt-iMinRad) <= PETSC_SQRT_MACHINE_EPSILON && c != iCellIdx[iMaxIdx-1]) {
862               iCellIdx[iMaxIdx++] = c;
863             }
864           }
865         }
866       }
867     }
868     for (k=0;k<nr;k++) {
869       ierr = DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE);CHKERRQ(ierr);
870     }
871     if (ctx->sphere) {
872       for (c = 0; c < eMaxIdx; c++) {
873         ierr = DMLabelSetValue(adaptLabel, eCellIdx[c], DM_ADAPT_REFINE);CHKERRQ(ierr);
874         ierr = PetscInfo3(sol, "\t\tPhase:%s: refine sphere e cell %D r=%g\n","adaptToleranceFEM",eCellIdx[c],eMinRad);
875       }
876       for (c = 0; c < iMaxIdx; c++) {
877         ierr = DMLabelSetValue(adaptLabel, iCellIdx[c], DM_ADAPT_REFINE);CHKERRQ(ierr);
878         ierr = PetscInfo3(sol, "\t\tPhase:%s: refine sphere i cell %D r=%g\n","adaptToleranceFEM",iCellIdx[c],iMinRad);
879       }
880     }
881     ierr = PetscInfo4(sol, "Phase:%s: Adaptive refine origin cells %D,%D r=%g\n","adaptToleranceFEM",rCellIdx[0],rCellIdx[1],minRad);
882   } else if (type==0 || type==1 || type==3) { /* refine along r=0 axis */
883     PetscScalar  *coef = NULL;
884     Vec          coords;
885     PetscInt     csize,Nv,d,nz;
886     DM           cdm;
887     PetscSection cs;
888     ierr = DMGetCoordinatesLocal(dm, &coords);CHKERRQ(ierr);
889     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
890     ierr = DMGetLocalSection(cdm, &cs);CHKERRQ(ierr);
891     for (c = cStart; c < cEnd; c++) {
892       PetscInt doit = 0, outside = 0;
893       ierr = DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef);CHKERRQ(ierr);
894       Nv = csize/dim;
895       for (nz = d = 0; d < Nv; d++) {
896         PetscReal z = PetscRealPart(coef[d*dim + (dim-1)]), x = PetscSqr(PetscRealPart(coef[d*dim + 0])) + ((dim==3) ? PetscSqr(PetscRealPart(coef[d*dim + 1])) : 0);
897         x = PetscSqrtReal(x);
898         if (x < PETSC_MACHINE_EPSILON*10. && PetscAbsReal(z)<PETSC_MACHINE_EPSILON*10.) doit = 1;             /* refine origin */
899         else if (type==0 && (z < -PETSC_MACHINE_EPSILON*10. || z > ctx->re_radius+PETSC_MACHINE_EPSILON*10.)) outside++;   /* first pass don't refine bottom */
900         else if (type==1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) outside++; /* don't refine outside electron refine radius */
901         else if (type==3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) outside++; /* don't refine outside ion refine radius */
902         if (x < PETSC_MACHINE_EPSILON*10.) nz++;
903       }
904       ierr = DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef);CHKERRQ(ierr);
905       if (doit || (outside<Nv && nz)) {
906         ierr = DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE);CHKERRQ(ierr);
907       }
908     }
909     ierr = PetscInfo1(sol, "Phase:%s: RE refinement\n","adaptToleranceFEM");
910   }
911   /* ierr = VecDestroy(&locX);CHKERRQ(ierr); */
912   ierr = DMDestroy(&plex);CHKERRQ(ierr);
913   ierr = DMAdaptLabel(dm, adaptLabel, &adaptedDM);CHKERRQ(ierr);
914   ierr = DMLabelDestroy(&adaptLabel);CHKERRQ(ierr);
915   *newDM = adaptedDM;
916   if (adaptedDM) {
917     if (isForest) {
918       ierr = DMForestSetAdaptivityForest(adaptedDM,NULL);CHKERRQ(ierr);
919     }
920     ierr = DMConvert(adaptedDM, DMPLEX, &plex);CHKERRQ(ierr);
921     ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
922     ierr = PetscInfo2(sol, "\tPhase: adaptToleranceFEM: %D cells, %d total quadrature points\n",cEnd-cStart,Nq*(cEnd-cStart));CHKERRQ(ierr);
923     ierr = DMDestroy(&plex);CHKERRQ(ierr);
924   }
925   PetscFunctionReturn(0);
926 }
927 
928 static PetscErrorCode adapt(DM *dm, LandauCtx *ctx, Vec *uu)
929 {
930   PetscErrorCode  ierr;
931   PetscInt        type, limits[5] = {ctx->numRERefine,ctx->nZRefine1,ctx->maxRefIts,ctx->nZRefine2,ctx->postAMRRefine};
932   PetscInt        adaptIter;
933 
934   PetscFunctionBegin;
935   for (type=0;type<5;type++) {
936     for (adaptIter = 0; adaptIter<limits[type];adaptIter++) {
937       DM  dmNew = NULL;
938       ierr = adaptToleranceFEM(ctx->fe[0], *uu, ctx->refineTol, ctx->coarsenTol, type, ctx, &dmNew);CHKERRQ(ierr);
939       if (!dmNew) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"should not happen");
940       else {
941         ierr = DMDestroy(dm);CHKERRQ(ierr);
942         ierr = VecDestroy(uu);CHKERRQ(ierr);
943         ierr = DMCreateGlobalVector(dmNew,uu);CHKERRQ(ierr);
944         ierr = PetscObjectSetName((PetscObject) *uu, "u");CHKERRQ(ierr);
945         ierr = LandauSetInitialCondition(dmNew, *uu, ctx);CHKERRQ(ierr);
946         *dm = dmNew;
947       }
948     }
949   }
950   PetscFunctionReturn(0);
951 }
952 
953 static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
954 {
955   PetscErrorCode    ierr;
956   PetscBool         flg, sph_flg;
957   PetscInt          ii,nt,nm,nc;
958   DM                dummy;
959 
960   PetscFunctionBegin;
961   ierr = DMCreate(PETSC_COMM_WORLD,&dummy);CHKERRQ(ierr);
962   /* get options - initialize context */
963   ctx->normJ = 0;
964   ctx->verbose = 1;
965   ctx->interpolate = PETSC_TRUE;
966   ctx->simplex = PETSC_FALSE;
967   ctx->sphere = PETSC_FALSE;
968   ctx->inflate = PETSC_FALSE;
969   ctx->electronShift = 0;
970   ctx->errorIndicator = NULL;
971   ctx->radius = 5.; /* electron thermal radius (velocity) */
972   ctx->re_radius = 0.;
973   ctx->vperp0_radius1 = 0;
974   ctx->vperp0_radius2 = 0;
975   ctx->e_radius = .1;
976   ctx->i_radius = .01;
977   ctx->maxRefIts = 5;
978   ctx->postAMRRefine = 0;
979   ctx->nZRefine1 = 0;
980   ctx->nZRefine2 = 0;
981   ctx->numRERefine = 0;
982   ctx->num_sections = 3; /* 2, 3 or 4 */
983   /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
984   ctx->charges[0] = -1;  /* electron charge (MKS) */
985   ctx->masses[0] = 1/1835.5; /* temporary value in proton mass */
986   ctx->n[0] = 1;
987   ctx->thermal_temps[0] = 1;
988   /* constants, etc. */
