Date: 2022-08-02T03:14:55+00:00

Actual source code: ex14.c

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

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

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

     16:     with boundary conditions

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

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

     24:   ------------------------------------------------------------------------- */

     26: /*
     27:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     28:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     29:    file automatically includes:
     30:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     31:      petscmat.h - matrices
     32:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     33:      petscviewer.h - viewers               petscpc.h  - preconditioners
     34:      petscksp.h   - linear solvers
     35: */
     36: #include <petscdm.h>
     37: #include <petscdmda.h>
     38: #include <petscsnes.h>

     40: /*
     41:    User-defined application context - contains data needed by the
     42:    application-provided call-back routines, FormJacobian() and
     43:    FormFunction().
     44: */
     45: typedef struct {
     46:   PetscReal param;             /* test problem parameter */
     47:   DM        da;                /* distributed array data structure */
     48: } AppCtx;

     50: /*
     51:    User-defined routines
     52: */
     53: extern PetscErrorCode FormFunctionLocal(SNES,Vec,Vec,void*);
     54: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
     55: extern PetscErrorCode FormInitialGuess(AppCtx*,Vec);
     56: extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);

     58: int main(int argc,char **argv)
     59: {
     60:   SNES           snes;                         /* nonlinear solver */
     61:   Vec            x,r;                          /* solution, residual vectors */
     62:   Mat            J = NULL;                            /* Jacobian matrix */
     63:   AppCtx         user;                         /* user-defined work context */
     64:   PetscInt       its;                          /* iterations for convergence */
     65:   MatFDColoring  matfdcoloring = NULL;
     66:   PetscBool      matrix_free = PETSC_FALSE,coloring = PETSC_FALSE, coloring_ds = PETSC_FALSE,local_coloring = PETSC_FALSE;
     67:   PetscReal      bratu_lambda_max = 6.81,bratu_lambda_min = 0.,fnorm;

     69:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     70:      Initialize program
     71:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     73:   PetscInitialize(&argc,&argv,(char*)0,help);

     75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76:      Initialize problem parameters
     77:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     78:   user.param = 6.0;
     79:   PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);

     82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     83:      Create nonlinear solver context
     84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     85:   SNESCreate(PETSC_COMM_WORLD,&snes);

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:      Create distributed array (DMDA) to manage parallel grid and vectors
     89:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     90:   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);
     91:   DMSetFromOptions(user.da);
     92:   DMSetUp(user.da);
     93:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:      Extract global vectors from DMDA; then duplicate for remaining
     95:      vectors that are the same types
     96:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     97:   DMCreateGlobalVector(user.da,&x);
     98:   VecDuplicate(x,&r);

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:      Set function evaluation routine and vector
    102:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    103:   SNESSetFunction(snes,r,FormFunction,(void*)&user);

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:      Create matrix data structure; set Jacobian evaluation routine

    108:      Set Jacobian matrix data structure and default Jacobian evaluation
    109:      routine. User can override with:
    110:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
    111:                 (unless user explicitly sets preconditioner)
    112:      -snes_mf_operator : form preconditioning matrix as set by the user,
    113:                          but use matrix-free approx for Jacobian-vector
    114:                          products within Newton-Krylov method
    115:      -fdcoloring : using finite differences with coloring to compute the Jacobian

    117:      Note one can use -matfd_coloring wp or ds the only reason for the -fdcoloring_ds option
    118:      below is to test the call to MatFDColoringSetType().
    119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    120:   PetscOptionsGetBool(NULL,NULL,"-snes_mf",&matrix_free,NULL);
    121:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring",&coloring,NULL);
    122:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring_ds",&coloring_ds,NULL);
    123:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring_local",&local_coloring,NULL);
    124:   if (!matrix_free) {
    125:     DMSetMatType(user.da,MATAIJ);
    126:     DMCreateMatrix(user.da,&J);
    127:     if (coloring) {
    128:       ISColoring iscoloring;
    129:       if (!local_coloring) {
    130:         DMCreateColoring(user.da,IS_COLORING_GLOBAL,&iscoloring);
    131:         MatFDColoringCreate(J,iscoloring,&matfdcoloring);
    132:         MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
    133:       } else {
    134:         DMCreateColoring(user.da,IS_COLORING_LOCAL,&iscoloring);
    135:         MatFDColoringCreate(J,iscoloring,&matfdcoloring);
    136:         MatFDColoringUseDM(J,matfdcoloring);
    137:         MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunctionLocal,&user);
    138:       }
    139:       if (coloring_ds) {
    140:         MatFDColoringSetType(matfdcoloring,MATMFFD_DS);
    141:       }
    142:       MatFDColoringSetFromOptions(matfdcoloring);
    143:       MatFDColoringSetUp(J,iscoloring,matfdcoloring);
    144:       SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
    145:       ISColoringDestroy(&iscoloring);
    146:     } else {
    147:       SNESSetJacobian(snes,J,J,FormJacobian,&user);
    148:     }
    149:   }

