Actual source code: ex28.c

petsc-3.10.2 2018-10-09
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  1: static const char help[] = "1D multiphysics prototype with analytic Jacobians to solve individual problems and a coupled problem.\n\n";

  3: /* Solve a PDE coupled to an algebraic system in 1D
  4:  *
  5:  * PDE (U):
  6:  *     -(k u_x)_x = 1 on (0,1), subject to u(0) = 0, u(1) = 1
  7:  * Algebraic (K):
  8:  *     exp(k-1) + k = 1/(1/(1+u) + 1/(1+u_x^2))
  9:  *
 10:  * The discretization places k at staggered points, and a separate DMDA is used for each "physics".
 11:  *
 12:  * This example is a prototype for coupling in multi-physics problems, therefore residual evaluation and assembly for
 13:  * each problem (referred to as U and K) are written separately.  This permits the same "physics" code to be used for
 14:  * solving each uncoupled problem as well as the coupled system.  In particular, run with -problem_type 0 to solve only
 15:  * problem U (with K fixed), -problem_type 1 to solve only K (with U fixed), and -problem_type 2 to solve both at once.
 16:  *
 17:  * In all cases, a fully-assembled analytic Jacobian is available, so the systems can be solved with a direct solve or
 18:  * any other standard method.  Additionally, by running with
 19:  *
 20:  *   -pack_dm_mat_type nest
 21:  *
 22:  * The same code assembles a coupled matrix where each block is stored separately, which allows the use of PCFieldSplit
 23:  * without copying values to extract submatrices.
 24:  */

 26: /*T
 27:    TODO: Need to determine if deprecated
 28: T*/

 30:  #include <petscsnes.h>
 31:  #include <petscdm.h>
 32:  #include <petscdmda.h>
 33:  #include <petscdmcomposite.h>

 35: typedef struct _UserCtx *User;
 36: struct _UserCtx {
 37:   PetscInt ptype;
 38:   DM       pack;
 39:   Vec      Uloc,Kloc;
 40: };

 42: static PetscErrorCode FormFunctionLocal_U(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],PetscScalar f[])
 43: {
 44:   PetscReal hx = 1./info->mx;
 45:   PetscInt  i;

 48:   for (i=info->xs; i<info->xs+info->xm; i++) {
 49:     if (i == 0) f[i] = 1./hx*u[i];
 50:     else if (i == info->mx-1) f[i] = 1./hx*(u[i] - 1.0);
 51:     else f[i] = hx*((k[i-1]*(u[i]-u[i-1]) - k[i]*(u[i+1]-u[i]))/(hx*hx) - 1.0);
 52:   }
 53:   return(0);
 54: }

 56: static PetscErrorCode FormFunctionLocal_K(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],PetscScalar f[])
 57: {
 58:   PetscReal hx = 1./info->mx;
 59:   PetscInt  i;

 62:   for (i=info->xs; i<info->xs+info->xm; i++) {
 63:     const PetscScalar
 64:       ubar  = 0.5*(u[i+1]+u[i]),
 65:       gradu = (u[i+1]-u[i])/hx,
 66:       g     = 1. + gradu*gradu,
 67:       w     = 1./(1.+ubar) + 1./g;
 68:     f[i] = hx*(PetscExpScalar(k[i]-1.0) + k[i] - 1./w);
 69:   }
 70:   return(0);
 71: }

 73: static PetscErrorCode FormFunction_All(SNES snes,Vec X,Vec F,void *ctx)
 74: {
 75:   User           user = (User)ctx;
 76:   DM             dau,dak;
 77:   DMDALocalInfo  infou,infok;
 78:   PetscScalar    *u,*k;
 79:   PetscScalar    *fu,*fk;
 81:   Vec            Uloc,Kloc,Fu,Fk;

