Actual source code: ex12.c

      1: static char help[] = "Poisson Problem in 2d and 3d with simplicial finite elements.\n\
      2: We solve the Poisson problem in a rectangular\n\
      3: domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\
      4: This example supports discretized auxiliary fields (conductivity) as well as\n\
      5: multilevel nonlinear solvers.\n\n\n";

      7: /*
      8: A visualization of the adaptation can be accomplished using:

     10:   -dm_adapt_view hdf5:$PWD/adapt.h5 -sol_adapt_view hdf5:$PWD/adapt.h5::append -dm_adapt_pre_view hdf5:$PWD/orig.h5 -sol_adapt_pre_view hdf5:$PWD/orig.h5::append

     12: Information on refinement:

     14:    -info :~sys,vec,is,mat,ksp,snes,ts
     15: */

     17: #include <petscdmplex.h>
     18: #include <petscdmadaptor.h>
     19: #include <petscsnes.h>
     20: #include <petscds.h>
     21: #include <petscviewerhdf5.h>

     23: typedef enum {NEUMANN, DIRICHLET, NONE} BCType;
     24: typedef enum {RUN_FULL, RUN_EXACT, RUN_TEST, RUN_PERF} RunType;
     25: typedef enum {COEFF_NONE, COEFF_ANALYTIC, COEFF_FIELD, COEFF_NONLINEAR, COEFF_BALL, COEFF_CROSS, COEFF_CHECKERBOARD_0, COEFF_CHECKERBOARD_1} CoeffType;

     27: typedef struct {
     28:   RunType        runType;           /* Whether to run tests, or solve the full problem */
     29:   PetscBool      jacobianMF;        /* Whether to calculate the Jacobian action on the fly */
     30:   PetscBool      showInitial, showSolution, restart, quiet, nonzInit;
     31:   /* Problem definition */
     32:   BCType         bcType;
     33:   CoeffType      variableCoefficient;
     34:   PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx);
     35:   PetscBool      fieldBC;
     36:   void           (**exactFields)(PetscInt, PetscInt, PetscInt,
     37:                                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
     38:                                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
     39:                                  PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]);
     40:   PetscBool      bdIntegral;        /* Compute the integral of the solution on the boundary */
     41:   /* Reproducing tests from SISC 40(3), pp. A1473-A1493, 2018 */
     42:   PetscInt       div;               /* Number of divisions */
     43:   PetscInt       k;                 /* Parameter for checkerboard coefficient */
     44:   PetscInt      *kgrid;             /* Random parameter grid */
     45:   PetscBool      rand;              /* Make random assignments */
     46:   /* Solver */
     47:   PC             pcmg;              /* This is needed for error monitoring */
     48:   PetscBool      checkksp;          /* Whether to check the KSPSolve for runType == RUN_TEST */
     49: } AppCtx;

     51: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
     52: {
     53:   u[0] = 0.0;
     54:   return 0;
     55: }

     57: static PetscErrorCode ecks(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
     58: {
     59:   u[0] = x[0];
     60:   return 0;
     61: }

     63: /*
     64:   In 2D for Dirichlet conditions, we use exact solution:

     66:     u = x^2 + y^2
     67:     f = 4

     69:   so that

     71:     -\Delta u + f = -4 + 4 = 0

     73:   For Neumann conditions, we have

     75:     -\nabla u \cdot -\hat y |_{y=0} =  (2y)|_{y=0} =  0 (bottom)
     76:     -\nabla u \cdot  \hat y |_{y=1} = -(2y)|_{y=1} = -2 (top)
     77:     -\nabla u \cdot -\hat x |_{x=0} =  (2x)|_{x=0} =  0 (left)
     78:     -\nabla u \cdot  \hat x |_{x=1} = -(2x)|_{x=1} = -2 (right)

     80:   Which we can express as

     82:     \nabla u \cdot  \hat n|_\Gamma = {2 x, 2 y} \cdot \hat n = 2 (x + y)

     84:   The boundary integral of this solution is (assuming we are not orienting the edges)

     86:     \int^1_0 x^2 dx + \int^1_0 (1 + y^2) dy + \int^1_0 (x^2 + 1) dx + \int^1_0 y^2 dy = 1/3 + 4/3 + 4/3 + 1/3 = 3 1/3
     87: */
     88: static PetscErrorCode quadratic_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
     89: {
     90:   *u = x[0]*x[0] + x[1]*x[1];
     91:   return 0;
     92: }

     94: static void quadratic_u_field_2d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
     95:                                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
     96:                                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
     97:                                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
     98: {
     99:   uexact[0] = a[0];
    100: }

    102: static PetscErrorCode ball_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    103: {
    104:   const PetscReal alpha   = 500.;
    105:   const PetscReal radius2 = PetscSqr(0.15);
    106:   const PetscReal r2      = PetscSqr(x[0] - 0.5) + PetscSqr(x[1] - 0.5);
    107:   const PetscReal xi      = alpha*(radius2 - r2);

    109:   *u = PetscTanhScalar(xi) + 1.0;
    110:   return 0;
    111: }

    113: static PetscErrorCode cross_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    114: {
    115:   const PetscReal alpha = 50*4;
    116:   const PetscReal xy    = (x[0]-0.5)*(x[1]-0.5);

    118:   *u = PetscSinReal(alpha*xy) * (alpha*PetscAbsReal(xy) < 2*PETSC_PI ? 1 : 0.01);
    119:   return 0;
    120: }

    122: static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    123:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    124:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    125:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    126: {
    127:   f0[0] = 4.0;
    128: }

    130: static void f0_ball_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    131:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    132:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    133:                       PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    134: {
    135:   PetscInt        d;
    136:   const PetscReal alpha = 500., radius2 = PetscSqr(0.15);
    137:   PetscReal       r2, xi;

    139:   for (d = 0, r2 = 0.0; d < dim; ++d) r2 += PetscSqr(x[d] - 0.5);
    140:   xi = alpha*(radius2 - r2);
    141:   f0[0] = (-2.0*dim*alpha - 8.0*PetscSqr(alpha)*r2*PetscTanhReal(xi)) * PetscSqr(1.0/PetscCoshReal(xi));
    142: }

    144: static void f0_cross_u_2d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    145:                           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    146:                           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    147:                           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    148: {
    149:   const PetscReal alpha = 50*4;
    150:   const PetscReal xy    = (x[0]-0.5)*(x[1]-0.5);

    152:   f0[0] = PetscSinReal(alpha*xy) * (alpha*PetscAbsReal(xy) < 2*PETSC_PI ? 1 : 0.01);
    153: }

    155: static void f0_checkerboard_0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    156:                                 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    157:                                 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    158:                                 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    159: {
    160:   f0[0] = -20.0*PetscExpReal(-(PetscSqr(x[0] - 0.5) + PetscSqr(x[1] - 0.5)));
    161: }

    163: static void f0_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    164:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    165:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    166:                     PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    167: {
    168:   PetscInt d;
    169:   for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += -n[d]*2.0*x[d];
    170: }

    172: /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
    173: static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    174:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    175:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    176:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
    177: {
    178:   PetscInt d;
    179:   for (d = 0; d < dim; ++d) f1[d] = u_x[d];
    180: }

    182: /* < \nabla v, \nabla u + {\nabla u}^T >
    183:    This just gives \nabla u, give the perdiagonal for the transpose */
    184: static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    185:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    186:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    187:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
    188: {
    189:   PetscInt d;
    190:   for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0;
    191: }

    193: /*
    194:   In 2D for x periodicity and y Dirichlet conditions, we use exact solution:

    196:     u = sin(2 pi x)
    197:     f = -4 pi^2 sin(2 pi x)

    199:   so that

    201:     -\Delta u + f = 4 pi^2 sin(2 pi x) - 4 pi^2 sin(2 pi x) = 0
    202: */
    203: static PetscErrorCode xtrig_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    204: {
    205:   *u = PetscSinReal(2.0*PETSC_PI*x[0]);
    206:   return 0;
    207: }

    209: static void f0_xtrig_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    210:                        const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    211:                        const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    212:                        PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    213: {
    214:   f0[0] = -4.0*PetscSqr(PETSC_PI)*PetscSinReal(2.0*PETSC_PI*x[0]);
    215: }

    217: /*
    218:   In 2D for x-y periodicity, we use exact solution:

    220:     u = sin(2 pi x) sin(2 pi y)
    221:     f = -8 pi^2 sin(2 pi x)

    223:   so that

    225:     -\Delta u + f = 4 pi^2 sin(2 pi x) sin(2 pi y) + 4 pi^2 sin(2 pi x) sin(2 pi y) - 8 pi^2 sin(2 pi x) = 0
    226: */
    227: static PetscErrorCode xytrig_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    228: {
    229:   *u = PetscSinReal(2.0*PETSC_PI*x[0])*PetscSinReal(2.0*PETSC_PI*x[1]);
    230:   return 0;
    231: }

    233: static void f0_xytrig_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    234:                         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    235:                         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    236:                         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    237: {
    238:   f0[0] = -8.0*PetscSqr(PETSC_PI)*PetscSinReal(2.0*PETSC_PI*x[0]);
    239: }

    241: /*
    242:   In 2D for Dirichlet conditions with a variable coefficient, we use exact solution:

    244:     u  = x^2 + y^2
    245:     f  = 6 (x + y)
    246:     nu = (x + y)

    248:   so that

    250:     -\div \nu \grad u + f = -6 (x + y) + 6 (x + y) = 0
    251: */
    252: static PetscErrorCode nu_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    253: {
    254:   *u = x[0] + x[1];
    255:   return 0;
    256: }

    258: static PetscErrorCode checkerboardCoeff(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    259: {
    260:   AppCtx  *user = (AppCtx *) ctx;
    261:   PetscInt div  = user->div;
    262:   PetscInt k    = user->k;
    263:   PetscInt mask = 0, ind = 0, d;

    266:   for (d = 0; d < dim; ++d) mask = (mask + (PetscInt) (x[d]*div)) % 2;
    267:   if (user->kgrid) {
    268:     for (d = 0; d < dim; ++d) {
    269:       if (d > 0) ind *= dim;
    270:       ind += (PetscInt) (x[d]*div);
    271:     }
    272:     k = user->kgrid[ind];
    273:   }
    274:   u[0] = mask ? 1.0 : PetscPowRealInt(10.0, -k);
    275:   return 0;
    276: }

    278: void f0_analytic_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    279:                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    280:                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    281:                    PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    282: {
    283:   f0[0] = 6.0*(x[0] + x[1]);
    284: }

    286: /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
    287: void f1_analytic_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    288:                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    289:                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    290:                    PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
    291: {
    292:   PetscInt d;
    293:   for (d = 0; d < dim; ++d) f1[d] = (x[0] + x[1])*u_x[d];
    294: }

    296: void f1_field_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    297:                 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    298:                 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    299:                 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
    300: {
    301:   PetscInt d;
    302:   for (d = 0; d < dim; ++d) f1[d] = a[0]*u_x[d];
    303: }

    305: /* < \nabla v, \nabla u + {\nabla u}^T >
    306:    This just gives \nabla u, give the perdiagonal for the transpose */
    307: void g3_analytic_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    308:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    309:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    310:                     PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
    311: {
    312:   PetscInt d;
    313:   for (d = 0; d < dim; ++d) g3[d*dim+d] = x[0] + x[1];
    314: }

    316: void g3_field_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    317:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    318:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    319:                  PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
    320: {
    321:   PetscInt d;
    322:   for (d = 0; d < dim; ++d) g3[d*dim+d] = a[0];
    323: }

    325: /*
    326:   In 2D for Dirichlet conditions with a nonlinear coefficient (p-Laplacian with p = 4), we use exact solution:

