Actual source code: ex14.c
petsc-3.12.4 2020-02-04
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      2: static char help[] = "Bratu nonlinear PDE in 3d.\n\
      3: We solve the  Bratu (SFI - solid fuel ignition) problem in a 3D rectangular\n\
      4: domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\
      5: The command line options include:\n\
      6:   -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
      7:      problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n";

      9: /*T
     10:    Concepts: SNES^parallel Bratu example
     11:    Concepts: DMDA^using distributed arrays;
     12:    Processors: n
     13: T*/

     17: /* ------------------------------------------------------------------------

     19:     Solid Fuel Ignition (SFI) problem.  This problem is modeled by
     20:     the partial differential equation

     22:             -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,

     24:     with boundary conditions

     26:              u = 0  for  x = 0, x = 1, y = 0, y = 1, z = 0, z = 1

     28:     A finite difference approximation with the usual 7-point stencil
     29:     is used to discretize the boundary value problem to obtain a nonlinear
     30:     system of equations.

     33:   ------------------------------------------------------------------------- */

     35: /*
     36:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     37:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     38:    file automatically includes:
     39:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     40:      petscmat.h - matrices
     41:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     42:      petscviewer.h - viewers               petscpc.h  - preconditioners
     43:      petscksp.h   - linear solvers
     44: */
     45:  #include <petscdm.h>
     46:  #include <petscdmda.h>
     47:  #include <petscsnes.h>

     50: /*
     51:    User-defined application context - contains data needed by the
     52:    application-provided call-back routines, FormJacobian() and
     53:    FormFunction().
     54: */
     55: typedef struct {
     56:   PetscReal param;             /* test problem parameter */
     57:   DM        da;                /* distributed array data structure */
     58: } AppCtx;

     60: /*
     61:    User-defined routines
     62: */
     63: extern PetscErrorCode FormFunctionLocal(SNES,Vec,Vec,void*);
     64: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
     65: extern PetscErrorCode FormInitialGuess(AppCtx*,Vec);
     66: extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);

     68: int main(int argc,char **argv)
     69: {
     70:   SNES           snes;                         /* nonlinear solver */
     71:   Vec            x,r;                          /* solution, residual vectors */
     72:   Mat            J = NULL;                            /* Jacobian matrix */
     73:   AppCtx         user;                         /* user-defined work context */
     74:   PetscInt       its;                          /* iterations for convergence */
     75:   MatFDColoring  matfdcoloring = NULL;
     76:   PetscBool      matrix_free = PETSC_FALSE,coloring = PETSC_FALSE, coloring_ds = PETSC_FALSE,local_coloring = PETSC_FALSE;
     78:   PetscReal      bratu_lambda_max = 6.81,bratu_lambda_min = 0.,fnorm;

     80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     81:      Initialize program
     82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     84:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:      Initialize problem parameters
     88:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     89:   user.param = 6.0;
     90:   PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);
     91:   if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) SETERRQ(PETSC_COMM_SELF,1,"Lambda is out of range");

     93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:      Create nonlinear solver context
     95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     96:   SNESCreate(PETSC_COMM_WORLD,&snes);

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:      Create distributed array (DMDA) to manage parallel grid and vectors
    100:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    101:   DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,4,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,NULL,&user.da);
    102:   DMSetFromOptions(user.da);
    103:   DMSetUp(user.da);
    104:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:      Extract global vectors from DMDA; then duplicate for remaining
    106:      vectors that are the same types
    107:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    108:   DMCreateGlobalVector(user.da,&x);
    109:   VecDuplicate(x,&r);

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:      Set function evaluation routine and vector
    113:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    114:   SNESSetFunction(snes,r,FormFunction,(void*)&user);

    116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    117:      Create matrix data structure; set Jacobian evaluation routine

    119:      Set Jacobian matrix data structure and default Jacobian evaluation
    120:      routine. User can override with:
    121:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
    122:                 (unless user explicitly sets preconditioner)
    123:      -snes_mf_operator : form preconditioning matrix as set by the user,
    124:                          but use matrix-free approx for Jacobian-vector
    125:                          products within Newton-Krylov method
    126:      -fdcoloring : using finite differences with coloring to compute the Jacobian