 84:   DMCompositeGetEntries(user->pack,&dau,&dak);
 85:   DMDAGetLocalInfo(dau,&infou);
 86:   DMDAGetLocalInfo(dak,&infok);
 87:   DMCompositeGetLocalVectors(user->pack,&Uloc,&Kloc);
 88:   switch (user->ptype) {
 89:   case 0:
 90:     DMGlobalToLocalBegin(dau,X,INSERT_VALUES,Uloc);
 91:     DMGlobalToLocalEnd  (dau,X,INSERT_VALUES,Uloc);
 92:     DMDAVecGetArray(dau,Uloc,&u);
 93:     DMDAVecGetArray(dak,user->Kloc,&k);
 94:     DMDAVecGetArray(dau,F,&fu);
 95:     FormFunctionLocal_U(user,&infou,u,k,fu);
 96:     DMDAVecRestoreArray(dau,F,&fu);
 97:     DMDAVecRestoreArray(dau,Uloc,&u);
 98:     DMDAVecRestoreArray(dak,user->Kloc,&k);
 99:     break;
100:   case 1:
101:     DMGlobalToLocalBegin(dak,X,INSERT_VALUES,Kloc);
102:     DMGlobalToLocalEnd  (dak,X,INSERT_VALUES,Kloc);
103:     DMDAVecGetArray(dau,user->Uloc,&u);
104:     DMDAVecGetArray(dak,Kloc,&k);
105:     DMDAVecGetArray(dak,F,&fk);
106:     FormFunctionLocal_K(user,&infok,u,k,fk);
107:     DMDAVecRestoreArray(dak,F,&fk);
108:     DMDAVecRestoreArray(dau,user->Uloc,&u);
109:     DMDAVecRestoreArray(dak,Kloc,&k);
110:     break;
111:   case 2:
112:     DMCompositeScatter(user->pack,X,Uloc,Kloc);
113:     DMDAVecGetArray(dau,Uloc,&u);
114:     DMDAVecGetArray(dak,Kloc,&k);
115:     DMCompositeGetAccess(user->pack,F,&Fu,&Fk);
116:     DMDAVecGetArray(dau,Fu,&fu);
117:     DMDAVecGetArray(dak,Fk,&fk);
118:     FormFunctionLocal_U(user,&infou,u,k,fu);
119:     FormFunctionLocal_K(user,&infok,u,k,fk);
120:     DMDAVecRestoreArray(dau,Fu,&fu);
121:     DMDAVecRestoreArray(dak,Fk,&fk);
122:     DMCompositeRestoreAccess(user->pack,F,&Fu,&Fk);
123:     DMDAVecRestoreArray(dau,Uloc,&u);
124:     DMDAVecRestoreArray(dak,Kloc,&k);
125:     break;
126:   }
127:   DMCompositeRestoreLocalVectors(user->pack,&Uloc,&Kloc);
128:   return(0);
129: }

131: static PetscErrorCode FormJacobianLocal_U(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],Mat Buu)
132: {
133:   PetscReal      hx = 1./info->mx;
135:   PetscInt       i;

138:   for (i=info->xs; i<info->xs+info->xm; i++) {
139:     PetscInt    row = i-info->gxs,cols[] = {row-1,row,row+1};
140:     PetscScalar val = 1./hx;
141:     if (i == 0) {
142:       MatSetValuesLocal(Buu,1,&row,1,&row,&val,INSERT_VALUES);
143:     } else if (i == info->mx-1) {
144:       MatSetValuesLocal(Buu,1,&row,1,&row,&val,INSERT_VALUES);
145:     } else {
146:       PetscScalar vals[] = {-k[i-1]/hx,(k[i-1]+k[i])/hx,-k[i]/hx};
147:       MatSetValuesLocal(Buu,1,&row,3,cols,vals,INSERT_VALUES);
148:     }
149:   }
150:   return(0);
151: }

153: static PetscErrorCode FormJacobianLocal_K(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],Mat Bkk)
154: {
155:   PetscReal      hx = 1./info->mx;
157:   PetscInt       i;

160:   for (i=info->xs; i<info->xs+info->xm; i++) {
161:     PetscInt    row    = i-info->gxs;
162:     PetscScalar vals[] = {hx*(PetscExpScalar(k[i]-1.)+1.)};
163:     MatSetValuesLocal(Bkk,1,&row,1,&row,vals,INSERT_VALUES);
164:   }
165:   return(0);
166: }

168: static PetscErrorCode FormJacobianLocal_UK(User user,DMDALocalInfo *info,DMDALocalInfo *infok,const PetscScalar u[],const PetscScalar k[],Mat Buk)
169: {
170:   PetscReal      hx = 1./info->mx;
172:   PetscInt       i;
173:   PetscInt       row,cols[2];
174:   PetscScalar    vals[2];