    328:     u  = x^2 + y^2
    329:     f  = 16 (x^2 + y^2)
    330:     nu = 1/2 |grad u|^2

    332:   so that

    334:     -\div \nu \grad u + f = -16 (x^2 + y^2) + 16 (x^2 + y^2) = 0
    335: */
    336: void f0_analytic_nonlinear_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    337:                              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    338:                              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    339:                              PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    340: {
    341:   f0[0] = 16.0*(x[0]*x[0] + x[1]*x[1]);
    342: }

    344: /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
    345: void f1_analytic_nonlinear_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    346:                              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    347:                              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    348:                              PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
    349: {
    350:   PetscScalar nu = 0.0;
    351:   PetscInt    d;
    352:   for (d = 0; d < dim; ++d) nu += u_x[d]*u_x[d];
    353:   for (d = 0; d < dim; ++d) f1[d] = 0.5*nu*u_x[d];
    354: }

    356: /*
    357:   grad (u + eps w) - grad u = eps grad w

    359:   1/2 |grad (u + eps w)|^2 grad (u + eps w) - 1/2 |grad u|^2 grad u
    360: = 1/2 (|grad u|^2 + 2 eps <grad u,grad w>) (grad u + eps grad w) - 1/2 |grad u|^2 grad u
    361: = 1/2 (eps |grad u|^2 grad w + 2 eps <grad u,grad w> grad u)
    362: = eps (1/2 |grad u|^2 grad w + grad u <grad u,grad w>)
    363: */
    364: void g3_analytic_nonlinear_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    365:                               const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    366:                               const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    367:                               PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
    368: {
    369:   PetscScalar nu = 0.0;
    370:   PetscInt    d, e;
    371:   for (d = 0; d < dim; ++d) nu += u_x[d]*u_x[d];
    372:   for (d = 0; d < dim; ++d) {
    373:     g3[d*dim+d] = 0.5*nu;
    374:     for (e = 0; e < dim; ++e) {
    375:       g3[d*dim+e] += u_x[d]*u_x[e];
    376:     }
    377:   }
    378: }

    380: /*
    381:   In 3D for Dirichlet conditions we use exact solution:

    383:     u = 2/3 (x^2 + y^2 + z^2)
    384:     f = 4

    386:   so that

    388:     -\Delta u + f = -2/3 * 6 + 4 = 0

    390:   For Neumann conditions, we have

    392:     -\nabla u \cdot -\hat z |_{z=0} =  (2z)|_{z=0} =  0 (bottom)
    393:     -\nabla u \cdot  \hat z |_{z=1} = -(2z)|_{z=1} = -2 (top)
    394:     -\nabla u \cdot -\hat y |_{y=0} =  (2y)|_{y=0} =  0 (front)
    395:     -\nabla u \cdot  \hat y |_{y=1} = -(2y)|_{y=1} = -2 (back)
    396:     -\nabla u \cdot -\hat x |_{x=0} =  (2x)|_{x=0} =  0 (left)
    397:     -\nabla u \cdot  \hat x |_{x=1} = -(2x)|_{x=1} = -2 (right)

    399:   Which we can express as

    401:     \nabla u \cdot  \hat n|_\Gamma = {2 x, 2 y, 2z} \cdot \hat n = 2 (x + y + z)
    402: */
    403: static PetscErrorCode quadratic_u_3d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    404: {
    405:   *u = 2.0*(x[0]*x[0] + x[1]*x[1] + x[2]*x[2])/3.0;
    406:   return 0;
    407: }

    409: static PetscErrorCode ball_u_3d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    410: {
    411:   const PetscReal alpha   = 500.;
    412:   const PetscReal radius2 = PetscSqr(0.15);
    413:   const PetscReal r2      = PetscSqr(x[0] - 0.5) + PetscSqr(x[1] - 0.5) + PetscSqr(x[2] - 0.5);
    414:   const PetscReal xi      = alpha*(radius2 - r2);

    416:   *u = PetscTanhScalar(xi) + 1.0;
    417:   return 0;
    418: }

    420: static void quadratic_u_field_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    421:                                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    422:                                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    423:                                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uexact[])
    424: {
    425:   uexact[0] = a[0];
    426: }

    428: static PetscErrorCode cross_u_3d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
    429: {
    430:   const PetscReal alpha = 50*4;
    431:   const PetscReal xyz   = (x[0]-0.5)*(x[1]-0.5)*(x[2]-0.5);

    433:   *u = PetscSinReal(alpha*xyz) * (alpha*PetscAbsReal(xyz) < 2*PETSC_PI ? (alpha*PetscAbsReal(xyz) > -2*PETSC_PI ? 1.0 : 0.01) : 0.01);
    434:   return 0;
    435: }

    437: static void f0_cross_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    438:                           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    439:                           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    440:                           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    441: {
    442:   const PetscReal alpha = 50*4;
    443:   const PetscReal xyz   = (x[0]-0.5)*(x[1]-0.5)*(x[2]-0.5);

    445:   f0[0] = PetscSinReal(alpha*xyz) * (alpha*PetscAbsReal(xyz) < 2*PETSC_PI ? (alpha*PetscAbsReal(xyz) > -2*PETSC_PI ? 1.0 : 0.01) : 0.01);
    446: }

    448: static void bd_integral_2d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    449:                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    450:                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    451:                            PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *uint)
    452: {
    453:   uint[0] = u[0];
    454: }

    456: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
    457: {
    458:   const char    *bcTypes[3]  = {"neumann", "dirichlet", "none"};
    459:   const char    *runTypes[4] = {"full", "exact", "test", "perf"};
    460:   const char    *coeffTypes[8] = {"none", "analytic", "field", "nonlinear", "ball", "cross", "checkerboard_0", "checkerboard_1"};
    461:   PetscInt       bc, run, coeff;

    465:   options->runType             = RUN_FULL;
    466:   options->bcType              = DIRICHLET;
    467:   options->variableCoefficient = COEFF_NONE;
    468:   options->fieldBC             = PETSC_FALSE;
    469:   options->jacobianMF          = PETSC_FALSE;
    470:   options->showInitial         = PETSC_FALSE;
    471:   options->showSolution        = PETSC_FALSE;
    472:   options->restart             = PETSC_FALSE;
    473:   options->quiet               = PETSC_FALSE;
    474:   options->nonzInit            = PETSC_FALSE;
    475:   options->bdIntegral          = PETSC_FALSE;
    476:   options->checkksp            = PETSC_FALSE;
    477:   options->div                 = 4;
    478:   options->k                   = 1;
    479:   options->kgrid               = NULL;
    480:   options->rand                = PETSC_FALSE;

    482:   PetscOptionsBegin(comm, "", "Poisson Problem Options", "DMPLEX");
    483:   run  = options->runType;
    484:   PetscOptionsEList("-run_type", "The run type", "ex12.c", runTypes, 4, runTypes[options->runType], &run, NULL);
    485:   options->runType = (RunType) run;
    486:   bc   = options->bcType;
    487:   PetscOptionsEList("-bc_type","Type of boundary condition","ex12.c",bcTypes,3,bcTypes[options->bcType],&bc,NULL);
    488:   options->bcType = (BCType) bc;
    489:   coeff = options->variableCoefficient;
    490:   PetscOptionsEList("-variable_coefficient","Type of variable coefficent","ex12.c",coeffTypes,8,coeffTypes[options->variableCoefficient],&coeff,NULL);
    491:   options->variableCoefficient = (CoeffType) coeff;

    493:   PetscOptionsBool("-field_bc", "Use a field representation for the BC", "ex12.c", options->fieldBC, &options->fieldBC, NULL);
    494:   PetscOptionsBool("-jacobian_mf", "Calculate the action of the Jacobian on the fly", "ex12.c", options->jacobianMF, &options->jacobianMF, NULL);
    495:   PetscOptionsBool("-show_initial", "Output the initial guess for verification", "ex12.c", options->showInitial, &options->showInitial, NULL);
    496:   PetscOptionsBool("-show_solution", "Output the solution for verification", "ex12.c", options->showSolution, &options->showSolution, NULL);
    497:   PetscOptionsBool("-restart", "Read in the mesh and solution from a file", "ex12.c", options->restart, &options->restart, NULL);
    498:   PetscOptionsBool("-quiet", "Don't print any vecs", "ex12.c", options->quiet, &options->quiet, NULL);
    499:   PetscOptionsBool("-nonzero_initial_guess", "nonzero initial guess", "ex12.c", options->nonzInit, &options->nonzInit, NULL);
    500:   PetscOptionsBool("-bd_integral", "Compute the integral of the solution on the boundary", "ex12.c", options->bdIntegral, &options->bdIntegral, NULL);
    501:   if (options->runType == RUN_TEST) {
    502:     PetscOptionsBool("-run_test_check_ksp", "Check solution of KSP", "ex12.c", options->checkksp, &options->checkksp, NULL);
    503:   }
    504:   PetscOptionsInt("-div", "The number of division for the checkerboard coefficient", "ex12.c", options->div, &options->div, NULL);
    505:   PetscOptionsInt("-k", "The exponent for the checkerboard coefficient", "ex12.c", options->k, &options->k, NULL);
    506:   PetscOptionsBool("-k_random", "Assign random k values to checkerboard", "ex12.c", options->rand, &options->rand, NULL);
    507:   PetscOptionsEnd();
    508:   return 0;
    509: }

    511: static PetscErrorCode CreateBCLabel(DM dm, const char name[])
    512: {
    513:   DM             plex;
    514:   DMLabel        label;

    517:   DMCreateLabel(dm, name);
    518:   DMGetLabel(dm, name, &label);
    519:   DMConvert(dm, DMPLEX, &plex);
    520:   DMPlexMarkBoundaryFaces(plex, 1, label);
    521:   DMDestroy(&plex);
    522:   return 0;
    523: }

    525: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
    526: {

    530:   DMCreate(comm, dm);
    531:   DMSetType(*dm, DMPLEX);
    532:   DMSetFromOptions(*dm);
    533:   {
    534:     char      convType[256];
    535:     PetscBool flg;

    537:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
    538:     PetscOptionsFList("-dm_plex_convert_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
    539:     PetscOptionsEnd();
    540:     if (flg) {
    541:       DM dmConv;

    543:       DMConvert(*dm,convType,&dmConv);
    544:       if (dmConv) {
    545:         DMDestroy(dm);
    546:         *dm  = dmConv;
    547:       }
    548:       DMSetFromOptions(*dm);
    549:       DMSetUp(*dm);
    550:     }
    551:   }
    552:   DMViewFromOptions(*dm, NULL, "-dm_view");
    553:   if (user->rand) {
    554:     PetscRandom r;
    555:     PetscReal   val;
    556:     PetscInt    dim, N, i;

    558:     DMGetDimension(*dm, &dim);
    559:     N    = PetscPowInt(user->div, dim);
    560:     PetscMalloc1(N, &user->kgrid);
    561:     PetscRandomCreate(PETSC_COMM_SELF, &r);
    562:     PetscRandomSetFromOptions(r);
    563:     PetscRandomSetInterval(r, 0.0, user->k);
    564:     PetscRandomSetSeed(r, 1973);
    565:     PetscRandomSeed(r);
    566:     for (i = 0; i < N; ++i) {
    567:       PetscRandomGetValueReal(r, &val);
    568:       user->kgrid[i] = 1 + (PetscInt) val;
    569:     }
    570:     PetscRandomDestroy(&r);
    571:   }
    572:   return 0;
    573: }

    575: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
    576: {
    577:   PetscDS         ds;
    578:   DMLabel         label;
    579:   PetscWeakForm   wf;
    580:   const DMBoundaryType *periodicity;
    581:   const PetscInt  id = 1;
    582:   PetscInt        bd, dim;