989   ctx->epsilon0 = 8.8542e-12; /* permittivity of free space (MKS) F/m */
990   ctx->k = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
991   ctx->lnLam = 10;         /* cross section ratio large - small angle collisions */
992   ctx->n_0 = 1.e20;        /* typical plasma n, but could set it to 1 */
993   ctx->Ez = 0;
994   ctx->v_0 = 1; /* in electron thermal velocity */
995   ctx->subThreadBlockSize = 1; /* for device and maybe OMP */
996   ierr = PetscOptionsBegin(PETSC_COMM_WORLD, prefix, "Options for Fokker-Plank-Landau collision operator", "none");CHKERRQ(ierr);
997   {
998     char opstring[256];
999 #if defined(PETSC_HAVE_KOKKOS)
1000     ctx->deviceType = LANDAU_KOKKOS;
1001     ierr = PetscStrcpy(opstring,"kokkos");CHKERRQ(ierr);
1002 #if !defined(PETSC_HAVE_CUDA)
1003     ctx->subThreadBlockSize = 0;
1004 #endif
1005 #elif defined(PETSC_HAVE_CUDA)
1006     ctx->deviceType = LANDAU_CUDA;
1007     ierr = PetscStrcpy(opstring,"cuda");CHKERRQ(ierr);
1008 #else
1009     ctx->deviceType = LANDAU_CPU;
1010     ierr = PetscStrcpy(opstring,"cpu");CHKERRQ(ierr);
1011     ctx->subThreadBlockSize = 0;
1012 #endif
1013     ierr = PetscOptionsString("-dm_landau_device_type","Use kernels on 'cpu', 'cuda', or 'kokkos'","plexland.c",opstring,opstring,256,NULL);CHKERRQ(ierr);
1014     ierr = PetscStrcmp("cpu",opstring,&flg);CHKERRQ(ierr);
1015     if (flg) {
1016       ctx->deviceType = LANDAU_CPU;
1017       ctx->subThreadBlockSize = 0;
1018     } else {
1019       ierr = PetscStrcmp("cuda",opstring,&flg);CHKERRQ(ierr);
1020       if (flg) ctx->deviceType = LANDAU_CUDA;
1021       else {
1022         ierr = PetscStrcmp("kokkos",opstring,&flg);CHKERRQ(ierr);
1023         if (flg) ctx->deviceType = LANDAU_KOKKOS;
1024         else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"-dm_landau_device_type %s",opstring);
1025       }
1026     }
1027   }
1028   ierr = PetscOptionsReal("-dm_landau_electron_shift","Shift in thermal velocity of electrons","none",ctx->electronShift,&ctx->electronShift, NULL);CHKERRQ(ierr);
1029   ierr = PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, &sph_flg);CHKERRQ(ierr);
1030   ierr = PetscOptionsBool("-dm_landau_inflate", "With sphere, inflate for curved edges (no AMR)", "plexland.c", ctx->inflate, &ctx->inflate, NULL);CHKERRQ(ierr);
1031   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);
1032   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);
1033   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);
1034   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);
1035   ierr = PetscOptionsInt("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &ctx->postAMRRefine, NULL);CHKERRQ(ierr);
1036   ierr = PetscOptionsInt("-dm_landau_verbose", "", "plexland.c", ctx->verbose, &ctx->verbose, NULL);CHKERRQ(ierr);
1037   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);
1038   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);
1039   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);
1040   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);
1041   ierr = PetscOptionsReal("-dm_landau_n_0","Normalization constant for number density","plexland.c",ctx->n_0,&ctx->n_0, NULL);CHKERRQ(ierr);
1042   ierr = PetscOptionsReal("-dm_landau_ln_lambda","Cross section parameter","plexland.c",ctx->lnLam,&ctx->lnLam, NULL);CHKERRQ(ierr);
1043   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);
1044   ctx->simplex = PETSC_FALSE;
1045   /* get num species with tempurature*/
1046   {
1047     PetscReal arr[100];
1048     nt = 100;
1049     ierr = PetscOptionsRealArray("-dm_landau_thermal_temps", "Temperature of each species [e,i_0,i_1,...] in keV", "plexland.c", arr, &nt, &flg);CHKERRQ(ierr);
1050     if (flg && nt > LANDAU_MAX_SPECIES) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"-thermal_temps ,t1,t2,.. number of species %D > MAX %D",nt,LANDAU_MAX_SPECIES);
1051   }
1052   nt = LANDAU_MAX_SPECIES;
1053   for (ii=1;ii<LANDAU_MAX_SPECIES;ii++) {
1054     ctx->thermal_temps[ii] = 1.;
1055     ctx->charges[ii] = 1;
1056     ctx->masses[ii] = 1;
1057     ctx->n[ii] = (ii==1) ? 1 : 0;
1058   }
1059   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);
1060   if (flg) {
1061     PetscInfo1(dummy, "num_species set to number of thermal temps provided (%D)\n",nt);
1062     ctx->num_species = nt;
1063   } else SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
1064   for (ii=0;ii<ctx->num_species;ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
1065   nm = LANDAU_MAX_SPECIES-1;
1066   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);
1067   if (flg && nm != ctx->num_species-1) {
1068     SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"num ion masses %D != num species %D",nm,ctx->num_species-1);
1069   }
1070   nm = LANDAU_MAX_SPECIES;
1071   ierr = PetscOptionsRealArray("-dm_landau_n", "Normalized (by -n_0) number density of each species", "plexland.c", ctx->n, &nm, &flg);CHKERRQ(ierr);
1072   if (flg && nm != ctx->num_species) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"wrong num n: %D != num species %D",nm,ctx->num_species);
1073   ctx->n_0 *= ctx->n[0]; /* normalized number density */
1074   for (ii=1;ii<ctx->num_species;ii++) ctx->n[ii] = ctx->n[ii]/ctx->n[0];
1075   ctx->n[0] = 1;
1076   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
1077   ctx->masses[0] = 9.10938356e-31; /* electron mass kg (should be about right already) */
1078   ctx->m_0 = ctx->masses[0]; /* arbitrary reference mass, electrons */
1079   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);
1080   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) */
1081   nc = LANDAU_MAX_SPECIES-1;
1082   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);
1083   if (flg && nc != ctx->num_species-1) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"num charges %D != num species %D",nc,ctx->num_species-1);
1084   for (ii=0;ii<LANDAU_MAX_SPECIES;ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
