Actual source code: ex5.c

      1: static char help[] = "Bratu nonlinear PDE in 2d.\n\
      2: We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
      3: domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\
      4: The command line options include:\n\
      5:   -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
      6:      problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n\
      7:   -m_par/n_par <parameter>, where <parameter> indicates an integer\n \
      8:       that MMS3 will be evaluated with 2^m_par, 2^n_par";

     10: /*T
     11:    Concepts: SNES^parallel Bratu example
     12:    Concepts: DMDA^using distributed arrays;
     13:    Concepts: IS coloirng types;
     14:    Processors: n
     15: T*/

     19: /* ------------------------------------------------------------------------

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

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

     26:     with boundary conditions

     28:              u = 0  for  x = 0, x = 1, y = 0, y = 1.

     30:     A finite difference approximation with the usual 5-point stencil
     31:     is used to discretize the boundary value problem to obtain a nonlinear
     32:     system of equations.

     35:       This example shows how geometric multigrid can be run transparently with a nonlinear solver so long
     36:       as SNESSetDM() is provided. Example usage

     38:       ./ex5 -pc_type mg -ksp_monitor  -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17
     39:              -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full

     41:       or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
     42:          multigrid levels, it will be determined automatically based on the number of refinements done)

     44:       ./ex5 -pc_type mg -ksp_monitor  -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
     45:              -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full

     47:   ------------------------------------------------------------------------- */

     49: /*
     50:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     51:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     52: */
     53: #include <petscdm.h>
     54: #include <petscdmda.h>
     55: #include <petscsnes.h>
     56: #include <petscmatlab.h>
     57: #include <petsc/private/snesimpl.h>

     59: /*
     60:    User-defined application context - contains data needed by the
     61:    application-provided call-back routines, FormJacobianLocal() and
     62:    FormFunctionLocal().
     63: */
     64: typedef struct AppCtx AppCtx;
     65: struct AppCtx {
     66:   PetscReal param;          /* test problem parameter */
     67:   PetscInt  m,n;            /* MMS3 parameters */
     68:   PetscErrorCode (*mms_solution)(AppCtx*,const DMDACoor2d*,PetscScalar*);
     69:   PetscErrorCode (*mms_forcing)(AppCtx*,const DMDACoor2d*,PetscScalar*);
     70: };

     72: /*
     73:    User-defined routines
     74: */
     75: extern PetscErrorCode FormInitialGuess(DM,AppCtx*,Vec);
     76: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
     77: extern PetscErrorCode FormExactSolution(DM,AppCtx*,Vec);
     78: extern PetscErrorCode ZeroBCSolution(AppCtx*,const DMDACoor2d*,PetscScalar*);
     79: extern PetscErrorCode MMSSolution1(AppCtx*,const DMDACoor2d*,PetscScalar*);
     80: extern PetscErrorCode MMSForcing1(AppCtx*,const DMDACoor2d*,PetscScalar*);
     81: extern PetscErrorCode MMSSolution2(AppCtx*,const DMDACoor2d*,PetscScalar*);
     82: extern PetscErrorCode MMSForcing2(AppCtx*,const DMDACoor2d*,PetscScalar*);
     83: extern PetscErrorCode MMSSolution3(AppCtx*,const DMDACoor2d*,PetscScalar*);
     84: extern PetscErrorCode MMSForcing3(AppCtx*,const DMDACoor2d*,PetscScalar*);
     85: extern PetscErrorCode MMSSolution4(AppCtx*,const DMDACoor2d*,PetscScalar*);
     86: extern PetscErrorCode MMSForcing4(AppCtx*,const DMDACoor2d*,PetscScalar*);
     87: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,Mat,AppCtx*);
     88: extern PetscErrorCode FormObjectiveLocal(DMDALocalInfo*,PetscScalar**,PetscReal*,AppCtx*);
     89: extern PetscErrorCode FormFunctionMatlab(SNES,Vec,Vec,void*);
     90: extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*);

     92: int main(int argc,char **argv)
     93: {
     94:   SNES           snes;                         /* nonlinear solver */
     95:   Vec            x;                            /* solution vector */
     96:   AppCtx         user;                         /* user-defined work context */
     97:   PetscInt       its;                          /* iterations for convergence */
     99:   PetscReal      bratu_lambda_max = 6.81;
    100:   PetscReal      bratu_lambda_min = 0.;
    101:   PetscInt       MMS              = 0;
    102:   PetscBool      flg              = PETSC_FALSE;
    103:   DM             da;
    104:   Vec            r               = NULL;
    105:   KSP            ksp;
    106:   PetscInt       lits,slits;