    585:   DMGetDS(dm, &ds);
    586:   DMGetDimension(dm, &dim);
    587:   DMGetPeriodicity(dm, NULL, NULL, NULL, &periodicity);
    588:   switch (user->variableCoefficient) {
    589:   case COEFF_NONE:
    590:     if (periodicity && periodicity[0]) {
    591:       if (periodicity && periodicity[1]) {
    592:         PetscDSSetResidual(ds, 0, f0_xytrig_u, f1_u);
    593:         PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
    594:       } else {
    595:         PetscDSSetResidual(ds, 0, f0_xtrig_u,  f1_u);
    596:         PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
    597:       }
    598:     } else {
    599:       PetscDSSetResidual(ds, 0, f0_u, f1_u);
    600:       PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
    601:     }
    602:     break;
    603:   case COEFF_ANALYTIC:
    604:     PetscDSSetResidual(ds, 0, f0_analytic_u, f1_analytic_u);
    605:     PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_analytic_uu);
    606:     break;
    607:   case COEFF_FIELD:
    608:     PetscDSSetResidual(ds, 0, f0_analytic_u, f1_field_u);
    609:     PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_field_uu);
    610:     break;
    611:   case COEFF_NONLINEAR:
    612:     PetscDSSetResidual(ds, 0, f0_analytic_nonlinear_u, f1_analytic_nonlinear_u);
    613:     PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_analytic_nonlinear_uu);
    614:     break;
    615:   case COEFF_BALL:
    616:     PetscDSSetResidual(ds, 0, f0_ball_u, f1_u);
    617:     PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
    618:     break;
    619:   case COEFF_CROSS:
    620:     switch (dim) {
    621:     case 2:
    622:       PetscDSSetResidual(ds, 0, f0_cross_u_2d, f1_u);
    623:       break;
    624:     case 3:
    625:       PetscDSSetResidual(ds, 0, f0_cross_u_3d, f1_u);
    626:       break;
    627:     default:
    628:       SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %d", dim);
    629:     }
    630:     PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu);
    631:     break;
    632:   case COEFF_CHECKERBOARD_0:
    633:     PetscDSSetResidual(ds, 0, f0_checkerboard_0_u, f1_field_u);
    634:     PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_field_uu);
    635:     break;
    636:   default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid variable coefficient type %d", user->variableCoefficient);
    637:   }
    638:   switch (dim) {
    639:   case 2:
    640:     switch (user->variableCoefficient) {
    641:     case COEFF_BALL:
    642:       user->exactFuncs[0]  = ball_u_2d;break;
    643:     case COEFF_CROSS:
    644:       user->exactFuncs[0]  = cross_u_2d;break;
    645:     case COEFF_CHECKERBOARD_0:
    646:       user->exactFuncs[0]  = zero;break;
    647:     default:
    648:       if (periodicity && periodicity[0]) {
    649:         if (periodicity && periodicity[1]) {
    650:           user->exactFuncs[0] = xytrig_u_2d;
    651:         } else {
    652:           user->exactFuncs[0] = xtrig_u_2d;
    653:         }
    654:       } else {
    655:         user->exactFuncs[0]  = quadratic_u_2d;
    656:         user->exactFields[0] = quadratic_u_field_2d;
    657:       }
    658:     }
    659:     if (user->bcType == NEUMANN) {
    660:       DMGetLabel(dm, "boundary", &label);
    661:       DMAddBoundary(dm, DM_BC_NATURAL, "wall", label, 1, &id, 0, 0, NULL, NULL, NULL, user, &bd);
    662:       PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
    663:       PetscWeakFormSetIndexBdResidual(wf, label, id, 0, 0, 0, f0_bd_u, 0, NULL);
    664:     }
    665:     break;
    666:   case 3:
    667:     switch (user->variableCoefficient) {
    668:     case COEFF_BALL:
    669:       user->exactFuncs[0]  = ball_u_3d;break;
    670:     case COEFF_CROSS:
    671:       user->exactFuncs[0]  = cross_u_3d;break;
    672:     default:
    673:       user->exactFuncs[0]  = quadratic_u_3d;
    674:       user->exactFields[0] = quadratic_u_field_3d;
    675:     }
    676:     if (user->bcType == NEUMANN) {
    677:       DMGetLabel(dm, "boundary", &label);
    678:       DMAddBoundary(dm, DM_BC_NATURAL, "wall", label, 1, &id, 0, 0, NULL, NULL, NULL, user, &bd);
    679:       PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
    680:       PetscWeakFormSetIndexBdResidual(wf, label, id, 0, 0, 0, f0_bd_u, 0, NULL);
    681:     }
    682:     break;
    683:   default:
    684:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %d", dim);
    685:   }
    686:   /* Setup constants */
    687:   switch (user->variableCoefficient) {
    688:   case COEFF_CHECKERBOARD_0:
    689:   {
    690:     PetscScalar constants[2];

    692:     constants[0] = user->div;
    693:     constants[1] = user->k;
    694:     PetscDSSetConstants(ds, 2, constants);
    695:   }
    696:   break;
    697:   default: break;
    698:   }
    699:   PetscDSSetExactSolution(ds, 0, user->exactFuncs[0], user);
    700:   /* Setup Boundary Conditions */
    701:   if (user->bcType == DIRICHLET) {
    702:     DMGetLabel(dm, "marker", &label);
    703:     if (!label) {
    704:       /* Right now, p4est cannot create labels immediately */
    705:       PetscDSAddBoundaryByName(ds, user->fieldBC ? DM_BC_ESSENTIAL_FIELD : DM_BC_ESSENTIAL, "wall", "marker", 1, &id, 0, 0, NULL, user->fieldBC ? (void (*)(void)) user->exactFields[0] : (void (*)(void)) user->exactFuncs[0], NULL, user, NULL);
    706:     } else {
    707:       DMAddBoundary(dm, user->fieldBC ? DM_BC_ESSENTIAL_FIELD : DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, user->fieldBC ? (void (*)(void)) user->exactFields[0] : (void (*)(void)) user->exactFuncs[0], NULL, user, NULL);
    708:     }
    709:   }
    710:   return 0;
    711: }

    713: static PetscErrorCode SetupMaterial(DM dm, DM dmAux, AppCtx *user)
    714: {
    715:   PetscErrorCode (*matFuncs[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx) = {nu_2d};
    716:   void            *ctx[1];
    717:   Vec              nu;

    719:   ctx[0] = user;
    720:   if (user->variableCoefficient == COEFF_CHECKERBOARD_0) {matFuncs[0] = checkerboardCoeff;}
    721:   DMCreateLocalVector(dmAux, &nu);
    722:   PetscObjectSetName((PetscObject) nu, "Coefficient");
    723:   DMProjectFunctionLocal(dmAux, 0.0, matFuncs, ctx, INSERT_ALL_VALUES, nu);
    724:   DMSetAuxiliaryVec(dm, NULL, 0, 0, nu);
    725:   VecDestroy(&nu);
    726:   return 0;
    727: }

    729: static PetscErrorCode SetupBC(DM dm, DM dmAux, AppCtx *user)
    730: {
    731:   PetscErrorCode (*bcFuncs[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx);
    732:   Vec            uexact;
    733:   PetscInt       dim;

    735:   DMGetDimension(dm, &dim);
    736:   if (dim == 2) bcFuncs[0] = quadratic_u_2d;
    737:   else          bcFuncs[0] = quadratic_u_3d;
    738:   DMCreateLocalVector(dmAux, &uexact);
    739:   DMProjectFunctionLocal(dmAux, 0.0, bcFuncs, NULL, INSERT_ALL_VALUES, uexact);
    740:   DMSetAuxiliaryVec(dm, NULL, 0, 0, uexact);
    741:   VecDestroy(&uexact);
    742:   return 0;
    743: }

    745: static PetscErrorCode SetupAuxDM(DM dm, PetscFE feAux, AppCtx *user)
    746: {
    747:   DM             dmAux, coordDM;

    749:   /* MUST call DMGetCoordinateDM() in order to get p4est setup if present */
    750:   DMGetCoordinateDM(dm, &coordDM);
    751:   if (!feAux) return 0;
    752:   DMClone(dm, &dmAux);
    753:   DMSetCoordinateDM(dmAux, coordDM);
    754:   DMSetField(dmAux, 0, NULL, (PetscObject) feAux);
    755:   DMCreateDS(dmAux);
    756:   if (user->fieldBC) SetupBC(dm, dmAux, user);
    757:   else               SetupMaterial(dm, dmAux, user);
    758:   DMDestroy(&dmAux);
    759:   return 0;
    760: }

    762: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
    763: {
    764:   DM             plex, cdm = dm;
    765:   PetscFE        fe, feAux = NULL;
    766:   PetscBool      simplex;
    767:   PetscInt       dim;
    768:   MPI_Comm       comm;

    771:   DMGetDimension(dm, &dim);
    772:   DMConvert(dm, DMPLEX, &plex);
    773:   DMPlexIsSimplex(plex, &simplex);
    774:   DMDestroy(&plex);
    775:   PetscObjectGetComm((PetscObject) dm, &comm);
    776:   PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe);
    777:   PetscObjectSetName((PetscObject) fe, "potential");
    778:   if (user->variableCoefficient == COEFF_FIELD || user->variableCoefficient == COEFF_CHECKERBOARD_0) {
    779:     PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "mat_", -1, &feAux);
    780:     PetscObjectSetName((PetscObject) feAux, "coefficient");
    781:     PetscFECopyQuadrature(fe, feAux);
    782:   } else if (user->fieldBC) {
    783:     PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "bc_", -1, &feAux);
    784:     PetscFECopyQuadrature(fe, feAux);
    785:   }
    786:   /* Set discretization and boundary conditions for each mesh */
    787:   DMSetField(dm, 0, NULL, (PetscObject) fe);
    788:   DMCreateDS(dm);
    789:   SetupProblem(dm, user);
    790:   while (cdm) {
    791:     SetupAuxDM(cdm, feAux, user);
    792:     if (user->bcType == DIRICHLET) {
    793:       PetscBool hasLabel;

    795:       DMHasLabel(cdm, "marker", &hasLabel);
    796:       if (!hasLabel) CreateBCLabel(cdm, "marker");
    797:     }
    798:     DMCopyDisc(dm, cdm);
    799:     DMGetCoarseDM(cdm, &cdm);
    800:   }
    801:   PetscFEDestroy(&fe);
    802:   PetscFEDestroy(&feAux);
    803:   return 0;
    804: }

    806: int main(int argc, char **argv)
    807: {
    808:   DM             dm;          /* Problem specification */
    809:   SNES           snes;        /* nonlinear solver */
    810:   Vec            u;           /* solution vector */
    811:   Mat            A,J;         /* Jacobian matrix */
    812:   MatNullSpace   nullSpace;   /* May be necessary for Neumann conditions */
    813:   AppCtx         user;        /* user-defined work context */
    814:   JacActionCtx   userJ;       /* context for Jacobian MF action */
    815:   PetscReal      error = 0.0; /* L_2 error in the solution */

    817:   PetscInitialize(&argc, &argv, NULL,help);
    818:   ProcessOptions(PETSC_COMM_WORLD, &user);
    819:   SNESCreate(PETSC_COMM_WORLD, &snes);
    820:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
    821:   SNESSetDM(snes, dm);
    822:   DMSetApplicationContext(dm, &user);

    824:   PetscMalloc2(1, &user.exactFuncs, 1, &user.exactFields);
    825:   SetupDiscretization(dm, &user);

    827:   DMCreateGlobalVector(dm, &u);
    828:   PetscObjectSetName((PetscObject) u, "potential");

    830:   DMCreateMatrix(dm, &J);
    831:   if (user.jacobianMF) {
    832:     PetscInt M, m, N, n;