1085   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 */
1086   /* geometry */
1087   for (ii=0;ii<ctx->num_species;ii++) ctx->refineTol[ii]  = PETSC_MAX_REAL;
1088   for (ii=0;ii<ctx->num_species;ii++) ctx->coarsenTol[ii] = 0.;
1089   ii = LANDAU_MAX_SPECIES;
1090   ierr = PetscOptionsRealArray("-dm_landau_refine_tol","tolerance for refining cells in AMR","plexland.c",ctx->refineTol, &ii, &flg);CHKERRQ(ierr);
1091   if (flg && ii != ctx->num_species) ierr = PetscInfo2(dummy, "Phase: Warning, #refine_tol %D != num_species %D\n",ii,ctx->num_species);CHKERRQ(ierr);
1092   ii = LANDAU_MAX_SPECIES;
1093   ierr = PetscOptionsRealArray("-dm_landau_coarsen_tol","tolerance for coarsening cells in AMR","plexland.c",ctx->coarsenTol, &ii, &flg);CHKERRQ(ierr);
1094   if (flg && ii != ctx->num_species) ierr = PetscInfo2(dummy, "Phase: Warning, #coarsen_tol %D != num_species %D\n",ii,ctx->num_species);CHKERRQ(ierr);
1095   ierr = PetscOptionsReal("-dm_landau_domain_radius","Phase space size in units of electron thermal velocity","plexland.c",ctx->radius,&ctx->radius, &flg);CHKERRQ(ierr);
1096   if (flg && ctx->radius <= 0) { /* negative is ratio of c */
1097     if (ctx->radius == 0) ctx->radius = 0.75;
1098     else ctx->radius = -ctx->radius;
1099     ctx->radius = ctx->radius*299792458/ctx->v_0;
1100     ierr = PetscInfo1(dummy, "Change domain radius to %e\n",ctx->radius);CHKERRQ(ierr);
1101   }
1102   ierr = PetscOptionsReal("-dm_landau_i_radius","Ion thermal velocity, used for circular meshes","plexland.c",ctx->i_radius,&ctx->i_radius, &flg);CHKERRQ(ierr);
1103   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an ion radius but did not set sphere, user error really */
1104   if (!flg) {
1105     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 */
1106   }
1107   ierr = PetscOptionsReal("-dm_landau_e_radius","Electron thermal velocity, used for circular meshes","plexland.c",ctx->e_radius,&ctx->e_radius, &flg);CHKERRQ(ierr);
1108   if (flg && !sph_flg) ctx->sphere = PETSC_TRUE; /* you gave me an e radius but did not set sphere, user error really */
1109   if (!flg) {
1110     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 */
1111   }
1112   if (ctx->sphere && (ctx->e_radius <= ctx->i_radius || ctx->radius <= ctx->e_radius)) SETERRQ3(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"bad radii: %g < %g < %g",ctx->i_radius,ctx->e_radius,ctx->radius);
1113   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);
1114   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1115   for (ii=ctx->num_species;ii<LANDAU_MAX_SPECIES;ii++) ctx->masses[ii] = ctx->thermal_temps[ii]  = ctx->charges[ii] = 0;
1116   if (ctx->verbose > 0) {
1117     ierr = PetscPrintf(PETSC_COMM_WORLD, "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);
1118     ierr = PetscPrintf(PETSC_COMM_WORLD, "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);
1119     ierr = PetscPrintf(PETSC_COMM_WORLD, "thermal T (K): e=%10.3e i=%10.3e imp=%10.3e. v_0=%10.3e n_0=%10.3e t_0=%10.3e domain=%10.3e\n",ctx->thermal_temps[0],ctx->thermal_temps[1],ctx->num_species>2 ? ctx->thermal_temps[2] : 0,ctx->v_0,ctx->n_0,ctx->t_0,ctx->radius);CHKERRQ(ierr);
1120   }
1121   ierr = DMDestroy(&dummy);CHKERRQ(ierr);
1122   {
1123     PetscMPIInt    rank;
1124     ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
1125     /* PetscLogStage  setup_stage; */
1126     ierr = PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[0]);CHKERRQ(ierr); /* 0 */
1127     ierr = PetscLogEventRegister(" Jac-vector", DM_CLASSID, &ctx->events[1]);CHKERRQ(ierr); /* 1 */
1128     ierr = PetscLogEventRegister(" Jac-kern-init", DM_CLASSID, &ctx->events[3]);CHKERRQ(ierr); /* 3 */
1129     ierr = PetscLogEventRegister(" Jac-kernel", DM_CLASSID, &ctx->events[4]);CHKERRQ(ierr); /* 4 */
1130     ierr = PetscLogEventRegister(" Jac-kernel-post", DM_CLASSID, &ctx->events[5]);CHKERRQ(ierr); /* 5 */
1131     ierr = PetscLogEventRegister(" Jac-assemble", DM_CLASSID, &ctx->events[6]);CHKERRQ(ierr); /* 6 */
1132     ierr = PetscLogEventRegister(" Jac-end", DM_CLASSID, &ctx->events[7]);CHKERRQ(ierr); /* 7 */
1133     ierr = PetscLogEventRegister("  Jac-geo-color", DM_CLASSID, &ctx->events[8]);CHKERRQ(ierr); /* 8 */
1134     ierr = PetscLogEventRegister("  Jac-cuda-sum", DM_CLASSID, &ctx->events[2]);CHKERRQ(ierr); /* 2 */
1135     ierr = PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[9]);CHKERRQ(ierr); /* 9 */
1136     if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
1137       ierr = PetscOptionsClearValue(NULL,"-snes_converged_reason");CHKERRQ(ierr);
1138       ierr = PetscOptionsClearValue(NULL,"-ksp_converged_reason");CHKERRQ(ierr);
1139       ierr = PetscOptionsClearValue(NULL,"-snes_monitor");CHKERRQ(ierr);
1140       ierr = PetscOptionsClearValue(NULL,"-ksp_monitor");CHKERRQ(ierr);
1141       ierr = PetscOptionsClearValue(NULL,"-ts_monitor");CHKERRQ(ierr);
1142       ierr = PetscOptionsClearValue(NULL,"-ts_adapt_monitor");CHKERRQ(ierr);
1143       ierr = PetscOptionsClearValue(NULL,"-dm_landau_amr_dm_view");CHKERRQ(ierr);
1144       ierr = PetscOptionsClearValue(NULL,"-dm_landau_amr_vec_view");CHKERRQ(ierr);
1145       ierr = PetscOptionsClearValue(NULL,"-dm_landau_pre_dm_view");CHKERRQ(ierr);
1146       ierr = PetscOptionsClearValue(NULL,"-dm_landau_pre_vec_view");CHKERRQ(ierr);
1147       ierr = PetscOptionsClearValue(NULL,"-info");CHKERRQ(ierr);
1148     }
1149   }
1150   PetscFunctionReturn(0);
1151 }
1152 
1153 /*@C
1154   LandauCreateVelocitySpace - Create a DMPlex velocity space mesh
1155 
1156   Collective on comm
1157 
1158   Input Parameters:
1159 +   comm  - The MPI communicator
1160 .   dim - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
1161 -   prefix - prefix for options
1162 
1163   Output Parameter:
1164 .   dm  - The DM object representing the mesh
1165 +   X - A vector (user destroys)
1166 -   J - Optional matrix (object destroys)
1167 
1168   Level: beginner
1169 
1170 .keywords: mesh