177:   if (!Buk) return(0); /* Not assembling this block */
178:   for (i=info->xs; i<info->xs+info->xm; i++) {
179:     if (i == 0 || i == info->mx-1) continue;
180:     row     = i-info->gxs;
181:     cols[0] = i-1-infok->gxs;  vals[0] = (u[i]-u[i-1])/hx;
182:     cols[1] = i-infok->gxs;    vals[1] = (u[i]-u[i+1])/hx;
183:     MatSetValuesLocal(Buk,1,&row,2,cols,vals,INSERT_VALUES);
184:   }
185:   return(0);
186: }

188: static PetscErrorCode FormJacobianLocal_KU(User user,DMDALocalInfo *info,DMDALocalInfo *infok,const PetscScalar u[],const PetscScalar k[],Mat Bku)
189: {
191:   PetscInt       i;
192:   PetscReal      hx = 1./(info->mx-1);

195:   if (!Bku) return(0); /* Not assembling this block */
196:   for (i=infok->xs; i<infok->xs+infok->xm; i++) {
197:     PetscInt    row = i-infok->gxs,cols[2];
198:     PetscScalar vals[2];
199:     const PetscScalar
200:       ubar     = 0.5*(u[i]+u[i+1]),
201:       ubar_L   = 0.5,
202:       ubar_R   = 0.5,
203:       gradu    = (u[i+1]-u[i])/hx,
204:       gradu_L  = -1./hx,
205:       gradu_R  = 1./hx,
206:       g        = 1. + PetscSqr(gradu),
207:       g_gradu  = 2.*gradu,
208:       w        = 1./(1.+ubar) + 1./g,
209:       w_ubar   = -1./PetscSqr(1.+ubar),
210:       w_gradu  = -g_gradu/PetscSqr(g),
211:       iw       = 1./w,
212:       iw_ubar  = -w_ubar * PetscSqr(iw),
213:       iw_gradu = -w_gradu * PetscSqr(iw);
214:     cols[0] = i-info->gxs;         vals[0] = -hx*(iw_ubar*ubar_L + iw_gradu*gradu_L);
215:     cols[1] = i+1-info->gxs;       vals[1] = -hx*(iw_ubar*ubar_R + iw_gradu*gradu_R);
216:     MatSetValuesLocal(Bku,1,&row,2,cols,vals,INSERT_VALUES);
217:   }
218:   return(0);
219: }

221: static PetscErrorCode FormJacobian_All(SNES snes,Vec X,Mat J,Mat B,void *ctx)
222: {
223:   User           user = (User)ctx;
224:   DM             dau,dak;
225:   DMDALocalInfo  infou,infok;
226:   PetscScalar    *u,*k;
228:   Vec            Uloc,Kloc;