    834:     MatGetSize(J, &M, &N);
    835:     MatGetLocalSize(J, &m, &n);
    836:     MatCreate(PETSC_COMM_WORLD, &A);
    837:     MatSetSizes(A, m, n, M, N);
    838:     MatSetType(A, MATSHELL);
    839:     MatSetUp(A);
    840: #if 0
    841:     MatShellSetOperation(A, MATOP_MULT, (void (*)(void))FormJacobianAction);
    842: #endif

    844:     userJ.dm   = dm;
    845:     userJ.J    = J;
    846:     userJ.user = &user;

    848:     DMCreateLocalVector(dm, &userJ.u);
    849:     if (user.fieldBC) DMProjectFieldLocal(dm, 0.0, userJ.u, user.exactFields, INSERT_BC_VALUES, userJ.u);
    850:     else              DMProjectFunctionLocal(dm, 0.0, user.exactFuncs, NULL, INSERT_BC_VALUES, userJ.u);
    851:     MatShellSetContext(A, &userJ);
    852:   } else {
    853:     A = J;
    854:   }

    856:   nullSpace = NULL;
    857:   if (user.bcType != DIRICHLET) {
    858:     MatNullSpaceCreate(PetscObjectComm((PetscObject) dm), PETSC_TRUE, 0, NULL, &nullSpace);
    859:     MatSetNullSpace(A, nullSpace);
    860:   }

    862:   DMPlexSetSNESLocalFEM(dm,&user,&user,&user);
    863:   SNESSetJacobian(snes, A, J, NULL, NULL);

    865:   SNESSetFromOptions(snes);

    867:   if (user.fieldBC) DMProjectField(dm, 0.0, u, user.exactFields, INSERT_ALL_VALUES, u);
    868:   else              DMProjectFunction(dm, 0.0, user.exactFuncs, NULL, INSERT_ALL_VALUES, u);
    869:   if (user.restart) {
    870: #if defined(PETSC_HAVE_HDF5)
    871:     PetscViewer viewer;
    872:     char        filename[PETSC_MAX_PATH_LEN];

    874:     PetscOptionsGetString(NULL, NULL, "-dm_plex_filename", filename, sizeof(filename), NULL);
    875:     PetscViewerCreate(PETSC_COMM_WORLD, &viewer);
    876:     PetscViewerSetType(viewer, PETSCVIEWERHDF5);
    877:     PetscViewerFileSetMode(viewer, FILE_MODE_READ);
    878:     PetscViewerFileSetName(viewer, filename);
    879:     PetscViewerHDF5PushGroup(viewer, "/fields");
    880:     VecLoad(u, viewer);
    881:     PetscViewerHDF5PopGroup(viewer);
    882:     PetscViewerDestroy(&viewer);
    883: #endif
    884:   }
    885:   if (user.showInitial) {
    886:     Vec lv;
    887:     DMGetLocalVector(dm, &lv);
    888:     DMGlobalToLocalBegin(dm, u, INSERT_VALUES, lv);
    889:     DMGlobalToLocalEnd(dm, u, INSERT_VALUES, lv);
    890:     DMPrintLocalVec(dm, "Local function", 1.0e-10, lv);
    891:     DMRestoreLocalVector(dm, &lv);
    892:   }
    893:   if (user.runType == RUN_FULL || user.runType == RUN_EXACT) {
    894:     PetscErrorCode (*initialGuess[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx) = {zero};

    896:     if (user.nonzInit) initialGuess[0] = ecks;
    897:     if (user.runType == RUN_FULL) {
    898:       DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);
    899:     }
    900:     VecViewFromOptions(u, NULL, "-guess_vec_view");
    901:     SNESSolve(snes, NULL, u);
    902:     SNESGetSolution(snes, &u);
    903:     SNESGetDM(snes, &dm);

    905:     if (user.showSolution) {
    906:       PetscPrintf(PETSC_COMM_WORLD, "Solution\n");
    907:       VecChop(u, 3.0e-9);
    908:       VecView(u, PETSC_VIEWER_STDOUT_WORLD);
    909:     }
    910:   } else if (user.runType == RUN_PERF) {
    911:     Vec       r;
    912:     PetscReal res = 0.0;

    914:     SNESGetFunction(snes, &r, NULL, NULL);
    915:     SNESComputeFunction(snes, u, r);
    916:     PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");
    917:     VecChop(r, 1.0e-10);
    918:     VecNorm(r, NORM_2, &res);
    919:     PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);
    920:   } else {
    921:     Vec       r;
    922:     PetscReal res = 0.0, tol = 1.0e-11;

    924:     /* Check discretization error */
    925:     SNESGetFunction(snes, &r, NULL, NULL);
    926:     PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");
    927:     if (!user.quiet) VecView(u, PETSC_VIEWER_STDOUT_WORLD);
    928:     DMComputeL2Diff(dm, 0.0, user.exactFuncs, NULL, u, &error);
    929:     if (error < tol) PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < %2.1e\n", (double)tol);
    930:     else             PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", (double)error);
    931:     /* Check residual */
    932:     SNESComputeFunction(snes, u, r);
    933:     PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");
    934:     VecChop(r, 1.0e-10);
    935:     if (!user.quiet) VecView(r, PETSC_VIEWER_STDOUT_WORLD);
    936:     VecNorm(r, NORM_2, &res);
    937:     PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);
    938:     /* Check Jacobian */
    939:     {
    940:       Vec b;

    942:       SNESComputeJacobian(snes, u, A, A);
    943:       VecDuplicate(u, &b);
    944:       VecSet(r, 0.0);
    945:       SNESComputeFunction(snes, r, b);
    946:       MatMult(A, u, r);
    947:       VecAXPY(r, 1.0, b);
    948:       PetscPrintf(PETSC_COMM_WORLD, "Au - b = Au + F(0)\n");
    949:       VecChop(r, 1.0e-10);
    950:       if (!user.quiet) VecView(r, PETSC_VIEWER_STDOUT_WORLD);
    951:       VecNorm(r, NORM_2, &res);
    952:       PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", (double)res);
    953:       /* check solver */
    954:       if (user.checkksp) {
    955:         KSP ksp;

    957:         if (nullSpace) {
    958:           MatNullSpaceRemove(nullSpace, u);
    959:         }
    960:         SNESComputeJacobian(snes, u, A, J);
    961:         MatMult(A, u, b);
    962:         SNESGetKSP(snes, &ksp);
    963:         KSPSetOperators(ksp, A, J);
    964:         KSPSolve(ksp, b, r);
    965:         VecAXPY(r, -1.0, u);
    966:         VecNorm(r, NORM_2, &res);
    967:         PetscPrintf(PETSC_COMM_WORLD, "KSP Error: %g\n", (double)res);
    968:       }
    969:       VecDestroy(&b);
    970:     }
    971:   }
    972:   VecViewFromOptions(u, NULL, "-vec_view");
    973:   {
    974:     Vec nu;

    976:     DMGetAuxiliaryVec(dm, NULL, 0, 0, &nu);
    977:     if (nu) VecViewFromOptions(nu, NULL, "-coeff_view");
    978:   }

    980:   if (user.bdIntegral) {
    981:     DMLabel   label;
    982:     PetscInt  id = 1;
    983:     PetscScalar bdInt = 0.0;
    984:     PetscReal   exact = 3.3333333333;

    986:     DMGetLabel(dm, "marker", &label);
    987:     DMPlexComputeBdIntegral(dm, u, label, 1, &id, bd_integral_2d, &bdInt, NULL);
    988:     PetscPrintf(PETSC_COMM_WORLD, "Solution boundary integral: %.4g\n", (double) PetscAbsScalar(bdInt));
    990:   }

    992:   MatNullSpaceDestroy(&nullSpace);
    993:   if (user.jacobianMF) VecDestroy(&userJ.u);
    994:   if (A != J) MatDestroy(&A);
    995:   MatDestroy(&J);
    996:   VecDestroy(&u);
    997:   SNESDestroy(&snes);
    998:   DMDestroy(&dm);
    999:   PetscFree2(user.exactFuncs, user.exactFields);
    1000:   PetscFree(user.kgrid);
    1001:   PetscFinalize();
    1002:   return 0;
    1003: }

    1005: /*TEST
    1006:   # 2D serial P1 test 0-4
    1007:   test:
    1008:     suffix: 2d_p1_0
    1009:     requires: triangle
    1010:     args: -run_type test -bc_type dirichlet -dm_plex_interpolate 0 -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1012:   test:
    1013:     suffix: 2d_p1_1
    1014:     requires: triangle
    1015:     args: -run_type test -bc_type dirichlet -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1017:   test:
    1018:     suffix: 2d_p1_2
    1019:     requires: triangle
    1020:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -bc_type dirichlet -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1022:   test:
    1023:     suffix: 2d_p1_neumann_0
    1024:     requires: triangle
    1025:     args: -dm_coord_space 0 -run_type test -bc_type neumann -dm_plex_boundary_label boundary -petscspace_degree 1 -show_initial -dm_plex_print_fem 1 -dm_view ascii::ascii_info_detail

    1027:   test:
    1028:     suffix: 2d_p1_neumann_1
    1029:     requires: triangle
    1030:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -bc_type neumann -dm_plex_boundary_label boundary -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1032:   # 2D serial P2 test 5-8
    1033:   test:
    1034:     suffix: 2d_p2_0
    1035:     requires: triangle
    1036:     args: -run_type test -bc_type dirichlet -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1038:   test:
    1039:     suffix: 2d_p2_1
    1040:     requires: triangle
    1041:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -bc_type dirichlet -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1043:   test:
    1044:     suffix: 2d_p2_neumann_0
    1045:     requires: triangle
    1046:     args: -dm_coord_space 0 -run_type test -bc_type neumann -dm_plex_boundary_label boundary -petscspace_degree 2 -show_initial -dm_plex_print_fem 1 -dm_view ascii::ascii_info_detail

    1048:   test:
    1049:     suffix: 2d_p2_neumann_1
    1050:     requires: triangle
    1051:     args: -dm_coord_space 0 -run_type test -dm_refine_volume_limit_pre 0.0625 -bc_type neumann -dm_plex_boundary_label boundary -petscspace_degree 2 -show_initial -dm_plex_print_fem 1 -dm_view ascii::ascii_info_detail

    1053:   test:
    1054:     suffix: bd_int_0
    1055:     requires: triangle
    1056:     args: -run_type test -bc_type dirichlet -petscspace_degree 2 -bd_integral -dm_view -quiet

    1058:   test:
    1059:     suffix: bd_int_1
    1060:     requires: triangle
    1061:     args: -run_type test -dm_refine 2 -bc_type dirichlet -petscspace_degree 2 -bd_integral -dm_view -quiet

    1063:   # 3D serial P1 test 9-12
    1064:   test:
    1065:     suffix: 3d_p1_0
    1066:     requires: ctetgen
    1067:     args: -run_type test -dm_plex_dim 3 -bc_type dirichlet -dm_plex_interpolate 0 -petscspace_degree 1 -show_initial -dm_plex_print_fem 1 -dm_view

    1069:   test:
    1070:     suffix: 3d_p1_1
    1071:     requires: ctetgen
    1072:     args: -run_type test -dm_plex_dim 3 -bc_type dirichlet -petscspace_degree 1 -show_initial -dm_plex_print_fem 1 -dm_view

    1074:   test:
    1075:     suffix: 3d_p1_2
    1076:     requires: ctetgen
    1077:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -bc_type dirichlet -petscspace_degree 1 -show_initial -dm_plex_print_fem 1 -dm_view

    1079:   test:
    1080:     suffix: 3d_p1_neumann_0
    1081:     requires: ctetgen
    1082:     args: -run_type test -dm_plex_dim 3 -bc_type neumann -dm_plex_boundary_label boundary -petscspace_degree 1 -snes_fd -show_initial -dm_plex_print_fem 1 -dm_view