    128:      Note one can use -matfd_coloring wp or ds the only reason for the -fdcoloring_ds option
    129:      below is to test the call to MatFDColoringSetType().
    130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    131:   PetscOptionsGetBool(NULL,NULL,"-snes_mf",&matrix_free,NULL);
    132:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring",&coloring,NULL);
    133:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring_ds",&coloring_ds,NULL);
    134:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring_local",&local_coloring,NULL);
    135:   if (!matrix_free) {
    136:     DMSetMatType(user.da,MATAIJ);
    137:     DMCreateMatrix(user.da,&J);
    138:     if (coloring) {
    139:       ISColoring iscoloring;
    140:       if (!local_coloring) {
    141:         DMCreateColoring(user.da,IS_COLORING_GLOBAL,&iscoloring);
    142:         MatFDColoringCreate(J,iscoloring,&matfdcoloring);
    143:         MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
    144:       } else {
    145:         DMCreateColoring(user.da,IS_COLORING_LOCAL,&iscoloring);
    146:         MatFDColoringCreate(J,iscoloring,&matfdcoloring);
    147:         MatFDColoringUseDM(J,matfdcoloring);
    148:         MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunctionLocal,&user);
    149:       }
    150:       if (coloring_ds) {
    151:         MatFDColoringSetType(matfdcoloring,MATMFFD_DS);
    152:       }
    153:       MatFDColoringSetFromOptions(matfdcoloring);
    154:       MatFDColoringSetUp(J,iscoloring,matfdcoloring);
    155:       SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
    156:       ISColoringDestroy(&iscoloring);
    157:     } else {
    158:       SNESSetJacobian(snes,J,J,FormJacobian,&user);
    159:     }
    160:   }

    162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    163:      Customize nonlinear solver; set runtime options
    164:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    165:   SNESSetDM(snes,user.da);
    166:   SNESSetFromOptions(snes);

    168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169:      Evaluate initial guess
    170:      Note: The user should initialize the vector, x, with the initial guess
    171:      for the nonlinear solver prior to calling SNESSolve().  In particular,
    172:      to employ an initial guess of zero, the user should explicitly set
    173:      this vector to zero by calling VecSet().
    174:   */
    175:   FormInitialGuess(&user,x);

    177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    178:      Solve nonlinear system
    179:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    180:   SNESSolve(snes,NULL,x);
    181:   SNESGetIterationNumber(snes,&its);

    183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    184:      Explicitly check norm of the residual of the solution
    185:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    186:   FormFunction(snes,x,r,(void*)&user);
    187:   VecNorm(r,NORM_2,&fnorm);
    188:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D fnorm %g\n",its,(double)fnorm);

    190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    191:      Free work space.  All PETSc objects should be destroyed when they
    192:      are no longer needed.
    193:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    195:   MatDestroy(&J);
    196:   VecDestroy(&x);
    197:   VecDestroy(&r);
    198:   SNESDestroy(&snes);
    199:   DMDestroy(&user.da);
    200:   MatFDColoringDestroy(&matfdcoloring);
    201:   PetscFinalize();
    202:   return ierr;
    203: }
    204: /* ------------------------------------------------------------------- */
    205: /*
    206:    FormInitialGuess - Forms initial approximation.

    208:    Input Parameters:
    209:    user - user-defined application context
    210:    X - vector

    212:    Output Parameter:
    213:    X - vector
    214:  */
    215: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
    216: {
    217:   PetscInt       i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
    219:   PetscReal      lambda,temp1,hx,hy,hz,tempk,tempj;
    220:   PetscScalar    ***x;

    223:   DMDAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    225:   lambda = user->param;
    226:   hx     = 1.0/(PetscReal)(Mx-1);
    227:   hy     = 1.0/(PetscReal)(My-1);
    228:   hz     = 1.0/(PetscReal)(Mz-1);
    229:   temp1  = lambda/(lambda + 1.0);

    231:   /*
    232:      Get a pointer to vector data.
    233:        - For default PETSc vectors, VecGetArray() returns a pointer to
    234:          the data array.  Otherwise, the routine is implementation dependent.
    235:        - You MUST call VecRestoreArray() when you no longer need access to
    236:          the array.
    237:   */
    238:   DMDAVecGetArray(user->da,X,&x);

    240:   /*
    241:      Get local grid boundaries (for 3-dimensional DMDA):
    242:        xs, ys, zs   - starting grid indices (no ghost points)
    243:        xm, ym, zm   - widths of local grid (no ghost points)

    245:   */
    246:   DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);

    248:   /*
    249:      Compute initial guess over the locally owned part of the grid
    250:   */
    251:   for (k=zs; k<zs+zm; k++) {
    252:     tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
    253:     for (j=ys; j<ys+ym; j++) {
    254:       tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
    255:       for (i=xs; i<xs+xm; i++) {
    256:         if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
    257:           /* boundary conditions are all zero Dirichlet */
    258:           x[k][j][i] = 0.0;
    259:         } else {
    260:           x[k][j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
    261:         }
    262:       }
    263:     }
    264:   }