1171 .seealso: DMPlexCreate(), LandauDestroyVelocitySpace()
1172 @*/
1173 PetscErrorCode LandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *dm)
1174 {
1175   PetscMPIInt    size;
1176   PetscErrorCode ierr;
1177   LandauCtx      *ctx;
1178   PetscBool      prealloc_only;
1179 
1180   PetscFunctionBegin;
1181   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1182   if (size!=1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Velocity space meshes should be serial (but should work in parallel)");
1183   if (dim!=2 && dim!=3) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Only 2D and 3D supported");
1184   ctx = (LandauCtx*)malloc(sizeof(LandauCtx));
1185   /* process options */
1186   ierr = ProcessOptions(ctx,prefix);CHKERRQ(ierr);
1187   /* Create Mesh */
1188   ierr = LandauDMCreateVMesh(comm, dim, prefix, ctx, dm);CHKERRQ(ierr);
1189   prealloc_only = (*dm)->prealloc_only;
1190   ierr = DMViewFromOptions(*dm,NULL,"-dm_landau_pre_dm_view");CHKERRQ(ierr);
1191   ierr = DMSetApplicationContext(*dm, ctx);CHKERRQ(ierr);
1192   /* create FEM */
1193   ierr = SetupDS(*dm,dim,ctx);CHKERRQ(ierr);
1194   /* set initial state */
1195   ierr = DMCreateGlobalVector(*dm,X);CHKERRQ(ierr);
1196   ierr = PetscObjectSetName((PetscObject) *X, "u");CHKERRQ(ierr);
1197   /* initial static refinement, no solve */
1198   ierr = LandauSetInitialCondition(*dm, *X, ctx);CHKERRQ(ierr);
1199   ierr = VecViewFromOptions(*X, NULL, "-dm_landau_pre_vec_view");CHKERRQ(ierr);
1200   /* forest refinement */
1201   if (ctx->errorIndicator) {
1202     /* AMR */
1203     ierr = adapt(dm,ctx,X);CHKERRQ(ierr);
1204     if ((*dm)->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"(*dm)->prealloc_only != prealloc_only");
1205     ierr = DMViewFromOptions(*dm,NULL,"-dm_landau_amr_dm_view");CHKERRQ(ierr);
1206     ierr = VecViewFromOptions(*X, NULL, "-dm_landau_amr_vec_view");CHKERRQ(ierr);
1207   }
1208   ierr = DMSetApplicationContext(*dm, ctx);CHKERRQ(ierr);
1209   ctx->dmv = *dm;
1210   if (ctx->dmv->prealloc_only != prealloc_only) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"ctx->dmv->prealloc_only != prealloc_only");
1211   ierr = DMCreateMatrix(ctx->dmv, &ctx->J);CHKERRQ(ierr);
1212   ierr = MatSetOption(ctx->J, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
1213   if (J) *J = ctx->J;
1214   PetscFunctionReturn(0);
1215 }
1216 
1217 /*@
1218   LandauDestroyVelocitySpace - Destroy a DMPlex velocity space mesh
1219 
1220   Collective on dm
1221 
1222   Input/Output Parameters:
1223   .   dm - the dm to destroy
1224 
1225   Level: beginner
1226 
1227 .keywords: mesh
1228 .seealso: LandauCreateVelocitySpace()
1229 @*/
1230 PetscErrorCode LandauDestroyVelocitySpace(DM *dm)
1231 {
1232   PetscErrorCode ierr,ii;
1233   LandauCtx        *ctx;
1234   PetscContainer container = NULL;
1235   PetscFunctionBegin;
1236   ierr = DMGetApplicationContext(*dm, &ctx);CHKERRQ(ierr);
1237   ierr = PetscObjectQuery((PetscObject)ctx->J,"coloring", (PetscObject*)&container);CHKERRQ(ierr);
1238   if (container) {
1239     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
1240   }
1241   ierr = MatDestroy(&ctx->M);CHKERRQ(ierr);
1242   ierr = MatDestroy(&ctx->J);CHKERRQ(ierr);
1243   for (ii=0;ii<ctx->num_species;ii++) {
1244     ierr = PetscFEDestroy(&ctx->fe[ii]);CHKERRQ(ierr);
1245   }
1246   free(ctx);
1247   ierr = DMDestroy(dm);CHKERRQ(ierr);
1248   PetscFunctionReturn(0);
1249 }
1250 
1251 /* < v, ru > */
1252 static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1253                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1254                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1255                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1256 {
1257   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1258   f0[0] = u[ii];
1259 }
1260 
1261 /* < v, ru > */
1262 static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1263                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1264                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1265                     PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1266 {
1267   PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
1268   f0[0] = x[jj]*u[ii]; /* x momentum */
1269 }
1270 
1271 static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1272                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1273                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1274                     PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1275 {
1276   PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
1277   double tmp1 = 0.;
1278   for (i = 0; i < dim; ++i) tmp1 += x[i]*x[i];
1279   f0[0] = tmp1*u[ii];
1280 }
1281 
1282 /* < v, ru > */
1283 static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1284                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1285                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1286                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1287 {
1288   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1289   f0[0] = 2.*PETSC_PI*x[0]*u[ii];
1290 }
1291 
1292 /* < v, ru > */
1293 static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1294                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1295                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1296                       PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1297 {
1298   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1299   f0[0] = 2.*PETSC_PI*x[0]*x[1]*u[ii];
1300 }
1301 
1302 static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1303                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1304                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1305                      PetscReal t, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
1306 {
1307   PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