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:      Customize nonlinear solver; set runtime options
    153:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    154:   SNESSetDM(snes,user.da);
    155:   SNESSetFromOptions(snes);

    157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158:      Evaluate initial guess
    159:      Note: The user should initialize the vector, x, with the initial guess
    160:      for the nonlinear solver prior to calling SNESSolve().  In particular,
    161:      to employ an initial guess of zero, the user should explicitly set
    162:      this vector to zero by calling VecSet().
    163:   */
    164:   FormInitialGuess(&user,x);

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:      Solve nonlinear system
    168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    169:   SNESSolve(snes,NULL,x);
    170:   SNESGetIterationNumber(snes,&its);

    172:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    173:      Explicitly check norm of the residual of the solution
    174:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    175:   FormFunction(snes,x,r,(void*)&user);
    176:   VecNorm(r,NORM_2,&fnorm);
    177:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D fnorm %g\n",its,(double)fnorm);

    179:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    180:      Free work space.  All PETSc objects should be destroyed when they
    181:      are no longer needed.
    182:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    184:   MatDestroy(&J);
    185:   VecDestroy(&x);
    186:   VecDestroy(&r);
    187:   SNESDestroy(&snes);
    188:   DMDestroy(&user.da);
    189:   MatFDColoringDestroy(&matfdcoloring);
    190:   PetscFinalize();
    191:   return 0;
    192: }
    193: /* ------------------------------------------------------------------- */
    194: /*
    195:    FormInitialGuess - Forms initial approximation.

    197:    Input Parameters:
    198:    user - user-defined application context
    199:    X - vector

    201:    Output Parameter:
    202:    X - vector
    203:  */
    204: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
    205: {
    206:   PetscInt       i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
    207:   PetscReal      lambda,temp1,hx,hy,hz,tempk,tempj;
    208:   PetscScalar    ***x;

    211:   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);

    213:   lambda = user->param;
    214:   hx     = 1.0/(PetscReal)(Mx-1);
    215:   hy     = 1.0/(PetscReal)(My-1);
    216:   hz     = 1.0/(PetscReal)(Mz-1);
    217:   temp1  = lambda/(lambda + 1.0);

    219:   /*
    220:      Get a pointer to vector data.
    221:        - For default PETSc vectors, VecGetArray() returns a pointer to
    222:          the data array.  Otherwise, the routine is implementation dependent.
    223:        - You MUST call VecRestoreArray() when you no longer need access to
    224:          the array.
    225:   */
    226:   DMDAVecGetArray(user->da,X,&x);

    228:   /*
    229:      Get local grid boundaries (for 3-dimensional DMDA):
    230:        xs, ys, zs   - starting grid indices (no ghost points)
    231:        xm, ym, zm   - widths of local grid (no ghost points)

    233:   */
    234:   DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);

    236:   /*
    237:      Compute initial guess over the locally owned part of the grid
    238:   */
    239:   for (k=zs; k<zs+zm; k++) {
    240:     tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
    241:     for (j=ys; j<ys+ym; j++) {
    242:       tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
    243:       for (i=xs; i<xs+xm; i++) {
    244:         if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
    245:           /* boundary conditions are all zero Dirichlet */
    246:           x[k][j][i] = 0.0;
    247:         } else {
    248:           x[k][j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
    249:         }
    250:       }
    251:     }
    252:   }

    254:   /*
    255:      Restore vector
    256:   */
    257:   DMDAVecRestoreArray(user->da,X,&x);
    258:   return 0;
    259: }
    260: /* ------------------------------------------------------------------- */
    261: /*
    262:    FormFunctionLocal - Evaluates nonlinear function, F(x) on a ghosted patch