    266:   /*
    267:      Restore vector
    268:   */
    269:   DMDAVecRestoreArray(user->da,X,&x);
    270:   return(0);
    271: }
    272: /* ------------------------------------------------------------------- */
    273: /*
    274:    FormFunctionLocal - Evaluates nonlinear function, F(x) on a ghosted patch

    276:    Input Parameters:
    277: .  snes - the SNES context
    278: .  localX - input vector, this contains the ghosted region needed
    279: .  ptr - optional user-defined context, as set by SNESSetFunction()

    281:    Output Parameter:
    282: .  F - function vector, this does not contain a ghosted region
    283:  */
    284: PetscErrorCode FormFunctionLocal(SNES snes,Vec localX,Vec F,void *ptr)
    285: {
    286:   AppCtx         *user = (AppCtx*)ptr;
    288:   PetscInt       i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
    289:   PetscReal      two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
    290:   PetscScalar    u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
    291:   DM             da;

    294:   SNESGetDM(snes,&da);
    295:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    297:   lambda  = user->param;
    298:   hx      = 1.0/(PetscReal)(Mx-1);
    299:   hy      = 1.0/(PetscReal)(My-1);
    300:   hz      = 1.0/(PetscReal)(Mz-1);
    301:   sc      = hx*hy*hz*lambda;
    302:   hxhzdhy = hx*hz/hy;
    303:   hyhzdhx = hy*hz/hx;
    304:   hxhydhz = hx*hy/hz;

    306:   /*
    307:      Get pointers to vector data
    308:   */
    309:   DMDAVecGetArrayRead(da,localX,&x);
    310:   DMDAVecGetArray(da,F,&f);

    312:   /*
    313:      Get local grid boundaries
    314:   */
    315:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

    317:   /*
    318:      Compute function over the locally owned part of the grid
    319:   */
    320:   for (k=zs; k<zs+zm; k++) {
    321:     for (j=ys; j<ys+ym; j++) {
    322:       for (i=xs; i<xs+xm; i++) {
    323:         if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
    324:           f[k][j][i] = x[k][j][i];
    325:         } else {
    326:           u          = x[k][j][i];
    327:           u_east     = x[k][j][i+1];
    328:           u_west     = x[k][j][i-1];
    329:           u_north    = x[k][j+1][i];
    330:           u_south    = x[k][j-1][i];
    331:           u_up       = x[k+1][j][i];
    332:           u_down     = x[k-1][j][i];
    333:           u_xx       = (-u_east + two*u - u_west)*hyhzdhx;
    334:           u_yy       = (-u_north + two*u - u_south)*hxhzdhy;
    335:           u_zz       = (-u_up + two*u - u_down)*hxhydhz;
    336:           f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
    337:         }
    338:       }
    339:     }
    340:   }

    342:   /*
    343:      Restore vectors
    344:   */
    345:   DMDAVecRestoreArrayRead(da,localX,&x);
    346:   DMDAVecRestoreArray(da,F,&f);
    347:   PetscLogFlops(11.0*ym*xm);
    348:   return(0);
    349: }
    350: /* ------------------------------------------------------------------- */
    351: /*
    352:    FormFunction - Evaluates nonlinear function, F(x) on the entire domain

    354:    Input Parameters:
    355: .  snes - the SNES context
    356: .  X - input vector
    357: .  ptr - optional user-defined context, as set by SNESSetFunction()

    359:    Output Parameter:
    360: .  F - function vector
    361:  */
    362: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
    363: {
    365:   Vec            localX;
    366:   DM             da;

    369:   SNESGetDM(snes,&da);
    370:   DMGetLocalVector(da,&localX);

    372:   /*
    373:      Scatter ghost points to local vector,using the 2-step process
    374:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    375:      By placing code between these two statements, computations can be
    376:      done while messages are in transition.
    377:   */
    378:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    379:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    381:   FormFunctionLocal(snes,localX,F,ptr);
    382:   DMRestoreLocalVector(da,&localX);
    383:   return(0);
    384: }
    385: /* ------------------------------------------------------------------- */
    386: /*
    387:    FormJacobian - Evaluates Jacobian matrix.