    108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    109:      Initialize program
    110:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:      Initialize problem parameters
    116:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    117:   user.param = 6.0;
    118:   PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);
    119:   if (user.param > bratu_lambda_max || user.param < bratu_lambda_min) SETERRQ3(PETSC_COMM_SELF,1,"Lambda, %g, is out of range, [%g, %g]", user.param, bratu_lambda_min, bratu_lambda_max);
    120:   PetscOptionsGetInt(NULL,NULL,"-mms",&MMS,NULL);
    121:   if (MMS == 3) {
    122:     PetscInt mPar = 2, nPar = 1;
    123:     PetscOptionsGetInt(NULL,NULL,"-m_par",&mPar,NULL);
    124:     PetscOptionsGetInt(NULL,NULL,"-n_par",&nPar,NULL);
    125:     user.m = PetscPowInt(2,mPar);
    126:     user.n = PetscPowInt(2,nPar);
    127:   }

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:      Create nonlinear solver context
    131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    132:   SNESCreate(PETSC_COMM_WORLD,&snes);
    133:   SNESSetCountersReset(snes,PETSC_FALSE);
    134:   SNESSetNGS(snes, NonlinearGS, NULL);

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:      Create distributed array (DMDA) to manage parallel grid and vectors
    138:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    139:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
    140:   DMSetFromOptions(da);
    141:   DMSetUp(da);
    142:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
    143:   DMSetApplicationContext(da,&user);
    144:   SNESSetDM(snes,da);
    145:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:      Extract global vectors from DMDA; then duplicate for remaining
    147:      vectors that are the same types
    148:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    149:   DMCreateGlobalVector(da,&x);

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:      Set local function evaluation routine
    153:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    154:   user.mms_solution = ZeroBCSolution;
    155:   switch (MMS) {
    156:   case 0: user.mms_solution = NULL; user.mms_forcing = NULL;
    157:   case 1: user.mms_solution = MMSSolution1; user.mms_forcing = MMSForcing1; break;
    158:   case 2: user.mms_solution = MMSSolution2; user.mms_forcing = MMSForcing2; break;
    159:   case 3: user.mms_solution = MMSSolution3; user.mms_forcing = MMSForcing3; break;
    160:   case 4: user.mms_solution = MMSSolution4; user.mms_forcing = MMSForcing4; break;
    161:   default: SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_USER,"Unknown MMS type %d",MMS);
    162:   }
    163:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(DMDASNESFunction)FormFunctionLocal,&user);
    164:   PetscOptionsGetBool(NULL,NULL,"-fd",&flg,NULL);
    165:   if (!flg) {
    166:     DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);
    167:   }

    169:   PetscOptionsGetBool(NULL,NULL,"-obj",&flg,NULL);
    170:   if (flg) {
    171:     DMDASNESSetObjectiveLocal(da,(DMDASNESObjective)FormObjectiveLocal,&user);
    172:   }

    174:   if (PetscDefined(HAVE_MATLAB_ENGINE)) {
    175:     PetscBool matlab_function = PETSC_FALSE;
    176:     PetscOptionsGetBool(NULL,NULL,"-matlab_function",&matlab_function,0);
    177:     if (matlab_function) {
    178:       VecDuplicate(x,&r);
    179:       SNESSetFunction(snes,r,FormFunctionMatlab,&user);
    180:     }
    181:   }

    183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    184:      Customize nonlinear solver; set runtime options
    185:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    186:   SNESSetFromOptions(snes);

    188:   FormInitialGuess(da,&user,x);

    190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    191:      Solve nonlinear system
    192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    193:   SNESSolve(snes,NULL,x);
    194:   SNESGetIterationNumber(snes,&its);

    196:   SNESGetLinearSolveIterations(snes,&slits);
    197:   SNESGetKSP(snes,&ksp);
    198:   KSPGetTotalIterations(ksp,&lits);
    199:   if (lits != slits) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Number of total linear iterations reported by SNES %D does not match reported by KSP %D",slits,lits);
    200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    201:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    204:      If using MMS, check the l_2 error
    205:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    206:   if (MMS) {
    207:     Vec       e;
    208:     PetscReal errorl2, errorinf;
    209:     PetscInt  N;