    264:    Input Parameters:
    265: .  snes - the SNES context
    266: .  localX - input vector, this contains the ghosted region needed
    267: .  ptr - optional user-defined context, as set by SNESSetFunction()

    269:    Output Parameter:
    270: .  F - function vector, this does not contain a ghosted region
    271:  */
    272: PetscErrorCode FormFunctionLocal(SNES snes,Vec localX,Vec F,void *ptr)
    273: {
    274:   AppCtx         *user = (AppCtx*)ptr;
    275:   PetscInt       i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
    276:   PetscReal      two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
    277:   PetscScalar    u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
    278:   DM             da;

    281:   SNESGetDM(snes,&da);
    282:   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);

    284:   lambda  = user->param;
    285:   hx      = 1.0/(PetscReal)(Mx-1);
    286:   hy      = 1.0/(PetscReal)(My-1);
    287:   hz      = 1.0/(PetscReal)(Mz-1);
    288:   sc      = hx*hy*hz*lambda;
    289:   hxhzdhy = hx*hz/hy;
    290:   hyhzdhx = hy*hz/hx;
    291:   hxhydhz = hx*hy/hz;

    293:   /*
    294:      Get pointers to vector data
    295:   */
    296:   DMDAVecGetArrayRead(da,localX,&x);
    297:   DMDAVecGetArray(da,F,&f);

    299:   /*
    300:      Get local grid boundaries
    301:   */
    302:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

    304:   /*
    305:      Compute function over the locally owned part of the grid
    306:   */
    307:   for (k=zs; k<zs+zm; k++) {
    308:     for (j=ys; j<ys+ym; j++) {
    309:       for (i=xs; i<xs+xm; i++) {
    310:         if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
    311:           f[k][j][i] = x[k][j][i];
    312:         } else {
    313:           u          = x[k][j][i];
    314:           u_east     = x[k][j][i+1];
    315:           u_west     = x[k][j][i-1];
    316:           u_north    = x[k][j+1][i];
    317:           u_south    = x[k][j-1][i];
    318:           u_up       = x[k+1][j][i];
    319:           u_down     = x[k-1][j][i];
    320:           u_xx       = (-u_east + two*u - u_west)*hyhzdhx;
    321:           u_yy       = (-u_north + two*u - u_south)*hxhzdhy;
    322:           u_zz       = (-u_up + two*u - u_down)*hxhydhz;
    323:           f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
    324:         }
    325:       }
    326:     }
    327:   }

    329:   /*
    330:      Restore vectors
    331:   */
    332:   DMDAVecRestoreArrayRead(da,localX,&x);
    333:   DMDAVecRestoreArray(da,F,&f);
    334:   PetscLogFlops(11.0*ym*xm);
    335:   return 0;
    336: }
    337: /* ------------------------------------------------------------------- */
    338: /*
    339:    FormFunction - Evaluates nonlinear function, F(x) on the entire domain

    341:    Input Parameters:
    342: .  snes - the SNES context
    343: .  X - input vector
    344: .  ptr - optional user-defined context, as set by SNESSetFunction()

    346:    Output Parameter:
    347: .  F - function vector
    348:  */
    349: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
    350: {
    351:   Vec            localX;
    352:   DM             da;

    355:   SNESGetDM(snes,&da);
    356:   DMGetLocalVector(da,&localX);

    358:   /*
    359:      Scatter ghost points to local vector,using the 2-step process
    360:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    361:      By placing code between these two statements, computations can be
    362:      done while messages are in transition.
    363:   */
    364:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    365:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    367:   FormFunctionLocal(snes,localX,F,ptr);
    368:   DMRestoreLocalVector(da,&localX);
    369:   return 0;
    370: }
    371: /* ------------------------------------------------------------------- */
    372: /*
    373:    FormJacobian - Evaluates Jacobian matrix.