231:   DMCompositeGetEntries(user->pack,&dau,&dak);
232:   DMDAGetLocalInfo(dau,&infou);
233:   DMDAGetLocalInfo(dak,&infok);
234:   DMCompositeGetLocalVectors(user->pack,&Uloc,&Kloc);
235:   switch (user->ptype) {
236:   case 0:
237:     DMGlobalToLocalBegin(dau,X,INSERT_VALUES,Uloc);
238:     DMGlobalToLocalEnd  (dau,X,INSERT_VALUES,Uloc);
239:     DMDAVecGetArray(dau,Uloc,&u);
240:     DMDAVecGetArray(dak,user->Kloc,&k);
241:     FormJacobianLocal_U(user,&infou,u,k,B);
242:     DMDAVecRestoreArray(dau,Uloc,&u);
243:     DMDAVecRestoreArray(dak,user->Kloc,&k);
244:     break;
245:   case 1:
246:     DMGlobalToLocalBegin(dak,X,INSERT_VALUES,Kloc);
247:     DMGlobalToLocalEnd  (dak,X,INSERT_VALUES,Kloc);
248:     DMDAVecGetArray(dau,user->Uloc,&u);
249:     DMDAVecGetArray(dak,Kloc,&k);
250:     FormJacobianLocal_K(user,&infok,u,k,B);
251:     DMDAVecRestoreArray(dau,user->Uloc,&u);
252:     DMDAVecRestoreArray(dak,Kloc,&k);
253:     break;
254:   case 2: {
255:     Mat       Buu,Buk,Bku,Bkk;
256:     PetscBool nest;
257:     IS        *is;
258:     DMCompositeScatter(user->pack,X,Uloc,Kloc);
259:     DMDAVecGetArray(dau,Uloc,&u);
260:     DMDAVecGetArray(dak,Kloc,&k);
261:     DMCompositeGetLocalISs(user->pack,&is);
262:     MatGetLocalSubMatrix(B,is[0],is[0],&Buu);
263:     MatGetLocalSubMatrix(B,is[0],is[1],&Buk);
264:     MatGetLocalSubMatrix(B,is[1],is[0],&Bku);
265:     MatGetLocalSubMatrix(B,is[1],is[1],&Bkk);
266:     FormJacobianLocal_U(user,&infou,u,k,Buu);
267:     PetscObjectTypeCompare((PetscObject)B,MATNEST,&nest);
268:     if (!nest) {
269:       /*
270:          DMCreateMatrix_Composite()  for a nested matrix does not generate off-block matrices that one can call MatSetValuesLocal() on, it just creates dummy
271:          matrices with no entries; there cannot insert values into them. Commit b6480e041dd2293a65f96222772d68cdb4ed6306
272:          changed Mat_Nest() from returning NULL pointers for these submatrices to dummy matrices because PCFIELDSPLIT could not
273:          handle the returned null matrices.
274:       */
275:       FormJacobianLocal_UK(user,&infou,&infok,u,k,Buk);
276:       FormJacobianLocal_KU(user,&infou,&infok,u,k,Bku);
277:     }
278:     FormJacobianLocal_K(user,&infok,u,k,Bkk);
279:     MatRestoreLocalSubMatrix(B,is[0],is[0],&Buu);
280:     MatRestoreLocalSubMatrix(B,is[0],is[1],&Buk);
281:     MatRestoreLocalSubMatrix(B,is[1],is[0],&Bku);
282:     MatRestoreLocalSubMatrix(B,is[1],is[1],&Bkk);
283:     DMDAVecRestoreArray(dau,Uloc,&u);
284:     DMDAVecRestoreArray(dak,Kloc,&k);

286:     ISDestroy(&is[0]);
287:     ISDestroy(&is[1]);
288:     PetscFree(is);
289:   } break;
290:   }
291:   DMCompositeRestoreLocalVectors(user->pack,&Uloc,&Kloc);
292:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
293:   MatAssemblyEnd  (B,MAT_FINAL_ASSEMBLY);
294:   if (J != B) {
295:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
296:     MatAssemblyEnd  (J,MAT_FINAL_ASSEMBLY);
297:   }
298:   return(0);
299: }

301: static PetscErrorCode FormInitial_Coupled(User user,Vec X)
302: {
304:   DM             dau,dak;
305:   DMDALocalInfo  infou,infok;
306:   Vec            Xu,Xk;
307:   PetscScalar    *u,*k,hx;
308:   PetscInt       i;

311:   DMCompositeGetEntries(user->pack,&dau,&dak);
312:   DMCompositeGetAccess(user->pack,X,&Xu,&Xk);
313:   DMDAVecGetArray(dau,Xu,&u);
314:   DMDAVecGetArray(dak,Xk,&k);
315:   DMDAGetLocalInfo(dau,&infou);
316:   DMDAGetLocalInfo(dak,&infok);
317:   hx   = 1./(infok.mx);
318:   for (i=infou.xs; i<infou.xs+infou.xm; i++) u[i] = (PetscScalar)i*hx * (1.-(PetscScalar)i*hx);
319:   for (i=infok.xs; i<infok.xs+infok.xm; i++) k[i] = 1.0 + 0.5*PetscSinScalar(2*PETSC_PI*i*hx);
320:   DMDAVecRestoreArray(dau,Xu,&u);
321:   DMDAVecRestoreArray(dak,Xk,&k);
322:   DMCompositeRestoreAccess(user->pack,X,&Xu,&Xk);
323:   DMCompositeScatter(user->pack,X,user->Uloc,user->Kloc);
324:   return(0);
325: }

327: int main(int argc, char *argv[])
328: {
330:   DM             dau,dak,pack;
331:   const PetscInt *lxu;
332:   PetscInt       *lxk,m,sizes;
333:   User           user;
334:   SNES           snes;
335:   Vec            X,F,Xu,Xk,Fu,Fk;
336:   Mat            B;
337:   IS             *isg;
338:   PetscBool      pass_dm;