    211:     VecDuplicate(x, &e);
    212:     PetscObjectViewFromOptions((PetscObject) x, NULL, "-sol_view");
    213:     FormExactSolution(da, &user, e);
    214:     PetscObjectViewFromOptions((PetscObject) e, NULL, "-exact_view");
    215:     VecAXPY(e, -1.0, x);
    216:     PetscObjectViewFromOptions((PetscObject) e, NULL, "-error_view");
    217:     VecNorm(e, NORM_2, &errorl2);
    218:     VecNorm(e, NORM_INFINITY, &errorinf);
    219:     VecGetSize(e, &N);
    220:     PetscPrintf(PETSC_COMM_WORLD, "N: %D error L2 %g inf %g\n", N, (double) errorl2/PetscSqrtReal(N), (double) errorinf);
    221:     VecDestroy(&e);
    222:     PetscLogEventSetDof(SNES_Solve, 0, N);
    223:     PetscLogEventSetError(SNES_Solve, 0, errorl2/PetscSqrtReal(N));
    224:   }

    226:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    227:      Free work space.  All PETSc objects should be destroyed when they
    228:      are no longer needed.
    229:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    230:   VecDestroy(&r);
    231:   VecDestroy(&x);
    232:   SNESDestroy(&snes);
    233:   DMDestroy(&da);
    234:   PetscFinalize();
    235:   return ierr;
    236: }
    237: /* ------------------------------------------------------------------- */
    238: /*
    239:    FormInitialGuess - Forms initial approximation.

    241:    Input Parameters:
    242:    da - The DM
    243:    user - user-defined application context

    245:    Output Parameter:
    246:    X - vector
    247:  */
    248: PetscErrorCode FormInitialGuess(DM da,AppCtx *user,Vec X)
    249: {
    250:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
    252:   PetscReal      lambda,temp1,temp,hx,hy;
    253:   PetscScalar    **x;

    256:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    258:   lambda = user->param;
    259:   hx     = 1.0/(PetscReal)(Mx-1);
    260:   hy     = 1.0/(PetscReal)(My-1);
    261:   temp1  = lambda/(lambda + 1.0);

    263:   /*
    264:      Get a pointer to vector data.
    265:        - For default PETSc vectors, VecGetArray() returns a pointer to
    266:          the data array.  Otherwise, the routine is implementation dependent.
    267:        - You MUST call VecRestoreArray() when you no longer need access to
    268:          the array.
    269:   */
    270:   DMDAVecGetArray(da,X,&x);

    272:   /*
    273:      Get local grid boundaries (for 2-dimensional DMDA):
    274:        xs, ys   - starting grid indices (no ghost points)
    275:        xm, ym   - widths of local grid (no ghost points)

    277:   */
    278:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    280:   /*
    281:      Compute initial guess over the locally owned part of the grid
    282:   */
    283:   for (j=ys; j<ys+ym; j++) {
    284:     temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
    285:     for (i=xs; i<xs+xm; i++) {
    286:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    287:         /* boundary conditions are all zero Dirichlet */
    288:         x[j][i] = 0.0;
    289:       } else {
    290:         x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
    291:       }
    292:     }
    293:   }

    295:   /*
    296:      Restore vector
    297:   */
    298:   DMDAVecRestoreArray(da,X,&x);
    299:   return(0);
    300: }

    302: /*
    303:   FormExactSolution - Forms MMS solution

    305:   Input Parameters:
    306:   da - The DM
    307:   user - user-defined application context

    309:   Output Parameter:
    310:   X - vector
    311:  */
    312: PetscErrorCode FormExactSolution(DM da, AppCtx *user, Vec U)
    313: {
    314:   DM             coordDA;
    315:   Vec            coordinates;
    316:   DMDACoor2d   **coords;
    317:   PetscScalar  **u;
    318:   PetscInt       xs, ys, xm, ym, i, j;

    322:   DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
    323:   DMGetCoordinateDM(da, &coordDA);
    324:   DMGetCoordinates(da, &coordinates);
    325:   DMDAVecGetArray(coordDA, coordinates, &coords);
    326:   DMDAVecGetArray(da, U, &u);
    327:   for (j = ys; j < ys+ym; ++j) {
    328:     for (i = xs; i < xs+xm; ++i) {
    329:       user->mms_solution(user,&coords[j][i],&u[j][i]);
    330:     }
    331:   }
    332:   DMDAVecRestoreArray(da, U, &u);
    333:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
    334:   return(0);
    335: }