    1084:   # Analytic variable coefficient 13-20
    1085:   test:
    1086:     suffix: 13
    1087:     requires: triangle
    1088:     args: -run_type test -variable_coefficient analytic -petscspace_degree 1 -show_initial -dm_plex_print_fem 1
    1089:   test:
    1090:     suffix: 14
    1091:     requires: triangle
    1092:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -variable_coefficient analytic -petscspace_degree 1 -show_initial -dm_plex_print_fem 1
    1093:   test:
    1094:     suffix: 15
    1095:     requires: triangle
    1096:     args: -run_type test -variable_coefficient analytic -petscspace_degree 2 -show_initial -dm_plex_print_fem 1
    1097:   test:
    1098:     suffix: 16
    1099:     requires: triangle
    1100:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -variable_coefficient analytic -petscspace_degree 2 -show_initial -dm_plex_print_fem 1
    1101:   test:
    1102:     suffix: 17
    1103:     requires: ctetgen
    1104:     args: -run_type test -dm_plex_dim 3 -variable_coefficient analytic -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1106:   test:
    1107:     suffix: 18
    1108:     requires: ctetgen
    1109:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -variable_coefficient analytic -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1111:   test:
    1112:     suffix: 19
    1113:     requires: ctetgen
    1114:     args: -run_type test -dm_plex_dim 3 -variable_coefficient analytic -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1116:   test:
    1117:     suffix: 20
    1118:     requires: ctetgen
    1119:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -variable_coefficient analytic -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1121:   # P1 variable coefficient 21-28
    1122:   test:
    1123:     suffix: 21
    1124:     requires: triangle
    1125:     args: -run_type test -variable_coefficient field -petscspace_degree 1 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1127:   test:
    1128:     suffix: 22
    1129:     requires: triangle
    1130:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -variable_coefficient field -petscspace_degree 1 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1132:   test:
    1133:     suffix: 23
    1134:     requires: triangle
    1135:     args: -run_type test -variable_coefficient field -petscspace_degree 2 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1137:   test:
    1138:     suffix: 24
    1139:     requires: triangle
    1140:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -variable_coefficient field -petscspace_degree 2 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1142:   test:
    1143:     suffix: 25
    1144:     requires: ctetgen
    1145:     args: -run_type test -dm_plex_dim 3 -variable_coefficient field -petscspace_degree 1 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1147:   test:
    1148:     suffix: 26
    1149:     requires: ctetgen
    1150:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -variable_coefficient field -petscspace_degree 1 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1152:   test:
    1153:     suffix: 27
    1154:     requires: ctetgen
    1155:     args: -run_type test -dm_plex_dim 3 -variable_coefficient field -petscspace_degree 2 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1157:   test:
    1158:     suffix: 28
    1159:     requires: ctetgen
    1160:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -variable_coefficient field -petscspace_degree 2 -mat_petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1162:   # P0 variable coefficient 29-36
    1163:   test:
    1164:     suffix: 29
    1165:     requires: triangle
    1166:     args: -run_type test -variable_coefficient field -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1168:   test:
    1169:     suffix: 30
    1170:     requires: triangle
    1171:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -variable_coefficient field -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1173:   test:
    1174:     suffix: 31
    1175:     requires: triangle
    1176:     args: -run_type test -variable_coefficient field -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1178:   test:
    1179:     requires: triangle
    1180:     suffix: 32
    1181:     args: -run_type test -dm_refine_volume_limit_pre 0.0625 -variable_coefficient field -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1183:   test:
    1184:     requires: ctetgen
    1185:     suffix: 33
    1186:     args: -run_type test -dm_plex_dim 3 -variable_coefficient field -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1188:   test:
    1189:     suffix: 34
    1190:     requires: ctetgen
    1191:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -variable_coefficient field -petscspace_degree 1 -show_initial -dm_plex_print_fem 1

    1193:   test:
    1194:     suffix: 35
    1195:     requires: ctetgen
    1196:     args: -run_type test -dm_plex_dim 3 -variable_coefficient field -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1198:   test:
    1199:     suffix: 36
    1200:     requires: ctetgen
    1201:     args: -run_type test -dm_plex_dim 3 -dm_refine_volume_limit_pre 0.0125 -variable_coefficient field -petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1203:   # Full solve 39-44
    1204:   test:
    1205:     suffix: 39
    1206:     requires: triangle !single
    1207:     args: -run_type full -dm_refine_volume_limit_pre 0.015625 -petscspace_degree 2 -pc_type gamg -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -ksp_rtol 1.0e-10 -ksp_monitor_short -ksp_converged_reason -snes_monitor_short -snes_converged_reason ::ascii_info_detail
    1208:   test:
    1209:     suffix: 40
    1210:     requires: triangle !single
    1211:     args: -run_type full -dm_refine_volume_limit_pre 0.015625 -variable_coefficient nonlinear -petscspace_degree 2 -pc_type svd -ksp_rtol 1.0e-10 -snes_monitor_short -snes_converged_reason ::ascii_info_detail
    1212:   test:
    1213:     suffix: 41
    1214:     requires: triangle !single
    1215:     args: -run_type full -dm_refine_volume_limit_pre 0.03125 -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 2 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -dm_refine_hierarchy 1 -snes_view -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short
    1216:   test:
    1217:     suffix: 42
    1218:     requires: triangle !single
    1219:     args: -run_type full -dm_refine_volume_limit_pre 0.0625 -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -dm_refine_hierarchy 2 -snes_view -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short -fas_levels_2_snes_type newtonls -fas_levels_2_pc_type svd -fas_levels_2_ksp_rtol 1.0e-10 -fas_levels_2_snes_atol 1.0e-11 -fas_levels_2_snes_monitor_short
    1220:   test:
    1221:     suffix: 43
    1222:     requires: triangle !single
    1223:     nsize: 2
    1224:     args: -run_type full -dm_refine_volume_limit_pre 0.03125 -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 2 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -dm_refine_hierarchy 1 -snes_view -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short

    1226:   test:
    1227:     suffix: 44
    1228:     requires: triangle !single
    1229:     nsize: 2
    1230:     args: -run_type full -dm_refine_volume_limit_pre 0.0625 -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short  -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -dm_refine_hierarchy 2 -dm_plex_print_fem 0 -snes_view -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short -fas_levels_2_snes_type newtonls -fas_levels_2_pc_type svd -fas_levels_2_ksp_rtol 1.0e-10 -fas_levels_2_snes_atol 1.0e-11 -fas_levels_2_snes_monitor_short

    1232:   # These tests use a loose tolerance just to exercise the PtAP operations for MATIS and multiple PCBDDC setup calls inside PCMG
    1233:   testset:
    1234:     requires: triangle !single
    1235:     nsize: 3
    1236:     args: -run_type full -petscspace_degree 1 -dm_mat_type is -pc_type mg -pc_mg_levels 2 -mg_coarse_pc_type bddc -pc_mg_galerkin pmat -ksp_rtol 1.0e-2 -snes_converged_reason -dm_refine_hierarchy 2 -snes_max_it 4
    1237:     test:
    1238:       suffix: gmg_bddc
    1239:       filter: sed -e "s/CONVERGED_FNORM_RELATIVE iterations 3/CONVERGED_FNORM_RELATIVE iterations 4/g"
    1240:       args: -mg_levels_pc_type jacobi
    1241:     test:
    1242:       filter: sed -e "s/iterations [0-4]/iterations 4/g"
    1243:       suffix: gmg_bddc_lev
    1244:       args: -mg_levels_pc_type bddc

    1246:   # Restarting
    1247:   testset:
    1248:     suffix: restart
    1249:     requires: hdf5 triangle !complex
    1250:     args: -run_type test -bc_type dirichlet -petscspace_degree 1
    1251:     test:
    1252:       args: -dm_view hdf5:sol.h5 -vec_view hdf5:sol.h5::append
    1253:     test:
    1254:       args: -dm_plex_filename sol.h5 -dm_plex_name box -restart

    1256:   # Periodicity
    1257:   test:
    1258:     suffix: periodic_0
    1259:     requires: triangle
    1260:     args: -run_type full -bc_type dirichlet -petscspace_degree 1 -snes_converged_reason ::ascii_info_detail

    1262:   test:
    1263:     requires: !complex
    1264:     suffix: periodic_1
    1265:     args: -quiet -run_type test -dm_plex_simplex 0 -dm_plex_box_faces 3,3 -dm_plex_box_bd periodic,periodic -vec_view vtk:test.vtu:vtk_vtu -petscspace_degree 1 -dm_refine 1

    1267:   # 2D serial P1 test with field bc
    1268:   test:
    1269:     suffix: field_bc_2d_p1_0
    1270:     requires: triangle
    1271:     args: -run_type test -bc_type dirichlet -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1273:   test:
    1274:     suffix: field_bc_2d_p1_1
    1275:     requires: triangle
    1276:     args: -run_type test -dm_refine 1 -bc_type dirichlet -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1278:   test:
    1279:     suffix: field_bc_2d_p1_neumann_0
    1280:     requires: triangle
    1281:     args: -run_type test -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1283:   test:
    1284:     suffix: field_bc_2d_p1_neumann_1
    1285:     requires: triangle
    1286:     args: -run_type test -dm_refine 1 -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1288:   # 3D serial P1 test with field bc
    1289:   test:
    1290:     suffix: field_bc_3d_p1_0
    1291:     requires: ctetgen
    1292:     args: -run_type test -dm_plex_dim 3 -bc_type dirichlet -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1294:   test:
    1295:     suffix: field_bc_3d_p1_1
    1296:     requires: ctetgen
    1297:     args: -run_type test -dm_plex_dim 3 -dm_refine 1 -bc_type dirichlet -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1299:   test:
    1300:     suffix: field_bc_3d_p1_neumann_0
    1301:     requires: ctetgen
    1302:     args: -run_type test -dm_plex_dim 3 -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1304:   test:
    1305:     suffix: field_bc_3d_p1_neumann_1
    1306:     requires: ctetgen
    1307:     args: -run_type test -dm_plex_dim 3 -dm_refine 1 -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 1 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1309:   # 2D serial P2 test with field bc
    1310:   test:
    1311:     suffix: field_bc_2d_p2_0
    1312:     requires: triangle
    1313:     args: -run_type test -bc_type dirichlet -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1315:   test:
    1316:     suffix: field_bc_2d_p2_1
    1317:     requires: triangle
    1318:     args: -run_type test -dm_refine 1 -bc_type dirichlet -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1320:   test:
    1321:     suffix: field_bc_2d_p2_neumann_0
    1322:     requires: triangle
    1323:     args: -run_type test -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1325:   test:
    1326:     suffix: field_bc_2d_p2_neumann_1
    1327:     requires: triangle
    1328:     args: -run_type test -dm_refine 1 -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1330:   # 3D serial P2 test with field bc
    1331:   test:
    1332:     suffix: field_bc_3d_p2_0
    1333:     requires: ctetgen
    1334:     args: -run_type test -dm_plex_dim 3 -bc_type dirichlet -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1336:   test:
    1337:     suffix: field_bc_3d_p2_1
    1338:     requires: ctetgen
    1339:     args: -run_type test -dm_plex_dim 3 -dm_refine 1 -bc_type dirichlet -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1341:   test:
    1342:     suffix: field_bc_3d_p2_neumann_0
    1343:     requires: ctetgen
    1344:     args: -run_type test -dm_plex_dim 3 -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1346:   test:
    1347:     suffix: field_bc_3d_p2_neumann_1
    1348:     requires: ctetgen
    1349:     args: -run_type test -dm_plex_dim 3 -dm_refine 1 -bc_type neumann -dm_plex_boundary_label boundary -field_bc -petscspace_degree 2 -bc_petscspace_degree 2 -show_initial -dm_plex_print_fem 1