    389:    Input Parameters:
    390: .  snes - the SNES context
    391: .  x - input vector
    392: .  ptr - optional user-defined context, as set by SNESSetJacobian()

    394:    Output Parameters:
    395: .  A - Jacobian matrix
    396: .  B - optionally different preconditioning matrix

    398: */
    399: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat jac,void *ptr)
    400: {
    401:   AppCtx         *user = (AppCtx*)ptr;  /* user-defined application context */
    402:   Vec            localX;
    404:   PetscInt       i,j,k,Mx,My,Mz;
    405:   MatStencil     col[7],row;
    406:   PetscInt       xs,ys,zs,xm,ym,zm;
    407:   PetscScalar    lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
    408:   DM             da;

    411:   SNESGetDM(snes,&da);
    412:   DMGetLocalVector(da,&localX);
    413:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    415:   lambda  = user->param;
    416:   hx      = 1.0/(PetscReal)(Mx-1);
    417:   hy      = 1.0/(PetscReal)(My-1);
    418:   hz      = 1.0/(PetscReal)(Mz-1);
    419:   sc      = hx*hy*hz*lambda;
    420:   hxhzdhy = hx*hz/hy;
    421:   hyhzdhx = hy*hz/hx;
    422:   hxhydhz = hx*hy/hz;

    424:   /*
    425:      Scatter ghost points to local vector, using the 2-step process
    426:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
    427:      By placing code between these two statements, computations can be
    428:      done while messages are in transition.
    429:   */
    430:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    431:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    433:   /*
    434:      Get pointer to vector data
    435:   */
    436:   DMDAVecGetArrayRead(da,localX,&x);

    438:   /*
    439:      Get local grid boundaries
    440:   */
    441:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

    443:   /*
    444:      Compute entries for the locally owned part of the Jacobian.
    445:       - Currently, all PETSc parallel matrix formats are partitioned by
    446:         contiguous chunks of rows across the processors.
    447:       - Each processor needs to insert only elements that it owns
    448:         locally (but any non-local elements will be sent to the
    449:         appropriate processor during matrix assembly).
    450:       - Here, we set all entries for a particular row at once.
    451:       - We can set matrix entries either using either
    452:         MatSetValuesLocal() or MatSetValues(), as discussed above.
    453:   */
    454:   for (k=zs; k<zs+zm; k++) {
    455:     for (j=ys; j<ys+ym; j++) {
    456:       for (i=xs; i<xs+xm; i++) {
    457:         row.k = k; row.j = j; row.i = i;
    458:         /* boundary points */
    459:         if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
    460:           v[0] = 1.0;
    461:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    462:         } else {
    463:           /* interior grid points */
    464:           v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j;  col[0].i = i;
    465:           v[1] = -hxhzdhy; col[1].k=k;  col[1].j=j-1;col[1].i = i;
    466:           v[2] = -hyhzdhx; col[2].k=k;  col[2].j=j;  col[2].i = i-1;
    467:           v[3] = 2.0*(hyhzdhx+hxhzdhy+hxhydhz)-sc*PetscExpScalar(x[k][j][i]);col[3].k=row.k;col[3].j=row.j;col[3].i = row.i;
    468:           v[4] = -hyhzdhx; col[4].k=k;  col[4].j=j;  col[4].i = i+1;
    469:           v[5] = -hxhzdhy; col[5].k=k;  col[5].j=j+1;col[5].i = i;
    470:           v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j;  col[6].i = i;
    471:           MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
    472:         }
    473:       }
    474:     }
    475:   }
    476:   DMDAVecRestoreArrayRead(da,localX,&x);
    477:   DMRestoreLocalVector(da,&localX);

    479:   /*
    480:      Assemble matrix, using the 2-step process:
    481:        MatAssemblyBegin(), MatAssemblyEnd().
    482:   */
    483:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    484:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

    486:   /*
    487:      Normally since the matrix has already been assembled above; this
    488:      would do nothing. But in the matrix free mode -snes_mf_operator
    489:      this tells the "matrix-free" matrix that a new linear system solve
    490:      is about to be done.
    491:   */

    493:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    494:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);

    496:   /*
    497:      Tell the matrix we will never add a new nonzero location to the
    498:      matrix. If we do, it will generate an error.
    499:   */
    500:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    501:   return(0);
    502: }

    506: /*TEST

    508:    test:
    509:       nsize: 4
    510:       args: -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    512:    test:
    513:       suffix: 2
    514:       nsize: 4
    515:       args: -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    517:    test:
    518:       suffix: 3
    519:       nsize: 4
    520:       args: -fdcoloring -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    522:    test:
    523:       suffix: 3_ds
    524:       nsize: 4
    525:       args: -fdcoloring -fdcoloring_ds -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    527:    test:
    528:       suffix: 4
    529:       nsize: 4
    530:       args: -fdcoloring_local -fdcoloring -ksp_monitor_short -da_refine 1
    531:       requires: !single

    533: TEST*/