    337: PetscErrorCode ZeroBCSolution(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    338: {
    339:   u[0] = 0.;
    340:   return 0;
    341: }

    343: /* The functions below evaluate the MMS solution u(x,y) and associated forcing

    345:      f(x,y) = -u_xx - u_yy - lambda exp(u)

    347:   such that u(x,y) is an exact solution with f(x,y) as the right hand side forcing term.
    348:  */
    349: PetscErrorCode MMSSolution1(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    350: {
    351:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    352:   u[0] = x*(1 - x)*y*(1 - y);
    353:   PetscLogFlops(5);
    354:   return 0;
    355: }
    356: PetscErrorCode MMSForcing1(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    357: {
    358:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    359:   f[0] = 2*x*(1 - x) + 2*y*(1 - y) - user->param*PetscExpReal(x*(1 - x)*y*(1 - y));
    360:   return 0;
    361: }

    363: PetscErrorCode MMSSolution2(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    364: {
    365:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    366:   u[0] = PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y);
    367:   PetscLogFlops(5);
    368:   return 0;
    369: }
    370: PetscErrorCode MMSForcing2(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    371: {
    372:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    373:   f[0] = 2*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y) - user->param*PetscExpReal(PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y));
    374:   return 0;
    375: }

    377: PetscErrorCode MMSSolution3(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    378: {
    379:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    380:   u[0] = PetscSinReal(user->m*PETSC_PI*x*(1-y))*PetscSinReal(user->n*PETSC_PI*y*(1-x));
    381:   PetscLogFlops(5);
    382:   return 0;
    383: }
    384: PetscErrorCode MMSForcing3(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    385: {
    386:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    387:   PetscReal m = user->m, n = user->n, lambda = user->param;
    388:   f[0] = (-(PetscExpReal(PetscSinReal(m*PETSC_PI*x*(1 - y))*PetscSinReal(n*PETSC_PI*(1 - x)*y))*lambda)
    389:           + PetscSqr(PETSC_PI)*(-2*m*n*((-1 + x)*x + (-1 + y)*y)*PetscCosReal(m*PETSC_PI*x*(-1 + y))*PetscCosReal(n*PETSC_PI*(-1 + x)*y)
    390:                                 + (PetscSqr(m)*(PetscSqr(x) + PetscSqr(-1 + y)) + PetscSqr(n)*(PetscSqr(-1 + x) + PetscSqr(y)))
    391:                                 *PetscSinReal(m*PETSC_PI*x*(-1 + y))*PetscSinReal(n*PETSC_PI*(-1 + x)*y)));
    392:   return 0;
    393: }

    395: PetscErrorCode MMSSolution4(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    396: {
    397:   const PetscReal Lx = 1.,Ly = 1.;
    398:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    399:   u[0] = (PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y));
    400:   PetscLogFlops(9);
    401:   return 0;
    402: }
    403: PetscErrorCode MMSForcing4(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    404: {
    405:   const PetscReal Lx = 1.,Ly = 1.;
    406:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    407:   f[0] = (2*PetscSqr(x)*(PetscSqr(x)-PetscSqr(Lx))*(PetscSqr(Ly)-6*PetscSqr(y))
    408:           + 2*PetscSqr(y)*(PetscSqr(Lx)-6*PetscSqr(x))*(PetscSqr(y)-PetscSqr(Ly))
    409:           - user->param*PetscExpReal((PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y))));
    410:   return 0;
    411: }

    413: /* ------------------------------------------------------------------- */
    414: /*
    415:    FormFunctionLocal - Evaluates nonlinear function, F(x) on local process patch

    418:  */
    419: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
    420: {
    422:   PetscInt       i,j;
    423:   PetscReal      lambda,hx,hy,hxdhy,hydhx;
    424:   PetscScalar    u,ue,uw,un,us,uxx,uyy,mms_solution,mms_forcing;
    425:   DMDACoor2d     c;

    428:   lambda = user->param;
    429:   hx     = 1.0/(PetscReal)(info->mx-1);
    430:   hy     = 1.0/(PetscReal)(info->my-1);
    431:   hxdhy  = hx/hy;
    432:   hydhx  = hy/hx;
    433:   /*
    434:      Compute function over the locally owned part of the grid
    435:   */
    436:   for (j=info->ys; j<info->ys+info->ym; j++) {
    437:     for (i=info->xs; i<info->xs+info->xm; i++) {
    438:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
    439:         c.x = i*hx; c.y = j*hy;
    440:         user->mms_solution(user,&c,&mms_solution);
    441:         f[j][i] = 2.0*(hydhx+hxdhy)*(x[j][i] - mms_solution);
    442:       } else {
    443:         u  = x[j][i];
    444:         uw = x[j][i-1];
    445:         ue = x[j][i+1];
    446:         un = x[j-1][i];
    447:         us = x[j+1][i];