    1351:   # Full solve simplex: Convergence
    1352:   test:
    1353:     suffix: 3d_p1_conv
    1354:     requires: ctetgen
    1355:     args: -run_type full -dm_plex_dim 3 -dm_refine 1 -bc_type dirichlet -petscspace_degree 1 \
    1356:       -snes_convergence_estimate -convest_num_refine 1 -pc_type lu

    1358:   # Full solve simplex: PCBDDC
    1359:   test:
    1360:     suffix: tri_bddc
    1361:     requires: triangle !single
    1362:     nsize: 5
    1363:     args: -run_type full -petscpartitioner_type simple -dm_refine 2 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -dm_mat_type is -pc_type bddc -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0

    1365:   # Full solve simplex: PCBDDC
    1366:   test:
    1367:     suffix: tri_parmetis_bddc
    1368:     requires: triangle !single parmetis
    1369:     nsize: 4
    1370:     args: -run_type full -petscpartitioner_type parmetis -dm_refine 2 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -dm_mat_type is -pc_type bddc -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0

    1372:   testset:
    1373:     args: -run_type full -dm_plex_simplex 0 -dm_plex_box_faces 3,3 -petscpartitioner_type simple -dm_refine 2 -bc_type dirichlet -petscspace_degree 2 -dm_mat_type is -pc_type bddc -ksp_type gmres -snes_monitor_short -ksp_monitor_short -snes_view -petscspace_poly_tensor -pc_bddc_corner_selection -ksp_rtol 1.e-9 -pc_bddc_use_edges 0
    1374:     nsize: 5
    1375:     output_file: output/ex12_quad_bddc.out
    1376:     filter: sed -e "s/aijcusparse/aij/g" -e "s/aijviennacl/aij/g" -e "s/factorization: cusparse/factorization: petsc/g"
    1377:     test:
    1378:       requires: !single
    1379:       suffix: quad_bddc
    1380:     test:
    1381:       requires: !single cuda
    1382:       suffix: quad_bddc_cuda
    1383:       args: -matis_localmat_type aijcusparse -pc_bddc_dirichlet_pc_factor_mat_solver_type cusparse -pc_bddc_neumann_pc_factor_mat_solver_type cusparse
    1384:     test:
    1385:       requires: !single viennacl
    1386:       suffix: quad_bddc_viennacl
    1387:       args: -matis_localmat_type aijviennacl

    1389:   # Full solve simplex: ASM
    1390:   test:
    1391:     suffix: tri_q2q1_asm_lu
    1392:     requires: triangle !single
    1393:     args: -run_type full -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -pc_type asm -pc_asm_type restrict -pc_asm_blocks 4 -sub_pc_type lu -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0

    1395:   test:
    1396:     suffix: tri_q2q1_msm_lu
    1397:     requires: triangle !single
    1398:     args: -run_type full -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -pc_type asm -pc_asm_type restrict -pc_asm_local_type multiplicative -pc_asm_blocks 4 -sub_pc_type lu -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0

    1400:   test:
    1401:     suffix: tri_q2q1_asm_sor
    1402:     requires: triangle !single
    1403:     args: -run_type full -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -pc_type asm -pc_asm_type restrict -pc_asm_blocks 4 -sub_pc_type sor -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0

    1405:   test:
    1406:     suffix: tri_q2q1_msm_sor
    1407:     requires: triangle !single
    1408:     args: -run_type full -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -ksp_rtol 1.0e-9 -pc_type asm -pc_asm_type restrict -pc_asm_local_type multiplicative -pc_asm_blocks 4 -sub_pc_type sor -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0

    1410:   # Full solve simplex: FAS
    1411:   test:
    1412:     suffix: fas_newton_0
    1413:     requires: triangle !single
    1414:     args: -run_type full -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 2 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -dm_refine_hierarchy 1 -snes_view -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short

    1416:   test:
    1417:     suffix: fas_newton_1
    1418:     requires: triangle !single
    1419:     args: -run_type full -dm_refine_hierarchy 3 -petscspace_degree 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type lu -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_snes_linesearch_type basic -fas_levels_ksp_rtol 1.0e-10 -fas_levels_snes_monitor_short
    1420:     filter: sed -e "s/total number of linear solver iterations=14/total number of linear solver iterations=15/g"

    1422:   test:
    1423:     suffix: fas_ngs_0
    1424:     requires: triangle !single
    1425:     args: -run_type full -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 2 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -dm_refine_hierarchy 1 -snes_view -fas_levels_1_snes_type ngs -fas_levels_1_snes_monitor_short

    1427:   # These two tests are broken because DMPlexComputeInjectorFEM() only works for regularly refined meshes
    1428:   test:
    1429:     suffix: fas_newton_coarse_0
    1430:     requires: pragmatic triangle
    1431:     TODO: broken
    1432:     args: -run_type full -variable_coefficient nonlinear -petscspace_degree 1 \
    1433:           -dm_refine 2 -dm_coarsen_hierarchy 1 -dm_plex_hash_location -dm_adaptor pragmatic \
    1434:           -snes_type fas -snes_fas_levels 2 -snes_converged_reason ::ascii_info_detail -snes_monitor_short -snes_view \
    1435:             -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -fas_coarse_snes_linesearch_type basic \
    1436:             -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short

    1438:   test:
    1439:     suffix: mg_newton_coarse_0
    1440:     requires: triangle pragmatic
    1441:     TODO: broken
    1442:     args: -run_type full -petscspace_degree 1 \
    1443:           -dm_refine 3 -dm_coarsen_hierarchy 3 -dm_plex_hash_location -dm_adaptor pragmatic \
    1444:           -snes_atol 1.0e-8 -snes_rtol 0.0 -snes_monitor_short -snes_converged_reason ::ascii_info_detail -snes_view \
    1445:             -ksp_type richardson -ksp_atol 1.0e-8 -ksp_rtol 0.0 -ksp_norm_type unpreconditioned -ksp_monitor_true_residual \
    1446:               -pc_type mg -pc_mg_levels 4 \
    1447:               -mg_levels_ksp_type gmres -mg_levels_pc_type ilu -mg_levels_ksp_max_it 10

    1449:   # Full solve tensor
    1450:   test:
    1451:     suffix: tensor_plex_2d
    1452:     args: -run_type test -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -dm_refine_hierarchy 2

    1454:   test:
    1455:     suffix: tensor_p4est_2d
    1456:     requires: p4est
    1457:     args: -run_type test -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -dm_forest_initial_refinement 2 -dm_forest_minimum_refinement 0 -dm_plex_convert_type p4est

    1459:   test:
    1460:     suffix: tensor_plex_3d
    1461:     args: -run_type test -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -dm_plex_dim 3 -dm_refine_hierarchy 1 -dm_plex_box_faces 2,2,2

    1463:   test:
    1464:     suffix: tensor_p4est_3d
    1465:     requires: p4est
    1466:     args: -run_type test -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -dm_forest_initial_refinement 1 -dm_forest_minimum_refinement 0 -dm_plex_dim 3 -dm_plex_convert_type p8est -dm_plex_box_faces 2,2,2

    1468:   test:
    1469:     suffix: p4est_test_q2_conformal_serial
    1470:     requires: p4est
    1471:     args: -run_type test -petscspace_degree 2 -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2

    1473:   test:
    1474:     suffix: p4est_test_q2_conformal_parallel
    1475:     requires: p4est
    1476:     nsize: 7
    1477:     args: -run_type test -petscspace_degree 2 -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -petscpartitioner_type simple

    1479:   test:
    1480:     suffix: p4est_test_q2_conformal_parallel_parmetis
    1481:     requires: parmetis p4est
    1482:     nsize: 4
    1483:     args: -run_type test -petscspace_degree 2 -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -petscpartitioner_type parmetis

    1485:   test:
    1486:     suffix: p4est_test_q2_nonconformal_serial
    1487:     requires: p4est
    1488:     filter: grep -v "CG or CGNE: variant"
    1489:     args: -run_type test -petscspace_degree 2 -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash

    1491:   test:
    1492:     suffix: p4est_test_q2_nonconformal_parallel
    1493:     requires: p4est
    1494:     filter: grep -v "CG or CGNE: variant"
    1495:     nsize: 7
    1496:     args: -run_type test -petscspace_degree 2 -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type simple

    1498:   test:
    1499:     suffix: p4est_test_q2_nonconformal_parallel_parmetis
    1500:     requires: parmetis p4est
    1501:     nsize: 4
    1502:     args: -run_type test -petscspace_degree 2 -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type parmetis

    1504:   test:
    1505:     suffix: p4est_exact_q2_conformal_serial
    1506:     requires: p4est !single !complex !__float128
    1507:     args: -run_type exact -petscspace_degree 2 -fas_levels_snes_atol 1.e-10 -snes_max_it 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type none -fas_coarse_ksp_type preonly -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type none -fas_levels_ksp_type preonly -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2

    1509:   test:
    1510:     suffix: p4est_exact_q2_conformal_parallel
    1511:     requires: p4est !single !complex !__float128
    1512:     nsize: 4
    1513:     args: -run_type exact -petscspace_degree 2 -fas_levels_snes_atol 1.e-10 -snes_max_it 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type none -fas_coarse_ksp_type preonly -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type none -fas_levels_ksp_type preonly -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2

    1515:   test:
    1516:     suffix: p4est_exact_q2_conformal_parallel_parmetis
    1517:     requires: parmetis p4est !single
    1518:     nsize: 4
    1519:     args: -run_type exact -petscspace_degree 2 -fas_levels_snes_atol 1.e-10 -snes_max_it 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type none -fas_coarse_ksp_type preonly -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type none -fas_levels_ksp_type preonly -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -petscpartitioner_type parmetis

    1521:   test:
    1522:     suffix: p4est_exact_q2_nonconformal_serial
    1523:     requires: p4est
    1524:     args: -run_type exact -petscspace_degree 2 -fas_levels_snes_atol 1.e-10 -snes_max_it 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type none -fas_coarse_ksp_type preonly -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type none -fas_levels_ksp_type preonly -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash

    1526:   test:
    1527:     suffix: p4est_exact_q2_nonconformal_parallel
    1528:     requires: p4est
    1529:     nsize: 7
    1530:     args: -run_type exact -petscspace_degree 2 -fas_levels_snes_atol 1.e-10 -snes_max_it 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type none -fas_coarse_ksp_type preonly -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type none -fas_levels_ksp_type preonly -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type simple

    1532:   test:
    1533:     suffix: p4est_exact_q2_nonconformal_parallel_parmetis
    1534:     requires: parmetis p4est
    1535:     nsize: 4
    1536:     args: -run_type exact -petscspace_degree 2 -fas_levels_snes_atol 1.e-10 -snes_max_it 1 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type none -fas_coarse_ksp_type preonly -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type none -fas_levels_ksp_type preonly -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type parmetis

    1538:   test:
    1539:     suffix: p4est_full_q2_nonconformal_serial
    1540:     requires: p4est !single
    1541:     filter: grep -v "variant HERMITIAN"
    1542:     args: -run_type full -petscspace_degree 2 -snes_max_it 20 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type jacobi -fas_coarse_ksp_type cg -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type jacobi -fas_levels_ksp_type cg -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash

    1544:   test:
    1545:     suffix: p4est_full_q2_nonconformal_parallel
    1546:     requires: p4est !single
    1547:     filter: grep -v "variant HERMITIAN"
    1548:     nsize: 7
    1549:     args: -run_type full -petscspace_degree 2 -snes_max_it 20 -snes_type fas -snes_fas_levels 3 -fas_coarse_pc_type jacobi -fas_coarse_ksp_type cg -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type jacobi -fas_levels_ksp_type cg -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type simple