1308   f0[0] =  2.*PETSC_PI*x[0]*(x[0]*x[0] + x[1]*x[1])*u[ii];
1309 }
1310 
1311 /*@
1312   LandauPrintNorms - collects moments and prints them
1313 
1314   Collective on dm
1315 
1316   Input Parameters:
1317 +   X  - the state
1318 -   stepi - current step to print
1319 
1320   Level: beginner
1321 
1322 .keywords: mesh
1323 .seealso: LandauCreateVelocitySpace()
1324 @*/
1325 PetscErrorCode LandauPrintNorms(Vec X, PetscInt stepi)
1326 {
1327   PetscErrorCode ierr;
1328   LandauCtx      *ctx;
1329   PetscDS        prob;
1330   DM             plex,dm;
1331   PetscInt       cStart, cEnd, dim, ii;
1332   PetscScalar    xmomentumtot=0, ymomentumtot=0, zmomentumtot=0, energytot=0, densitytot=0, tt[LANDAU_MAX_SPECIES];
1333   PetscScalar    xmomentum[LANDAU_MAX_SPECIES],  ymomentum[LANDAU_MAX_SPECIES],  zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
1334 
1335   PetscFunctionBegin;
1336   ierr = VecGetDM(X, &dm);CHKERRQ(ierr);
1337   if (!dm) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no DM");
1338   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1339   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
1340   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1341   ierr = DMConvert(ctx->dmv, DMPLEX, &plex);CHKERRQ(ierr);
1342   ierr = DMCreateDS(plex);CHKERRQ(ierr);
1343   ierr = DMGetDS(plex, &prob);CHKERRQ(ierr);
1344   /* print momentum and energy */
1345   for (ii=0;ii<ctx->num_species;ii++) {
1346     PetscScalar user[2] = { (PetscScalar)ii, (PetscScalar)ctx->charges[ii]};
1347     ierr = PetscDSSetConstants(prob, 2, user);CHKERRQ(ierr);
1348     if (dim==2) { /* 2/3X + 3V (cylindrical coordinates) */
1349       ierr = PetscDSSetObjective(prob, 0, &f0_s_rden);CHKERRQ(ierr);
1350       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1351       density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1352       ierr = PetscDSSetObjective(prob, 0, &f0_s_rmom);CHKERRQ(ierr);
1353       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1354       zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1355       ierr = PetscDSSetObjective(prob, 0, &f0_s_rv2);CHKERRQ(ierr);
1356       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1357       energy[ii] = tt[0]*0.5*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1358       zmomentumtot += zmomentum[ii];
1359       energytot  += energy[ii];
1360       densitytot += density[ii];
1361       ierr = PetscPrintf(PETSC_COMM_WORLD, "%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);
1362     } else { /* 2/3X + 3V */
1363       ierr = PetscDSSetObjective(prob, 0, &f0_s_den);CHKERRQ(ierr);
1364       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1365       density[ii] = tt[0]*ctx->n_0*ctx->charges[ii];
1366       ierr = PetscDSSetObjective(prob, 0, &f0_s_mom);CHKERRQ(ierr);
1367       user[1] = 0;
1368       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1369       xmomentum[ii]  = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1370       user[1] = 1;
1371       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1372       ymomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1373       user[1] = 2;
1374       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1375       zmomentum[ii] = tt[0]*ctx->n_0*ctx->v_0*ctx->masses[ii];
1376       ierr = PetscDSSetObjective(prob, 0, &f0_s_v2);CHKERRQ(ierr);
1377       ierr = DMPlexComputeIntegralFEM(plex,X,tt,ctx);CHKERRQ(ierr);
1378       energy[ii]    = 0.5*tt[0]*ctx->n_0*ctx->v_0*ctx->v_0*ctx->masses[ii];
1379       ierr = PetscPrintf(PETSC_COMM_WORLD, "%3D) species %D: density=%20.13e, x-momentum=%20.13e, y-momentum=%20.13e, z-momentum=%20.13e, energy=%21.13e",
1380                          stepi,ii,PetscRealPart(density[ii]),PetscRealPart(xmomentum[ii]),PetscRealPart(ymomentum[ii]),PetscRealPart(zmomentum[ii]),PetscRealPart(energy[ii]));CHKERRQ(ierr);
1381       xmomentumtot += xmomentum[ii];
1382       ymomentumtot += ymomentum[ii];
1383       zmomentumtot += zmomentum[ii];
1384       energytot  += energy[ii];
1385       densitytot += density[ii];
1386     }
1387     if (ctx->num_species>1) PetscPrintf(PETSC_COMM_WORLD, "\n");
1388   }
1389   /* totals */
1390   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1391   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1392   if (ctx->num_species>1) {
1393     if (dim==2) {
1394       ierr = PetscPrintf(PETSC_COMM_WORLD, "\t%3D) Total: charge density=%21.13e, momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %D cells)",
1395                   stepi,PetscRealPart(densitytot),PetscRealPart(zmomentumtot),PetscRealPart(energytot),ctx->masses[1]/ctx->masses[0],cEnd-cStart);CHKERRQ(ierr);
1396     } else {
1397       ierr = PetscPrintf(PETSC_COMM_WORLD, "\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)",
1398                   stepi,PetscRealPart(densitytot),PetscRealPart(xmomentumtot),PetscRealPart(ymomentumtot),PetscRealPart(zmomentumtot),PetscRealPart(energytot),ctx->masses[1]/ctx->masses[0],cEnd-cStart);CHKERRQ(ierr);
1399     }
1400   } else {
1401     ierr = PetscPrintf(PETSC_COMM_WORLD, " -- %D cells",cEnd-cStart);CHKERRQ(ierr);
1402   }
1403   if (ctx->verbose > 1) {ierr = PetscPrintf(PETSC_COMM_WORLD,", %D sub (vector) threads\n",ctx->subThreadBlockSize);CHKERRQ(ierr);}
1404   else {ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr);}
1405   PetscFunctionReturn(0);
1406 }
1407 
1408 static PetscErrorCode destroy_coloring (void *is)
1409 {
1410   ISColoring tmp = (ISColoring)is;
1411   return ISColoringDestroy(&tmp);
1412 }
1413 
1414 /*@
1415   LandauCreateColoring - create a coloring and add to matrix (Landau context used just for 'print' flag, should be in DMPlex)
1416 
1417   Collective on JacP
1418 
1419   Input Parameters:
1420 +   JacP  - matrix to add coloring to
1421 -   plex - The DM
1422 
1423   Output Parameter:
1424 .   container  - Container with coloring
1425 
1426   Level: beginner