    449:         /* Enforce boundary conditions at neighboring points -- setting these values causes the Jacobian to be symmetric. */
    450:         if (i-1 == 0) {c.x = (i-1)*hx; c.y = j*hy; user->mms_solution(user,&c,&uw);}
    451:         if (i+1 == info->mx-1) {c.x = (i+1)*hx; c.y = j*hy; user->mms_solution(user,&c,&ue);}
    452:         if (j-1 == 0) {c.x = i*hx; c.y = (j-1)*hy; user->mms_solution(user,&c,&un);}
    453:         if (j+1 == info->my-1) {c.x = i*hx; c.y = (j+1)*hy; user->mms_solution(user,&c,&us);}

    455:         uxx     = (2.0*u - uw - ue)*hydhx;
    456:         uyy     = (2.0*u - un - us)*hxdhy;
    457:         mms_forcing = 0;
    458:         c.x = i*hx; c.y = j*hy;
    459:         if (user->mms_forcing) {user->mms_forcing(user,&c,&mms_forcing);}
    460:         f[j][i] = uxx + uyy - hx*hy*(lambda*PetscExpScalar(u) + mms_forcing);
    461:       }
    462:     }
    463:   }
    464:   PetscLogFlops(11.0*info->ym*info->xm);
    465:   return(0);
    466: }

    468: /* FormObjectiveLocal - Evaluates nonlinear function, F(x) on local process patch */
    469: PetscErrorCode FormObjectiveLocal(DMDALocalInfo *info,PetscScalar **x,PetscReal *obj,AppCtx *user)
    470: {
    472:   PetscInt       i,j;
    473:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc,lobj=0;
    474:   PetscScalar    u,ue,uw,un,us,uxux,uyuy;
    475:   MPI_Comm       comm;

    478:   *obj   = 0;
    479:   PetscObjectGetComm((PetscObject)info->da,&comm);
    480:   lambda = user->param;
    481:   hx     = 1.0/(PetscReal)(info->mx-1);
    482:   hy     = 1.0/(PetscReal)(info->my-1);
    483:   sc     = hx*hy*lambda;
    484:   hxdhy  = hx/hy;
    485:   hydhx  = hy/hx;
    486:   /*
    487:      Compute function over the locally owned part of the grid
    488:   */
    489:   for (j=info->ys; j<info->ys+info->ym; j++) {
    490:     for (i=info->xs; i<info->xs+info->xm; i++) {
    491:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
    492:         lobj += PetscRealPart((hydhx + hxdhy)*x[j][i]*x[j][i]);
    493:       } else {
    494:         u  = x[j][i];
    495:         uw = x[j][i-1];
    496:         ue = x[j][i+1];
    497:         un = x[j-1][i];
    498:         us = x[j+1][i];

    500:         if (i-1 == 0) uw = 0.;
    501:         if (i+1 == info->mx-1) ue = 0.;
    502:         if (j-1 == 0) un = 0.;
    503:         if (j+1 == info->my-1) us = 0.;

    505:         /* F[u] = 1/2\int_{\omega}\nabla^2u(x)*u(x)*dx */

    507:         uxux = u*(2.*u - ue - uw)*hydhx;
    508:         uyuy = u*(2.*u - un - us)*hxdhy;

    510:         lobj += PetscRealPart(0.5*(uxux + uyuy) - sc*PetscExpScalar(u));
    511:       }
    512:     }
    513:   }
    514:   PetscLogFlops(12.0*info->ym*info->xm);
    515:   MPI_Allreduce(&lobj,obj,1,MPIU_REAL,MPIU_SUM,comm);
    516:   return(0);
    517: }

    519: /*
    520:    FormJacobianLocal - Evaluates Jacobian matrix on local process patch
    521: */
    522: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,Mat jacpre,AppCtx *user)
    523: {
    525:   PetscInt       i,j,k;
    526:   MatStencil     col[5],row;
    527:   PetscScalar    lambda,v[5],hx,hy,hxdhy,hydhx,sc;
    528:   DM             coordDA;
    529:   Vec            coordinates;
    530:   DMDACoor2d   **coords;