    1551:   test:
    1552:     suffix: p4est_full_q2_nonconformal_parallel_bddcfas
    1553:     requires: p4est !single
    1554:     filter: grep -v "variant HERMITIAN"
    1555:     nsize: 7
    1556:     args: -run_type full -petscspace_degree 2 -snes_max_it 20 -snes_type fas -snes_fas_levels 3 -dm_mat_type is -fas_coarse_pc_type bddc -fas_coarse_ksp_type cg -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type bddc -fas_levels_ksp_type cg -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type simple

    1558:   test:
    1559:     suffix: p4est_full_q2_nonconformal_parallel_bddc
    1560:     requires: p4est !single
    1561:     filter: grep -v "variant HERMITIAN"
    1562:     nsize: 7
    1563:     args: -run_type full -petscspace_degree 2 -snes_max_it 20 -snes_type newtonls -dm_mat_type is -pc_type bddc -ksp_type cg -snes_monitor_short -snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type simple

    1565:   test:
    1566:     TODO: broken
    1567:     suffix: p4est_fas_q2_conformal_serial
    1568:     requires: p4est !complex !__float128
    1569:     args: -run_type full -variable_coefficient nonlinear -petscspace_degree 2 -snes_max_it 20 -snes_type fas -snes_fas_levels 3 -pc_type jacobi -ksp_type gmres -fas_coarse_pc_type svd -fas_coarse_ksp_type gmres -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type svd -fas_levels_ksp_type gmres -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_refine_hierarchy 3

    1571:   test:
    1572:     TODO: broken
    1573:     suffix: p4est_fas_q2_nonconformal_serial
    1574:     requires: p4est
    1575:     args: -run_type full -variable_coefficient nonlinear -petscspace_degree 2 -snes_max_it 20 -snes_type fas -snes_fas_levels 3 -pc_type jacobi -ksp_type gmres -fas_coarse_pc_type jacobi -fas_coarse_ksp_type gmres -fas_coarse_ksp_monitor_true_residual -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_snes_type newtonls -fas_levels_pc_type jacobi -fas_levels_ksp_type gmres -fas_levels_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash

    1577:   test:
    1578:     suffix: fas_newton_0_p4est
    1579:     requires: p4est !single !__float128
    1580:     args: -run_type full -variable_coefficient nonlinear -petscspace_degree 1 -snes_type fas -snes_fas_levels 2 -fas_coarse_pc_type svd -fas_coarse_ksp_rtol 1.0e-10 -fas_coarse_snes_monitor_short -snes_monitor_short -fas_coarse_snes_linesearch_type basic -snes_converged_reason ::ascii_info_detail -snes_view -fas_levels_1_snes_type newtonls -fas_levels_1_pc_type svd -fas_levels_1_ksp_rtol 1.0e-10 -fas_levels_1_snes_monitor_short -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash

    1582:   # Full solve simplicial AMR
    1583:   test:
    1584:     suffix: tri_p1_adapt_init_pragmatic
    1585:     requires: pragmatic
    1586:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_initial 1 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor pragmatic

    1588:   test:
    1589:     suffix: tri_p2_adapt_init_pragmatic
    1590:     requires: pragmatic
    1591:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_initial 1 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor pragmatic

    1593:   test:
    1594:     suffix: tri_p1_adapt_init_mmg
    1595:     requires: mmg
    1596:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_initial 1 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor mmg

    1598:   test:
    1599:     suffix: tri_p2_adapt_init_mmg
    1600:     requires: mmg
    1601:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_initial 1 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor mmg

    1603:   test:
    1604:     suffix: tri_p1_adapt_seq_pragmatic
    1605:     requires: pragmatic
    1606:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_sequence 2 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor pragmatic

    1608:   test:
    1609:     suffix: tri_p2_adapt_seq_pragmatic
    1610:     requires: pragmatic
    1611:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_sequence 2 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor pragmatic

    1613:   test:
    1614:     suffix: tri_p1_adapt_seq_mmg
    1615:     requires: mmg
    1616:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_sequence 2 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor mmg

    1618:   test:
    1619:     suffix: tri_p2_adapt_seq_mmg
    1620:     requires: mmg
    1621:     args: -run_type exact -dm_refine 5 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -snes_adapt_sequence 2 -adaptor_target_num 4000 -dm_plex_metric_h_max 0.5 -dm_adaptor mmg

    1623:   test:
    1624:     suffix: tri_p1_adapt_analytic_pragmatic
    1625:     requires: pragmatic
    1626:     args: -run_type exact -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient cross -snes_adapt_initial 4 -adaptor_target_num 500 -adaptor_monitor -dm_plex_metric_h_min 0.0001 -dm_plex_metric_h_max 0.05 -dm_adaptor pragmatic

    1628:   test:
    1629:     suffix: tri_p2_adapt_analytic_pragmatic
    1630:     requires: pragmatic
    1631:     args: -run_type exact -dm_refine 3 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient cross -snes_adapt_initial 4 -adaptor_target_num 500 -adaptor_monitor -dm_plex_metric_h_min 0.0001 -dm_plex_metric_h_max 0.05 -dm_adaptor pragmatic

    1633:   test:
    1634:     suffix: tri_p1_adapt_analytic_mmg
    1635:     requires: mmg
    1636:     args: -run_type exact -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient cross -snes_adapt_initial 4 -adaptor_target_num 500 -adaptor_monitor -dm_plex_metric_h_max 0.5 -dm_adaptor mmg

    1638:   test:
    1639:     suffix: tri_p2_adapt_analytic_mmg
    1640:     requires: mmg
    1641:     args: -run_type exact -dm_refine 3 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient cross -snes_adapt_initial 4 -adaptor_target_num 500 -adaptor_monitor -dm_plex_metric_h_max 0.5 -dm_adaptor mmg

    1643:   test:
    1644:     suffix: tri_p1_adapt_uniform_pragmatic
    1645:     requires: pragmatic tetgen
    1646:     nsize: 2
    1647:     args: -run_type full -dm_plex_box_faces 8,8,8 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient none -snes_converged_reason ::ascii_info_detail -ksp_type cg -pc_type sor -snes_adapt_sequence 3 -adaptor_target_num 400 -dm_plex_metric_h_max 0.5 -dm_plex_dim 3 -dm_adaptor pragmatic
    1648:     timeoutfactor: 2

    1650:   test:
    1651:     suffix: tri_p2_adapt_uniform_pragmatic
    1652:     requires: pragmatic tetgen
    1653:     nsize: 2
    1654:     args: -run_type full -dm_plex_box_faces 8,8,8 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient none -snes_converged_reason ::ascii_info_detail -ksp_type cg -pc_type sor -snes_adapt_sequence 1 -adaptor_target_num 400 -dm_plex_metric_h_max 0.5 -dm_plex_dim 3 -dm_adaptor pragmatic
    1655:     timeoutfactor: 1

    1657:   test:
    1658:     suffix: tri_p1_adapt_uniform_mmg
    1659:     requires: mmg tetgen
    1660:     args: -run_type full -dm_plex_box_faces 4,4,4 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient none -snes_converged_reason ::ascii_info_detail -ksp_type cg -pc_type sor -snes_adapt_sequence 3 -adaptor_target_num 400 -dm_plex_metric_h_max 0.5 -dm_plex_dim 3 -dm_adaptor mmg
    1661:     timeoutfactor: 2

    1663:   test:
    1664:     suffix: tri_p2_adapt_uniform_mmg
    1665:     requires: mmg tetgen
    1666:     args: -run_type full -dm_plex_box_faces 4,4,4 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient none -snes_converged_reason ::ascii_info_detail -ksp_type cg -pc_type sor -snes_adapt_sequence 1 -adaptor_target_num 400 -dm_plex_metric_h_max 0.5 -dm_plex_dim 3 -dm_adaptor mmg
    1667:     timeoutfactor: 1

    1669:   test:
    1670:     suffix: tri_p1_adapt_uniform_parmmg
    1671:     requires: parmmg tetgen
    1672:     nsize: 2
    1673:     args: -run_type full -dm_plex_box_faces 8,8,8 -bc_type dirichlet -petscspace_degree 1 -variable_coefficient none -snes_converged_reason ::ascii_info_detail -ksp_type cg -pc_type sor -snes_adapt_sequence 3 -adaptor_target_num 400 -dm_plex_metric_h_max 0.5 -dm_plex_dim 3 -dm_adaptor parmmg
    1674:     timeoutfactor: 2

    1676:   test:
    1677:     suffix: tri_p2_adapt_uniform_parmmg
    1678:     requires: parmmg tetgen
    1679:     nsize: 2
    1680:     args: -run_type full -dm_plex_box_faces 8,8,8 -bc_type dirichlet -petscspace_degree 2 -variable_coefficient none -snes_converged_reason ::ascii_info_detail -ksp_type cg -pc_type sor -snes_adapt_sequence 1 -adaptor_target_num 400 -dm_plex_metric_h_max 0.5 -dm_plex_dim 3 -dm_adaptor parmmg
    1681:     timeoutfactor: 1

    1683:   # Full solve tensor AMR
    1684:   test:
    1685:     suffix: quad_q1_adapt_0
    1686:     requires: p4est
    1687:     args: -run_type exact -dm_plex_simplex 0 -dm_plex_convert_type p4est -bc_type dirichlet -petscspace_degree 1 -variable_coefficient ball -snes_converged_reason ::ascii_info_detail -pc_type lu -dm_forest_initial_refinement 4 -snes_adapt_initial 1 -dm_view
    1688:     filter: grep -v DM_

    1690:   test:
    1691:     suffix: amr_0
    1692:     nsize: 5
    1693:     args: -run_type test -petscpartitioner_type simple -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -dm_refine 1

    1695:   test:
    1696:     suffix: amr_1
    1697:     requires: p4est !complex
    1698:     args: -run_type test -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -dm_plex_convert_type p4est -dm_p4est_refine_pattern center -dm_forest_maximum_refinement 5 -dm_view vtk:amr.vtu:vtk_vtu -vec_view vtk:amr.vtu:vtk_vtu:append

    1700:   test:
    1701:     suffix: p4est_solve_bddc
    1702:     requires: p4est !complex
    1703:     args: -run_type full -variable_coefficient nonlinear -nonzero_initial_guess 1 -petscspace_degree 2 -snes_max_it 20 -snes_type newtonls -dm_mat_type is -pc_type bddc -ksp_type cg -snes_monitor_short -ksp_monitor -snes_linesearch_type bt -snes_converged_reason -snes_view -dm_plex_simplex 0 -petscspace_poly_tensor -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -petscpartitioner_type simple -pc_bddc_detect_disconnected
    1704:     nsize: 4

    1706:   test:
    1707:     suffix: p4est_solve_fas
    1708:     requires: p4est
    1709:     args: -run_type full -variable_coefficient nonlinear -nonzero_initial_guess 1 -petscspace_degree 2 -snes_max_it 10 -snes_type fas -snes_linesearch_type bt -snes_fas_levels 3 -fas_coarse_snes_type newtonls -fas_coarse_snes_linesearch_type basic -fas_coarse_ksp_type cg -fas_coarse_pc_type jacobi -fas_coarse_snes_monitor_short -fas_levels_snes_max_it 4 -fas_levels_snes_type newtonls -fas_levels_snes_linesearch_type bt -fas_levels_ksp_type cg -fas_levels_pc_type jacobi -fas_levels_snes_monitor_short -fas_levels_cycle_snes_linesearch_type bt -snes_monitor_short -snes_converged_reason -snes_view -dm_plex_simplex 0 -petscspace_poly_tensor -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash
    1710:     nsize: 4
    1711:     TODO: identical machine two runs produce slightly different solver trackers