340:   PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
341:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,10,1,1,NULL,&dau);
342:   DMSetOptionsPrefix(dau,"u_");
343:   DMSetFromOptions(dau);
344:   DMSetUp(dau);
345:   DMDAGetOwnershipRanges(dau,&lxu,0,0);
346:   DMDAGetInfo(dau,0, &m,0,0, &sizes,0,0, 0,0,0,0,0,0);
347:   PetscMalloc1(sizes,&lxk);
348:   PetscMemcpy(lxk,lxu,sizes*sizeof(*lxk));
349:   lxk[0]--;
350:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,m-1,1,1,lxk,&dak);
351:   DMSetOptionsPrefix(dak,"k_");
352:   DMSetFromOptions(dak);
353:   DMSetUp(dak);
354:   PetscFree(lxk);

356:   DMCompositeCreate(PETSC_COMM_WORLD,&pack);
357:   DMSetOptionsPrefix(pack,"pack_");
358:   DMCompositeAddDM(pack,dau);
359:   DMCompositeAddDM(pack,dak);
360:   DMDASetFieldName(dau,0,"u");
361:   DMDASetFieldName(dak,0,"k");
362:   DMSetFromOptions(pack);

364:   DMCreateGlobalVector(pack,&X);
365:   VecDuplicate(X,&F);

367:   PetscNew(&user);

369:   user->pack = pack;

371:   DMCompositeGetGlobalISs(pack,&isg);
372:   DMCompositeGetLocalVectors(pack,&user->Uloc,&user->Kloc);
373:   DMCompositeScatter(pack,X,user->Uloc,user->Kloc);

375:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Coupled problem options","SNES");
376:   {
377:     user->ptype = 0; pass_dm = PETSC_TRUE;

379:     PetscOptionsInt("-problem_type","0: solve for u only, 1: solve for k only, 2: solve for both",0,user->ptype,&user->ptype,NULL);
380:     PetscOptionsBool("-pass_dm","Pass the packed DM to SNES to use when determining splits and forward into splits",0,pass_dm,&pass_dm,NULL);
381:   }
382:   PetscOptionsEnd();

384:   FormInitial_Coupled(user,X);

386:   SNESCreate(PETSC_COMM_WORLD,&snes);
387:   switch (user->ptype) {
388:   case 0:
389:     DMCompositeGetAccess(pack,X,&Xu,0);
390:     DMCompositeGetAccess(pack,F,&Fu,0);
391:     DMCreateMatrix(dau,&B);
392:     SNESSetFunction(snes,Fu,FormFunction_All,user);
393:     SNESSetJacobian(snes,B,B,FormJacobian_All,user);
394:     SNESSetFromOptions(snes);
395:     SNESSetDM(snes,dau);
396:     SNESSolve(snes,NULL,Xu);
397:     DMCompositeRestoreAccess(pack,X,&Xu,0);
398:     DMCompositeRestoreAccess(pack,F,&Fu,0);
399:     break;
400:   case 1:
401:     DMCompositeGetAccess(pack,X,0,&Xk);
402:     DMCompositeGetAccess(pack,F,0,&Fk);
403:     DMCreateMatrix(dak,&B);
404:     SNESSetFunction(snes,Fk,FormFunction_All,user);
405:     SNESSetJacobian(snes,B,B,FormJacobian_All,user);
406:     SNESSetFromOptions(snes);
407:     SNESSetDM(snes,dak);
408:     SNESSolve(snes,NULL,Xk);
409:     DMCompositeRestoreAccess(pack,X,0,&Xk);
410:     DMCompositeRestoreAccess(pack,F,0,&Fk);
411:     break;
412:   case 2:
413:     DMCreateMatrix(pack,&B);
414:     /* This example does not correctly allocate off-diagonal blocks. These options allows new nonzeros (slow). */
415:     MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
416:     MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
417:     SNESSetFunction(snes,F,FormFunction_All,user);
418:     SNESSetJacobian(snes,B,B,FormJacobian_All,user);
419:     SNESSetFromOptions(snes);
420:     if (!pass_dm) {             /* Manually provide index sets and names for the splits */
421:       KSP ksp;
422:       PC  pc;
423:       SNESGetKSP(snes,&ksp);
424:       KSPGetPC(ksp,&pc);
425:       PCFieldSplitSetIS(pc,"u",isg[0]);
426:       PCFieldSplitSetIS(pc,"k",isg[1]);
427:     } else {
428:       /* The same names come from the options prefix for dau and dak. This option can support geometric multigrid inside
429:        * of splits, but it requires using a DM (perhaps your own implementation). */
430:       SNESSetDM(snes,pack);
431:     }
432:     SNESSolve(snes,NULL,X);
433:     break;
434:   }
435:   VecViewFromOptions(X,NULL,"-view_sol");