    533:   lambda = user->param;
    534:   /* Extract coordinates */
    535:   DMGetCoordinateDM(info->da, &coordDA);
    536:   DMGetCoordinates(info->da, &coordinates);
    537:   DMDAVecGetArray(coordDA, coordinates, &coords);
    538:   hx     = info->xm > 1 ? PetscRealPart(coords[info->ys][info->xs+1].x) - PetscRealPart(coords[info->ys][info->xs].x) : 1.0;
    539:   hy     = info->ym > 1 ? PetscRealPart(coords[info->ys+1][info->xs].y) - PetscRealPart(coords[info->ys][info->xs].y) : 1.0;
    540:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
    541:   hxdhy  = hx/hy;
    542:   hydhx  = hy/hx;
    543:   sc     = hx*hy*lambda;

    546:   /*
    547:      Compute entries for the locally owned part of the Jacobian.
    548:       - Currently, all PETSc parallel matrix formats are partitioned by
    549:         contiguous chunks of rows across the processors.
    550:       - Each processor needs to insert only elements that it owns
    551:         locally (but any non-local elements will be sent to the
    552:         appropriate processor during matrix assembly).
    553:       - Here, we set all entries for a particular row at once.
    554:       - We can set matrix entries either using either
    555:         MatSetValuesLocal() or MatSetValues(), as discussed above.
    556:   */
    557:   for (j=info->ys; j<info->ys+info->ym; j++) {
    558:     for (i=info->xs; i<info->xs+info->xm; i++) {
    559:       row.j = j; row.i = i;
    560:       /* boundary points */
    561:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
    562:         v[0] =  2.0*(hydhx + hxdhy);
    563:         MatSetValuesStencil(jacpre,1,&row,1,&row,v,INSERT_VALUES);
    564:       } else {
    565:         k = 0;
    566:         /* interior grid points */
    567:         if (j-1 != 0) {
    568:           v[k]     = -hxdhy;
    569:           col[k].j = j - 1; col[k].i = i;
    570:           k++;
    571:         }
    572:         if (i-1 != 0) {
    573:           v[k]     = -hydhx;
    574:           col[k].j = j;     col[k].i = i-1;
    575:           k++;
    576:         }

    578:         v[k] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[k].j = row.j; col[k].i = row.i; k++;

    580:         if (i+1 != info->mx-1) {
    581:           v[k]     = -hydhx;
    582:           col[k].j = j;     col[k].i = i+1;
    583:           k++;
    584:         }
    585:         if (j+1 != info->mx-1) {
    586:           v[k]     = -hxdhy;
    587:           col[k].j = j + 1; col[k].i = i;
    588:           k++;
    589:         }
    590:         MatSetValuesStencil(jacpre,1,&row,k,col,v,INSERT_VALUES);
    591:       }
    592:     }
    593:   }

    595:   /*
    596:      Assemble matrix, using the 2-step process:
    597:        MatAssemblyBegin(), MatAssemblyEnd().
    598:   */
    599:   MatAssemblyBegin(jacpre,MAT_FINAL_ASSEMBLY);
    600:   MatAssemblyEnd(jacpre,MAT_FINAL_ASSEMBLY);
    601:   /*
    602:      Tell the matrix we will never add a new nonzero location to the
    603:      matrix. If we do, it will generate an error.
    604:   */
    605:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    606:   return(0);
    607: }

    609: PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
    610: {
    611: #if PetscDefined(HAVE_MATLAB_ENGINE)
    612:   AppCtx         *user = (AppCtx*)ptr;
    614:   PetscInt       Mx,My;
    615:   PetscReal      lambda,hx,hy;
    616:   Vec            localX,localF;
    617:   MPI_Comm       comm;
    618:   DM             da;

    621:   SNESGetDM(snes,&da);
    622:   DMGetLocalVector(da,&localX);
    623:   DMGetLocalVector(da,&localF);
    624:   PetscObjectSetName((PetscObject)localX,"localX");
    625:   PetscObjectSetName((PetscObject)localF,"localF");
    626:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    628:   lambda = user->param;
    629:   hx     = 1.0/(PetscReal)(Mx-1);
    630:   hy     = 1.0/(PetscReal)(My-1);

    632:   PetscObjectGetComm((PetscObject)snes,&comm);
    633:   /*
    634:      Scatter ghost points to local vector,using the 2-step process
    635:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    636:      By placing code between these two statements, computations can be
    637:      done while messages are in transition.
    638:   */
    639:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    640:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
    641:   PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);
    642:   PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);
    643:   PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);