    375:    Input Parameters:
    376: .  snes - the SNES context
    377: .  x - input vector
    378: .  ptr - optional user-defined context, as set by SNESSetJacobian()

    380:    Output Parameters:
    381: .  A - Jacobian matrix
    382: .  B - optionally different preconditioning matrix

    384: */
    385: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat jac,void *ptr)
    386: {
    387:   AppCtx         *user = (AppCtx*)ptr;  /* user-defined application context */
    388:   Vec            localX;
    389:   PetscInt       i,j,k,Mx,My,Mz;
    390:   MatStencil     col[7],row;
    391:   PetscInt       xs,ys,zs,xm,ym,zm;
    392:   PetscScalar    lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
    393:   DM             da;

    396:   SNESGetDM(snes,&da);
    397:   DMGetLocalVector(da,&localX);
    398:   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);

    400:   lambda  = user->param;
    401:   hx      = 1.0/(PetscReal)(Mx-1);
    402:   hy      = 1.0/(PetscReal)(My-1);
    403:   hz      = 1.0/(PetscReal)(Mz-1);
    404:   sc      = hx*hy*hz*lambda;
    405:   hxhzdhy = hx*hz/hy;
    406:   hyhzdhx = hy*hz/hx;
    407:   hxhydhz = hx*hy/hz;

    409:   /*
    410:      Scatter ghost points to local vector, using the 2-step process
    411:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
    412:      By placing code between these two statements, computations can be
    413:      done while messages are in transition.
    414:   */
    415:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    416:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    418:   /*
    419:      Get pointer to vector data
    420:   */
    421:   DMDAVecGetArrayRead(da,localX,&x);

    423:   /*
    424:      Get local grid boundaries
    425:   */
    426:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

    428:   /*
    429:      Compute entries for the locally owned part of the Jacobian.
    430:       - Currently, all PETSc parallel matrix formats are partitioned by
    431:         contiguous chunks of rows across the processors.
    432:       - Each processor needs to insert only elements that it owns
    433:         locally (but any non-local elements will be sent to the
    434:         appropriate processor during matrix assembly).
    435:       - Here, we set all entries for a particular row at once.
    436:       - We can set matrix entries either using either
    437:         MatSetValuesLocal() or MatSetValues(), as discussed above.
    438:   */
    439:   for (k=zs; k<zs+zm; k++) {
    440:     for (j=ys; j<ys+ym; j++) {
    441:       for (i=xs; i<xs+xm; i++) {
    442:         row.k = k; row.j = j; row.i = i;
    443:         /* boundary points */
    444:         if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
    445:           v[0] = 1.0;
    446:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    447:         } else {
    448:           /* interior grid points */
    449:           v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j;  col[0].i = i;
    450:           v[1] = -hxhzdhy; col[1].k=k;  col[1].j=j-1;col[1].i = i;
    451:           v[2] = -hyhzdhx; col[2].k=k;  col[2].j=j;  col[2].i = i-1;
    452:           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;
    453:           v[4] = -hyhzdhx; col[4].k=k;  col[4].j=j;  col[4].i = i+1;
    454:           v[5] = -hxhzdhy; col[5].k=k;  col[5].j=j+1;col[5].i = i;
    455:           v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j;  col[6].i = i;
    456:           MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
    457:         }
    458:       }
    459:     }
    460:   }
    461:   DMDAVecRestoreArrayRead(da,localX,&x);
    462:   DMRestoreLocalVector(da,&localX);

    464:   /*
    465:      Assemble matrix, using the 2-step process:
    466:        MatAssemblyBegin(), MatAssemblyEnd().
    467:   */
    468:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    469:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

    471:   /*
    472:      Normally since the matrix has already been assembled above; this
    473:      would do nothing. But in the matrix free mode -snes_mf_operator
    474:      this tells the "matrix-free" matrix that a new linear system solve
    475:      is about to be done.
    476:   */

    478:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    479:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);

    481:   /*
    482:      Tell the matrix we will never add a new nonzero location to the
    483:      matrix. If we do, it will generate an error.
    484:   */
    485:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    486:   return 0;
    487: }

    489: /*TEST

    491:    test:
    492:       nsize: 4
    493:       args: -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    495:    test:
    496:       suffix: 2
    497:       nsize: 4
    498:       args: -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    500:    test:
    501:       suffix: 3
    502:       nsize: 4
    503:       args: -fdcoloring -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    505:    test:
    506:       suffix: 3_ds
    507:       nsize: 4
    508:       args: -fdcoloring -fdcoloring_ds -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    510:    test:
    511:       suffix: 4
    512:       nsize: 4
    513:       args: -fdcoloring_local -fdcoloring -ksp_monitor_short -da_refine 1
    514:       requires: !single

    516:    test:
    517:       suffix: 5
    518:       nsize: 4
    519:       args: -fdcoloring_local -fdcoloring -ksp_monitor_short -da_refine 1 -snes_type newtontrdc
    520:       requires: !single

    522: TEST*/