437:   if (0) {
438:     PetscInt  col      = 0;
439:     PetscBool mult_dup = PETSC_FALSE,view_dup = PETSC_FALSE;
440:     Mat       D;
441:     Vec       Y;

443:     PetscOptionsGetInt(NULL,0,"-col",&col,0);
444:     PetscOptionsGetBool(NULL,0,"-mult_dup",&mult_dup,0);
445:     PetscOptionsGetBool(NULL,0,"-view_dup",&view_dup,0);

447:     VecDuplicate(X,&Y);
448:     /* MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY); */
449:     /* MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY); */
450:     MatConvert(B,MATAIJ,MAT_INITIAL_MATRIX,&D);
451:     VecZeroEntries(X);
452:     VecSetValue(X,col,1.0,INSERT_VALUES);
453:     VecAssemblyBegin(X);
454:     VecAssemblyEnd(X);
455:     MatMult(mult_dup ? D : B,X,Y);
456:     MatView(view_dup ? D : B,PETSC_VIEWER_STDOUT_WORLD);
457:     /* VecView(X,PETSC_VIEWER_STDOUT_WORLD); */
458:     VecView(Y,PETSC_VIEWER_STDOUT_WORLD);
459:     MatDestroy(&D);
460:     VecDestroy(&Y);
461:   }

463:   DMCompositeRestoreLocalVectors(pack,&user->Uloc,&user->Kloc);
464:   PetscFree(user);

466:   ISDestroy(&isg[0]);
467:   ISDestroy(&isg[1]);
468:   PetscFree(isg);
469:   VecDestroy(&X);
470:   VecDestroy(&F);
471:   MatDestroy(&B);
472:   DMDestroy(&dau);
473:   DMDestroy(&dak);
474:   DMDestroy(&pack);
475:   SNESDestroy(&snes);
476:   PetscFinalize();
477:   return ierr;
478: }

480: /*TEST

482:    build:
483:       requires: c99

485:    test:
486:       suffix: 0
487:       nsize: 3
488:       args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 0

490:    test:
491:       suffix: 1
492:       nsize: 3
493:       args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 1

495:    test:
496:       suffix: 2
497:       nsize: 3
498:       args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 2

500:    test:
501:       suffix: 3
502:       nsize: 3
503:       args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -ksp_monitor_short -problem_type 2 -snes_mf_operator -pack_dm_mat_type {{aij nest}} -pc_type fieldsplit -pc_fieldsplit_dm_splits -pc_fieldsplit_type additive -fieldsplit_u_ksp_type gmres -fieldsplit_k_pc_type jacobi

505:    test:
506:       suffix: 4
507:       nsize: 6
508:       args: -u_da_grid_x 257 -snes_converged_reason -snes_monitor_short -ksp_monitor_short -problem_type 2 -snes_mf_operator -pack_dm_mat_type aij -pc_type fieldsplit -pc_fieldsplit_type multiplicative -fieldsplit_u_ksp_type gmres -fieldsplit_u_ksp_pc_side right -fieldsplit_u_pc_type mg -fieldsplit_u_pc_mg_levels 4 -fieldsplit_u_mg_levels_ksp_type richardson -fieldsplit_u_mg_levels_ksp_max_it 1 -fieldsplit_u_mg_levels_pc_type sor -fieldsplit_u_pc_mg_galerkin pmat -fieldsplit_u_ksp_converged_reason -fieldsplit_k_pc_type jacobi
509:       requires: !single

511:    test:
512:       suffix: glvis_composite_da_1d
513:       args: -u_da_grid_x 20 -problem_type 0 -snes_monitor_solution glvis:

515: TEST*/