    645:   /*
    646:      Insert values into global vector
    647:   */
    648:   DMLocalToGlobalBegin(da,localF,INSERT_VALUES,F);
    649:   DMLocalToGlobalEnd(da,localF,INSERT_VALUES,F);
    650:   DMRestoreLocalVector(da,&localX);
    651:   DMRestoreLocalVector(da,&localF);
    652:   return(0);
    653: #else
    654:     return 0;                     /* Never called */
    655: #endif
    656: }

    658: /* ------------------------------------------------------------------- */
    659: /*
    660:       Applies some sweeps on nonlinear Gauss-Seidel on each process

    662:  */
    663: PetscErrorCode NonlinearGS(SNES snes,Vec X, Vec B, void *ctx)
    664: {
    665:   PetscInt       i,j,k,Mx,My,xs,ys,xm,ym,its,tot_its,sweeps,l;
    667:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc;
    668:   PetscScalar    **x,**b,bij,F,F0=0,J,u,un,us,ue,eu,uw,uxx,uyy,y;
    669:   PetscReal      atol,rtol,stol;
    670:   DM             da;
    671:   AppCtx         *user;
    672:   Vec            localX,localB;

    675:   tot_its = 0;
    676:   SNESNGSGetSweeps(snes,&sweeps);
    677:   SNESNGSGetTolerances(snes,&atol,&rtol,&stol,&its);
    678:   SNESGetDM(snes,&da);
    679:   DMGetApplicationContext(da,(void**)&user);

    681:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    683:   lambda = user->param;
    684:   hx     = 1.0/(PetscReal)(Mx-1);
    685:   hy     = 1.0/(PetscReal)(My-1);
    686:   sc     = hx*hy*lambda;
    687:   hxdhy  = hx/hy;
    688:   hydhx  = hy/hx;

    691:   DMGetLocalVector(da,&localX);
    692:   if (B) {
    693:     DMGetLocalVector(da,&localB);
    694:   }
    695:   for (l=0; l<sweeps; l++) {

    697:     DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    698:     DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
    699:     if (B) {
    700:       DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);
    701:       DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);
    702:     }
    703:     /*
    704:      Get a pointer to vector data.
    705:      - For default PETSc vectors, VecGetArray() returns a pointer to
    706:      the data array.  Otherwise, the routine is implementation dependent.
    707:      - You MUST call VecRestoreArray() when you no longer need access to
    708:      the array.
    709:      */
    710:     DMDAVecGetArray(da,localX,&x);
    711:     if (B) DMDAVecGetArray(da,localB,&b);
    712:     /*
    713:      Get local grid boundaries (for 2-dimensional DMDA):
    714:      xs, ys   - starting grid indices (no ghost points)
    715:      xm, ym   - widths of local grid (no ghost points)
    716:      */
    717:     DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    719:     for (j=ys; j<ys+ym; j++) {
    720:       for (i=xs; i<xs+xm; i++) {
    721:         if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    722:           /* boundary conditions are all zero Dirichlet */
    723:           x[j][i] = 0.0;
    724:         } else {
    725:           if (B) bij = b[j][i];
    726:           else   bij = 0.;

    728:           u  = x[j][i];
    729:           un = x[j-1][i];
    730:           us = x[j+1][i];
    731:           ue = x[j][i-1];
    732:           uw = x[j][i+1];

    734:           for (k=0; k<its; k++) {
    735:             eu  = PetscExpScalar(u);
    736:             uxx = (2.0*u - ue - uw)*hydhx;
    737:             uyy = (2.0*u - un - us)*hxdhy;
    738:             F   = uxx + uyy - sc*eu - bij;
    739:             if (k == 0) F0 = F;
    740:             J  = 2.0*(hydhx + hxdhy) - sc*eu;
    741:             y  = F/J;
    742:             u -= y;
    743:             tot_its++;