    1713:   test:
    1714:     suffix: p4est_convergence_test_1
    1715:     requires: p4est
    1716:     args:  -quiet -run_type test -petscspace_degree 1 -dm_plex_simplex 0 -petscspace_poly_tensor -dm_plex_convert_type p4est -dm_forest_minimum_refinement 2 -dm_forest_initial_refinement 2 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash
    1717:     nsize: 4

    1719:   test:
    1720:     suffix: p4est_convergence_test_2
    1721:     requires: p4est
    1722:     args: -quiet -run_type test -petscspace_degree 1 -dm_plex_simplex 0 -petscspace_poly_tensor -dm_plex_convert_type p4est -dm_forest_minimum_refinement 3 -dm_forest_initial_refinement 3 -dm_forest_maximum_refinement 5 -dm_p4est_refine_pattern hash

    1724:   test:
    1725:     suffix: p4est_convergence_test_3
    1726:     requires: p4est
    1727:     args: -quiet -run_type test -petscspace_degree 1 -dm_plex_simplex 0 -petscspace_poly_tensor -dm_plex_convert_type p4est -dm_forest_minimum_refinement 4 -dm_forest_initial_refinement 4 -dm_forest_maximum_refinement 6 -dm_p4est_refine_pattern hash

    1729:   test:
    1730:     suffix: p4est_convergence_test_4
    1731:     requires: p4est
    1732:     args: -quiet -run_type test -petscspace_degree 1 -dm_plex_simplex 0 -petscspace_poly_tensor -dm_plex_convert_type p4est -dm_forest_minimum_refinement 5 -dm_forest_initial_refinement 5 -dm_forest_maximum_refinement 7 -dm_p4est_refine_pattern hash
    1733:     timeoutfactor: 5

    1735:   # Serial tests with GLVis visualization
    1736:   test:
    1737:     suffix: glvis_2d_tet_p1
    1738:     args: -quiet -run_type test -bc_type dirichlet -petscspace_degree 1 -vec_view glvis: -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/square_periodic.msh -dm_plex_boundary_label marker -dm_plex_gmsh_periodic 0 -dm_coord_space 0
    1739:   test:
    1740:     suffix: glvis_2d_tet_p2
    1741:     args: -quiet -run_type test -bc_type dirichlet -petscspace_degree 2 -vec_view glvis: -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/square_periodic.msh -dm_plex_boundary_label marker -dm_plex_gmsh_periodic 0 -dm_coord_space 0
    1742:   test:
    1743:     suffix: glvis_2d_hex_p1
    1744:     args: -quiet -run_type test -bc_type dirichlet -petscspace_degree 1 -vec_view glvis: -dm_plex_simplex 0 -dm_refine 1 -dm_coord_space 0
    1745:   test:
    1746:     suffix: glvis_2d_hex_p2
    1747:     args: -quiet -run_type test -bc_type dirichlet -petscspace_degree 2 -vec_view glvis: -dm_plex_simplex 0 -dm_refine 1 -dm_coord_space 0
    1748:   test:
    1749:     suffix: glvis_2d_hex_p2_p4est
    1750:     requires: p4est
    1751:     args: -quiet -run_type test -bc_type dirichlet -petscspace_degree 2 -vec_view glvis: -dm_plex_simplex 0 -dm_plex_convert_type p4est -dm_forest_minimum_refinement 0 -dm_forest_initial_refinement 1 -dm_forest_maximum_refinement 4 -dm_p4est_refine_pattern hash -viewer_glvis_dm_plex_enable_ncmesh
    1752:   test:
    1753:     suffix: glvis_2d_tet_p0
    1754:     args: -run_type exact -guess_vec_view glvis: -nonzero_initial_guess 1 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/square_periodic.msh -dm_plex_boundary_label marker -petscspace_degree 0 -dm_coord_space 0
    1755:   test:
    1756:     suffix: glvis_2d_hex_p0
    1757:     args: -run_type exact -guess_vec_view glvis: -nonzero_initial_guess 1 -dm_plex_box_faces 5,7 -dm_plex_simplex 0 -petscspace_degree 0 -dm_coord_space 0

    1759:   # PCHPDDM tests
    1760:   testset:
    1761:     nsize: 4
    1762:     requires: hpddm slepc !single defined(PETSC_HAVE_DYNAMIC_LIBRARIES) defined(PETSC_USE_SHARED_LIBRARIES)
    1763:     args: -run_type test -run_test_check_ksp -quiet -petscspace_degree 1 -petscpartitioner_type simple -bc_type none -dm_plex_simplex 0 -pc_type hpddm -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_nev 2 -pc_hpddm_coarse_p 1 -pc_hpddm_coarse_pc_type svd -ksp_rtol 1.e-10 -pc_hpddm_levels_1_st_pc_factor_shift_type INBLOCKS -ksp_converged_reason
    1764:     test:
    1765:       suffix: quad_singular_hpddm
    1766:       args: -dm_plex_box_faces 6,7
    1767:     test:
    1768:       requires: p4est
    1769:       suffix: p4est_singular_2d_hpddm
    1770:       args: -dm_plex_convert_type p4est -dm_forest_minimum_refinement 1 -dm_forest_initial_refinement 3 -dm_forest_maximum_refinement 3
    1771:     test:
    1772:       requires: p4est
    1773:       suffix: p4est_nc_singular_2d_hpddm
    1774:       args: -dm_plex_convert_type p4est -dm_forest_minimum_refinement 1 -dm_forest_initial_refinement 1 -dm_forest_maximum_refinement 3 -dm_p4est_refine_pattern hash
    1775:   testset:
    1776:     nsize: 4
    1777:     requires: hpddm slepc triangle !single defined(PETSC_HAVE_DYNAMIC_LIBRARIES) defined(PETSC_USE_SHARED_LIBRARIES)
    1778:     args: -run_type full -petscpartitioner_type simple -dm_refine 2 -bc_type dirichlet -petscspace_degree 2 -ksp_type gmres -ksp_gmres_restart 100 -pc_type hpddm -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0 -pc_type hpddm -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_nev 4 -pc_hpddm_coarse_p 2 -pc_hpddm_coarse_pc_type redundant -ksp_rtol 1.e-1
    1779:     test:
    1780:       args: -pc_hpddm_coarse_mat_type baij -options_left no
    1781:       suffix: tri_hpddm_reuse_baij
    1782:     test:
    1783:       requires: !complex
    1784:       suffix: tri_hpddm_reuse
    1785:   testset:
    1786:     nsize: 4
    1787:     requires: hpddm slepc !single defined(PETSC_HAVE_DYNAMIC_LIBRARIES) defined(PETSC_USE_SHARED_LIBRARIES)
    1788:     args: -run_type full -petscpartitioner_type simple -dm_plex_box_faces 7,5 -dm_refine 2 -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 2 -ksp_type gmres -ksp_gmres_restart 100 -pc_type hpddm -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0 -pc_type hpddm -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_nev 4 -pc_hpddm_coarse_p 2 -pc_hpddm_coarse_pc_type redundant -ksp_rtol 1.e-1
    1789:     test:
    1790:       args: -pc_hpddm_coarse_mat_type baij -options_left no
    1791:       suffix: quad_hpddm_reuse_baij
    1792:     test:
    1793:       requires: !complex
    1794:       suffix: quad_hpddm_reuse
    1795:   testset:
    1796:     nsize: 4
    1797:     requires: hpddm slepc !single defined(PETSC_HAVE_DYNAMIC_LIBRARIES) defined(PETSC_USE_SHARED_LIBRARIES)
    1798:     args: -run_type full -petscpartitioner_type simple -dm_plex_box_faces 7,5 -dm_refine 2 -dm_plex_simplex 0 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -pc_type hpddm -snes_monitor_short -ksp_monitor_short -snes_converged_reason ::ascii_info_detail -ksp_converged_reason -snes_view -show_solution 0 -pc_type hpddm -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_threshold 0.1 -pc_hpddm_coarse_p 2 -pc_hpddm_coarse_pc_type redundant -ksp_rtol 1.e-1
    1799:     test:
    1800:       args: -pc_hpddm_coarse_mat_type baij -options_left no
    1801:       suffix: quad_hpddm_reuse_threshold_baij
    1802:     test:
    1803:       requires: !complex
    1804:       suffix: quad_hpddm_reuse_threshold
    1805:   testset:
    1806:     nsize: 4
    1807:     requires: hpddm slepc parmetis !single defined(PETSC_HAVE_DYNAMIC_LIBRARIES) defined(PETSC_USE_SHARED_LIBRARIES)
    1808:     filter: sed -e "s/linear solver iterations=17/linear solver iterations=16/g"
    1809:     args: -run_type full -petscpartitioner_type parmetis -dm_refine 3 -bc_type dirichlet -petscspace_degree 1 -ksp_type gmres -ksp_gmres_restart 100 -pc_type hpddm -snes_monitor_short -snes_converged_reason ::ascii_info_detail -snes_view -show_solution 0 -pc_type hpddm -pc_hpddm_levels_1_sub_pc_type icc -pc_hpddm_levels_1_eps_nev 20 -pc_hpddm_coarse_p 2 -pc_hpddm_coarse_pc_type redundant -ksp_rtol 1.e-10 -dm_plex_filename ${PETSC_DIR}/share/petsc/datafiles/meshes/square_periodic.msh -dm_plex_boundary_label marker -pc_hpddm_levels_1_sub_pc_factor_levels 3 -variable_coefficient ball -dm_plex_gmsh_periodic 0
    1810:     test:
    1811:       args: -pc_hpddm_coarse_mat_type baij -options_left no
    1812:       filter: grep -v "      total: nonzeros=" | grep -v "      rows=" | sed -e "s/total number of linear solver iterations=1[5-7]/total number of linear solver iterations=16/g"
    1813:       suffix: tri_parmetis_hpddm_baij
    1814:     test:
    1815:       filter: grep -v "      total: nonzeros=" | grep -v "      rows=" | sed -e "s/total number of linear solver iterations=1[5-7]/total number of linear solver iterations=16/g"
    1816:       requires: !complex
    1817:       suffix: tri_parmetis_hpddm

    1819:   # 2D serial P1 tests for adaptive MG
    1820:   test:
    1821:     suffix: 2d_p1_adaptmg_0
    1822:     requires: triangle bamg
    1823:     args: -dm_refine_hierarchy 3 -dm_plex_box_faces 4,4 -bc_type dirichlet -petscspace_degree 1 \
    1824:           -variable_coefficient checkerboard_0 -mat_petscspace_degree 0 -div 16 -k 3 \
    1825:           -snes_max_it 1 -ksp_converged_reason \
    1826:           -ksp_rtol 1e-8 -pc_type mg
    1827:   # -ksp_monitor_true_residual -ksp_converged_reason -mg_levels_ksp_monitor_true_residual -pc_mg_mesp_monitor -dm_adapt_interp_view_fine draw -dm_adapt_interp_view_coarse draw -draw_pause 1
    1828:   test:
    1829:     suffix: 2d_p1_adaptmg_1
    1830:     requires: triangle bamg
    1831:     args: -dm_refine_hierarchy 3 -dm_plex_box_faces 4,4 -bc_type dirichlet -petscspace_degree 1 \
    1832:           -variable_coefficient checkerboard_0 -mat_petscspace_degree 0 -div 16 -k 3 \
    1833:           -snes_max_it 1 -ksp_converged_reason \
    1834:           -ksp_rtol 1e-8 -pc_type mg -pc_mg_galerkin -pc_mg_adapt_interp -pc_mg_adapt_interp_coarse_space eigenvector -pc_mg_adapt_interp_n 1 \
    1835:             -pc_mg_mesp_ksp_type richardson -pc_mg_mesp_ksp_richardson_self_scale -pc_mg_mesp_ksp_max_it 100 -pc_mg_mesp_pc_type none

    1837: TEST*/