1427 
1428 .keywords: mesh
1429 .seealso: LandauCreateVelocitySpace()
1430 @*/
1431 PetscErrorCode LandauCreateColoring(Mat JacP, DM plex, PetscContainer *container)
1432 {
1433   PetscErrorCode  ierr;
1434   PetscInt        dim,cell,i,ej,nc,Nv,totDim,numGCells,cStart,cEnd;
1435   ISColoring      iscoloring = NULL;
1436   Mat             G,Q;
1437   PetscScalar     ones[128];
1438   MatColoring     mc;
1439   IS             *is;
1440   PetscInt        csize,colour,j,k;
1441   const PetscInt *indices;
1442   PetscInt       numComp[1];
1443   PetscInt       numDof[4];
1444   PetscFE        fe;
1445   DM             colordm;
1446   PetscSection   csection, section, globalSection;
1447   PetscDS        prob;
1448   LandauCtx      *ctx;
1449 
1450   PetscFunctionBegin;
1451   ierr = DMGetApplicationContext(plex, &ctx);CHKERRQ(ierr);
1452   ierr = DMGetLocalSection(plex, &section);CHKERRQ(ierr);
1453   ierr = DMGetGlobalSection(plex, &globalSection);CHKERRQ(ierr);
1454   ierr = DMGetDimension(plex, &dim);CHKERRQ(ierr);
1455   ierr = DMGetDS(plex, &prob);CHKERRQ(ierr);
1456   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1457   ierr = DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1458   numGCells = cEnd - cStart;
1459   /* create cell centered DM */
1460   ierr = DMClone(plex, &colordm);CHKERRQ(ierr);
1461   ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) plex), dim, 1, PETSC_FALSE, "color_", PETSC_DECIDE, &fe);CHKERRQ(ierr);
1462   ierr = PetscObjectSetName((PetscObject) fe, "color");CHKERRQ(ierr);
1463   ierr = DMSetField(colordm, 0, NULL, (PetscObject)fe);CHKERRQ(ierr);
1464   ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
1465   for (i = 0; i < (dim+1); ++i) numDof[i] = 0;
1466   numDof[dim] = 1;
1467   numComp[0] = 1;
1468   ierr = DMPlexCreateSection(colordm, NULL, numComp, numDof, 0, NULL, NULL, NULL, NULL, &csection);CHKERRQ(ierr);
1469   ierr = PetscSectionSetFieldName(csection, 0, "color");CHKERRQ(ierr);
1470   ierr = DMSetLocalSection(colordm, csection);CHKERRQ(ierr);
1471   ierr = DMViewFromOptions(colordm,NULL,"-color_dm_view");CHKERRQ(ierr);
1472   /* get vertex to element map Q and colroing graph G */
1473   ierr = MatGetSize(JacP,NULL,&Nv);CHKERRQ(ierr);
1474   ierr = MatCreateAIJ(PETSC_COMM_SELF,PETSC_DECIDE,PETSC_DECIDE,numGCells,Nv,totDim,NULL,0,NULL,&Q);CHKERRQ(ierr);
1475   for (i=0;i<128;i++) ones[i] = 1.0;
1476   for (cell = cStart, ej = 0 ; cell < cEnd; ++cell, ++ej) {
1477     PetscInt numindices,*indices;
1478     ierr = DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);CHKERRQ(ierr);
1479     if (numindices>128) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many indices. %D > %D",numindices,128);
1480     ierr = MatSetValues(Q,1,&ej,numindices,indices,ones,ADD_VALUES);CHKERRQ(ierr);
1481     ierr = DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, NULL);CHKERRQ(ierr);
1482   }
1483   ierr = MatAssemblyBegin(Q, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1484   ierr = MatAssemblyEnd(Q, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1485   ierr = MatMatTransposeMult(Q,Q,MAT_INITIAL_MATRIX,4.0,&G);CHKERRQ(ierr);
1486   ierr = PetscObjectSetName((PetscObject) Q, "Q");CHKERRQ(ierr);
1487   ierr = PetscObjectSetName((PetscObject) G, "coloring graph");CHKERRQ(ierr);
1488   ierr = MatViewFromOptions(G,NULL,"-coloring_mat_view");CHKERRQ(ierr);
1489   ierr = MatViewFromOptions(Q,NULL,"-coloring_mat_view");CHKERRQ(ierr);
1490   ierr = MatDestroy(&Q);CHKERRQ(ierr);
1491   /* coloring */
1492   ierr = MatColoringCreate(G,&mc);CHKERRQ(ierr);
1493   ierr = MatColoringSetDistance(mc,1);CHKERRQ(ierr);
1494   ierr = MatColoringSetType(mc,MATCOLORINGJP);CHKERRQ(ierr);
1495   ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
1496   ierr = MatColoringApply(mc,&iscoloring);CHKERRQ(ierr);
1497   ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
1498   /* view */
1499   ierr = ISColoringViewFromOptions(iscoloring,NULL,"-coloring_is_view");CHKERRQ(ierr);
1500   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);CHKERRQ(ierr);
1501   if (ctx && ctx->verbose > 5) {
1502     PetscViewer    viewer;
1503     Vec            color_vec, eidx_vec;
1504     ierr = DMGetGlobalVector(colordm, &color_vec);CHKERRQ(ierr);
1505     ierr = DMGetGlobalVector(colordm, &eidx_vec);CHKERRQ(ierr);
1506     for (colour=0; colour<nc; colour++) {
1507       ierr = ISGetLocalSize(is[colour],&csize);CHKERRQ(ierr);
1508       ierr = ISGetIndices(is[colour],&indices);CHKERRQ(ierr);
1509       for (j=0; j<csize; j++) {
1510         PetscScalar v = (PetscScalar)colour;
1511         k = indices[j];
1512         ierr = VecSetValues(color_vec,1,&k,&v,INSERT_VALUES);
1513         v = (PetscScalar)k;
1514         ierr = VecSetValues(eidx_vec,1,&k,&v,INSERT_VALUES);
1515       }
1516       ierr = ISRestoreIndices(is[colour],&indices);CHKERRQ(ierr);
1517     }
1518     /* view */
1519     ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD, "color.vtu", FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
1520     ierr = PetscObjectSetName((PetscObject) color_vec, "color");CHKERRQ(ierr);
1521     ierr = VecView(color_vec, viewer);CHKERRQ(ierr);
1522     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1523     ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD, "eidx.vtu", FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
1524     ierr = PetscObjectSetName((PetscObject) eidx_vec, "element-idx");CHKERRQ(ierr);
1525     ierr = VecView(eidx_vec, viewer);CHKERRQ(ierr);
1526     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1527     ierr = DMRestoreGlobalVector(colordm, &color_vec);CHKERRQ(ierr);
1528     ierr = DMRestoreGlobalVector(colordm, &eidx_vec);CHKERRQ(ierr);
1529   }
1530   ierr = PetscSectionDestroy(&csection);CHKERRQ(ierr);
1531   ierr = DMDestroy(&colordm);CHKERRQ(ierr);
1532   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);CHKERRQ(ierr);
1533   ierr = MatDestroy(&G);CHKERRQ(ierr);
1534   /* stash coloring */
1535   ierr = PetscContainerCreate(PETSC_COMM_SELF, container);CHKERRQ(ierr);
1536   ierr = PetscContainerSetPointer(*container,(void*)iscoloring);CHKERRQ(ierr);
1537   ierr = PetscContainerSetUserDestroy(*container, destroy_coloring);CHKERRQ(ierr);
1538   ierr = PetscObjectCompose((PetscObject)JacP,"coloring",(PetscObject)*container);CHKERRQ(ierr);
1539   if (ctx && ctx->verbose > 0) {
1540     ierr = PetscPrintf(PETSC_COMM_WORLD, "Made coloring with %D colors\n", nc);CHKERRQ(ierr);
1541   }
1542   PetscFunctionReturn(0);
1543   }
1544 
1545 PetscErrorCode LandauAssembleOpenMP(PetscInt cStart, PetscInt cEnd, PetscInt totDim, DM plex, PetscSection section, PetscSection globalSection, Mat JacP, PetscScalar elemMats[], PetscContainer container)
1546 {
1547   PetscErrorCode  ierr;
1548   IS             *is;
1549   PetscInt        nc,colour,j;
1550   const PetscInt *clr_idxs;
1551   ISColoring      iscoloring;
1552   PetscFunctionBegin;
1553   ierr = PetscContainerGetPointer(container,(void**)&iscoloring);CHKERRQ(ierr);
1554   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,&nc,&is);CHKERRQ(ierr);
1555   for (colour=0; colour<nc; colour++) {
1556     PetscInt    *idx_arr[1024]; /* need to make dynamic for general use */
1557     PetscScalar *new_el_mats[1024];
1558     PetscInt     idx_size[1024],csize;
1559     ierr = ISGetLocalSize(is[colour],&csize);CHKERRQ(ierr);
1560     if (csize>1024) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "too many elements in color. %D > %D",csize,1024);
1561     ierr = ISGetIndices(is[colour],&clr_idxs);CHKERRQ(ierr);
1562     /* get indices and mats */
1563     for (j=0; j<csize; j++) {
1564       PetscInt    cell = cStart + clr_idxs[j];
1565       PetscInt    numindices,*indices;
1566       PetscScalar *elMat = &elemMats[clr_idxs[j]*totDim*totDim];
1567       PetscScalar *valuesOrig = elMat;
1568       ierr = DMPlexGetClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
1569       idx_size[j] = numindices;
1570       ierr = PetscMalloc2(numindices,&idx_arr[j],numindices*numindices,&new_el_mats[j]);CHKERRQ(ierr);
1571       ierr = PetscMemcpy(idx_arr[j],indices,numindices*sizeof(PetscInt));CHKERRQ(ierr);
1572       ierr = PetscMemcpy(new_el_mats[j],elMat,numindices*numindices*sizeof(PetscScalar));CHKERRQ(ierr);
1573       ierr = DMPlexRestoreClosureIndices(plex, section, globalSection, cell, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **) &elMat);CHKERRQ(ierr);
1574       if (elMat != valuesOrig) {ierr = DMRestoreWorkArray(plex, numindices*numindices, MPIU_SCALAR, &elMat);}
1575     }
1576     /* assemble matrix - pragmas break CI ? */
1577     //#pragma omp parallel default(JacP,idx_size,idx_arr,new_el_mats,colour,clr_idxs)  private(j)
1578     //#pragma omp parallel for private(j)
1579     for (j=0; j<csize; j++) {
1580       PetscInt    numindices = idx_size[j], *indices = idx_arr[j];
1581       PetscScalar *elMat = new_el_mats[j];
1582       MatSetValues(JacP,numindices,indices,numindices,indices,elMat,ADD_VALUES);
1583     }
1584     /* free */
1585     ierr = ISRestoreIndices(is[colour],&clr_idxs);CHKERRQ(ierr);
1586     for (j=0; j<csize; j++) {
1587       ierr = PetscFree2(idx_arr[j],new_el_mats[j]);CHKERRQ(ierr);
1588     }
1589   }
1590   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&is);CHKERRQ(ierr);
1591   PetscFunctionReturn(0);
1592 }
1593 
1594 /* < v, u > */
1595 static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1596                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1597                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1598                   PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
1599 {
1600   g0[0] = 1.;
1601 }
1602 
1603 /* < v, u > */
1604 static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1605                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1606                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1607                   PetscReal t, PetscReal u_tShift, const PetscReal x[],  PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
1608 {
1609   g0[0] = 2.*PETSC_PI*x[0];
1610 }
1611 
1612 /*@
1613   LandauCreateMassMatrix - Create mass matrix for Landau
1614 
1615   Collective on dm
1616 
1617   Input Parameters:
1618 . dm     - the DM object
1619 
1620  Output Parameters:
1621 . Amat - The mass matrix (optional), mass matrix is added to the DM context
1622 
1623   Level: beginner
1624 
1625 .keywords: mesh
1626 .seealso: LandauCreateVelocitySpace()
1627 @*/
1628 PetscErrorCode LandauCreateMassMatrix(DM dm, Mat *Amat)
1629 {
1630   DM             massDM;
1631   PetscDS        prob;
1632   PetscInt       ii,dim,N1=1,N2;
1633   PetscErrorCode ierr;
1634   LandauCtx      *ctx;
1635   Mat            M;
1636 
1637   PetscFunctionBegin;
1638   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1639   if (Amat) PetscValidPointer(Amat,3);
1640   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
1641   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1642   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1643   ierr = DMClone(dm, &massDM);CHKERRQ(ierr);
1644   ierr = DMCopyFields(dm, massDM);CHKERRQ(ierr);
1645   ierr = DMCreateDS(massDM);CHKERRQ(ierr);
1646   ierr = DMGetDS(massDM, &prob);CHKERRQ(ierr);
1647   for (ii=0;ii<ctx->num_species;ii++) {
1648     if (dim==3) {ierr = PetscDSSetJacobian(prob, ii, ii, g0_1, NULL, NULL, NULL);CHKERRQ(ierr);}
1649     else        {ierr = PetscDSSetJacobian(prob, ii, ii, g0_r, NULL, NULL, NULL);CHKERRQ(ierr);}
1650   }
1651   ierr = DMViewFromOptions(massDM,NULL,"-dm_landau_mass_dm_view");CHKERRQ(ierr);
1652   ierr = DMCreateMatrix(massDM, &M);CHKERRQ(ierr);
1653   ierr = MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
1654   {
1655     Vec locX;
1656     DM  plex;
1657     ierr = DMConvert(massDM, DMPLEX, &plex);CHKERRQ(ierr);
1658     ierr = DMGetLocalVector(massDM, &locX);CHKERRQ(ierr);
1659     /* Mass matrix is independent of the input, so no need to fill locX */
1660     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);
1661     ierr = DMPlexSNESComputeJacobianFEM(plex, locX, M, M, ctx);CHKERRQ(ierr);
1662     ierr = DMRestoreLocalVector(massDM, &locX);CHKERRQ(ierr);
1663     ierr = DMDestroy(&plex);CHKERRQ(ierr);
1664   }
1665   ierr = DMDestroy(&massDM);CHKERRQ(ierr);
1666   ierr = MatGetSize(ctx->J, &N1, NULL);CHKERRQ(ierr);
1667   ierr = MatGetSize(M, &N2, NULL);CHKERRQ(ierr);
1668   if (N1 != N2) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Incorrect matrix sizes: |Jacobian| = %D, |Mass|=%D",N1,N2);
1669   ierr = PetscObjectSetName((PetscObject)M, "mass");CHKERRQ(ierr);
1670   ierr = MatViewFromOptions(M,NULL,"-dm_landau_mass_mat_view");CHKERRQ(ierr);
1671   ctx->M = M; /* this could be a noop, a = a */
1672   if (Amat) *Amat = M;
1673   PetscFunctionReturn(0);
1674 }
1675 
1676 /*@
1677   LandauIFunction - TS residual calculation
1678 
1679   Collective on ts
1680 
1681   Input Parameters:
1682 +   TS  - The time stepping context
1683 .   time_dummy - current time (not used)
1684 -   X - Current state
1685 +   X_t - Time derivative of current state
1686 .   actx - Landau context
1687 
1688   Output Parameter:
1689 .   F  - The residual
1690 
1691   Level: beginner
1692 
1693 .keywords: mesh
1694 .seealso: LandauCreateVelocitySpace(), LandauIJacobian()
1695 @*/
1696 PetscErrorCode LandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
1697 {
1698   PetscErrorCode ierr;
1699   LandauCtx      *ctx=(LandauCtx*)actx;
1700   PetscReal      unorm;
1701   PetscInt       dim;
1702   DM dm;
1703 
1704   PetscFunctionBegin;
1705   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1706   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
1707   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1708   ierr = VecNorm(X,NORM_2,&unorm);CHKERRQ(ierr);
1709   ierr = PetscLogEventBegin(ctx->events[0],0,0,0,0);CHKERRQ(ierr);
1710   ierr = DMGetDimension(ctx->dmv, &dim);CHKERRQ(ierr);
1711   if (ctx->normJ != unorm) {
1712     ctx->normJ = unorm;
1713     ierr = PetscInfo1(ts, "Create Landau Jacobian t=%g\n",time_dummy);CHKERRQ(ierr);
1714     ierr = LandauFormJacobian_Internal(X,ctx->J,dim,(void*)ctx);CHKERRQ(ierr);
1715     ctx->aux_bool = PETSC_TRUE; /* debug: set flag that we made a new Jacobian */
1716   } else {
1717     ctx->aux_bool = PETSC_FALSE;
1718     ierr = PetscInfo1(ts, "Skip Landau Jacobian t=%g\n",(double)time_dummy);CHKERRQ(ierr);
1719   }
1720   /* mat vec for op */
1721   ierr = MatMult(ctx->J,X,F);CHKERRQ(ierr);CHKERRQ(ierr); /* C*f */
1722   /* add time term */
1723   if (X_t) {
1724     ierr = MatMultAdd(ctx->M,X_t,F,F);CHKERRQ(ierr);
1725   }
1726   ierr = PetscLogEventEnd(ctx->events[0],0,0,0,0);CHKERRQ(ierr);
1727   PetscFunctionReturn(0);
1728 }
1729 
1730 /*@
1731   LandauIJacobian - TS Jacobian construction
1732 
1733   Collective on ts
1734 
1735   Input Parameters:
1736 +   TS  - The time stepping context
1737 .   time_dummy - current time (not used)
1738 -   X - Current state
1739 +   U_tdummy - Time derivative of current state (not used)
1740 .   shift - shift for du/dt term
1741 -   actx - Landau context
1742 
1743   Output Parameter:
1744 .   Amat  - Jacobian
1745 +   Pmat  - same as Amat
1746 
1747   Level: beginner
1748 
1749 .keywords: mesh
1750 .seealso: LandauCreateVelocitySpace(), LandauIFunction()
1751 @*/
1752 PetscErrorCode LandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
1753 {
1754   PetscErrorCode ierr;
1755   LandauCtx      *ctx=(LandauCtx*)actx;
1756   PetscReal      unorm;
1757   PetscInt       dim;
1758   DM dm;
1759 
1760   PetscFunctionBegin;
1761   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1762   ierr = DMGetApplicationContext(dm, &ctx);CHKERRQ(ierr);
1763   if (!ctx) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
1764   if (Amat!=Pmat || Amat!=ctx->J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Amat!=Pmat || Amat!=ctx->J");
1765   ierr = DMGetDimension(ctx->dmv, &dim);CHKERRQ(ierr);
1766   /* get collision Jacobian into A */
1767   ierr = PetscLogEventBegin(ctx->events[9],0,0,0,0);CHKERRQ(ierr);
1768   ierr = VecNorm(X,NORM_2,&unorm);CHKERRQ(ierr);
1769   if (ctx->normJ!=unorm) {
1770     ierr = PetscInfo2(ts, "Create Landau Jacobian t=%g, shift=%g\n",(double)time_dummy,(double)shift);CHKERRQ(ierr);
1771     ierr = LandauFormJacobian_Internal(X,ctx->J,dim,(void*)ctx);CHKERRQ(ierr);
1772     ctx->normJ = unorm;
1773     ctx->aux_bool = PETSC_TRUE; /* debug: set flag that we made a new Jacobian */
1774   } else {
1775     ctx->aux_bool = PETSC_FALSE;
1776     ierr = PetscInfo3(ts, "Skip Landau Jacobian t=%g, shift=%g shift*|u|=%20.12e\n",(double)time_dummy,(double)shift,(double)shift*unorm);CHKERRQ(ierr);
1777   }
1778   ierr = MatCopy(ctx->J,Pmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr); // these are the same
1779   {
1780     MatInfo info1, info2;
1781     double  nz_1, nz_2;
1782     ierr = MatGetInfo(Pmat,MAT_LOCAL,&info1);CHKERRQ(ierr);
1783     nz_1 = info1.nz_allocated;
1784     ierr = MatGetInfo(ctx->J,MAT_LOCAL,&info2);CHKERRQ(ierr);
1785     nz_2 = info2.nz_allocated;
1786     if (0){
1787       ierr = PetscInfo2(ts, "\t\tnnz A = %g, nnz M = %g\n",nz_1,nz_2);CHKERRQ(ierr);
1788     }
1789     /* add mass */
1790     if (nz_1 != nz_2||1) { /* there is a bug wit Q2 elements and this generates an error message instead of diverged solution, need to fix */
1791       ierr = MatAXPY(Pmat,shift,ctx->M,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
1792       //SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "nz_1 != nz_2 %g %g",(double)nz_1,(double)nz_2);
1793     } else {
1794       ierr = MatAXPY(Pmat,shift,ctx->M,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1795     }
1796   }
1797   ierr = PetscLogEventEnd(ctx->events[9],0,0,0,0);CHKERRQ(ierr);
1798   PetscFunctionReturn(0);
1799 }
1800