    745:             if (atol > PetscAbsReal(PetscRealPart(F)) ||
    746:                 rtol*PetscAbsReal(PetscRealPart(F0)) > PetscAbsReal(PetscRealPart(F)) ||
    747:                 stol*PetscAbsReal(PetscRealPart(u)) > PetscAbsReal(PetscRealPart(y))) {
    748:               break;
    749:             }
    750:           }
    751:           x[j][i] = u;
    752:         }
    753:       }
    754:     }
    755:     /*
    756:      Restore vector
    757:      */
    758:     DMDAVecRestoreArray(da,localX,&x);
    759:     DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
    760:     DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
    761:   }
    762:   PetscLogFlops(tot_its*(21.0));
    763:   DMRestoreLocalVector(da,&localX);
    764:   if (B) {
    765:     DMDAVecRestoreArray(da,localB,&b);
    766:     DMRestoreLocalVector(da,&localB);
    767:   }
    768:   return(0);
    769: }

    771: /*TEST

    773:    test:
    774:      suffix: asm_0
    775:      requires: !single
    776:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu

    778:    test:
    779:      suffix: msm_0
    780:      requires: !single
    781:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu

    783:    test:
    784:      suffix: asm_1
    785:      requires: !single
    786:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    788:    test:
    789:      suffix: msm_1
    790:      requires: !single
    791:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

    793:    test:
    794:      suffix: asm_2
    795:      requires: !single
    796:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    798:    test:
    799:      suffix: msm_2
    800:      requires: !single
    801:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

    803:    test:
    804:      suffix: asm_3
    805:      requires: !single
    806:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    808:    test:
    809:      suffix: msm_3
    810:      requires: !single
    811:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

    813:    test:
    814:      suffix: asm_4
    815:      requires: !single
    816:      nsize: 2
    817:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    819:    test:
    820:      suffix: msm_4
    821:      requires: !single
    822:      nsize: 2
    823:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

    825:    test:
    826:      suffix: asm_5
    827:      requires: !single
    828:      nsize: 2
    829:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    831:    test:
    832:      suffix: msm_5
    833:      requires: !single
    834:      nsize: 2
    835:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

    837:    test:
    838:      args: -snes_rtol 1.e-5 -pc_type mg -ksp_monitor_short -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17 -mg_levels_ksp_monitor_short -mg_levels_ksp_norm_type unpreconditioned -snes_monitor_short -mg_levels_ksp_chebyshev_esteig 0.5,1.1 -mg_levels_pc_type sor -pc_mg_type full
    839:      requires: !single

    841:    test:
    842:      suffix: 2
    843:      args: -pc_type mg -ksp_converged_reason -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3 -mg_levels_ksp_norm_type unpreconditioned -snes_monitor_short -mg_levels_ksp_chebyshev_esteig 0.5,1.1 -mg_levels_pc_type sor -pc_mg_type full -ksp_atol -1.

    845:    test:
    846:      suffix: 3
    847:      nsize: 2
    848:      args: -snes_grid_sequence 2 -snes_mf_operator -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -snes_rtol 1.e-2
    849:      filter: grep -v "otal number of function evaluations"

    851:    test:
    852:      suffix: 4
    853:      nsize: 2
    854:      args: -snes_grid_sequence 2 -snes_monitor_short -ksp_converged_reason -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -ksp_atol -1

    856:    test:
    857:      suffix: 5_anderson
    858:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type anderson

    860:    test:
    861:      suffix: 5_aspin
    862:      nsize: 4
    863:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type aspin -snes_view

    865:    test:
    866:      suffix: 5_broyden
    867:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type qn -snes_qn_type broyden -snes_qn_m 10

    869:    test:
    870:      suffix: 5_fas
    871:      args: -fas_coarse_snes_max_it 1 -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_monitor_short -snes_type fas -fas_coarse_ksp_type richardson -da_refine 6
    872:      requires: !single

    874:    test:
    875:      suffix: 5_fas_additive
    876:      args: -fas_coarse_snes_max_it 1 -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_monitor_short -snes_type fas -fas_coarse_ksp_type richardson -da_refine 6 -snes_fas_type additive -snes_max_it 50

    878:    test:
    879:      suffix: 5_fas_monitor
    880:      args: -da_refine 1 -snes_type fas -snes_fas_monitor
    881:      requires: !single

    883:    test:
    884:      suffix: 5_ls
    885:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls

    887:    test:
    888:      suffix: 5_ls_sell_sor
    889:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls -dm_mat_type sell -pc_type sor
    890:      output_file: output/ex5_5_ls.out

    892:    test:
    893:      suffix: 5_nasm
    894:      nsize: 4
    895:      args: -snes_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type nasm -snes_nasm_type restrict -snes_max_it 10

    897:    test:
    898:      suffix: 5_ncg
    899:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ncg -snes_ncg_type fr

    901:    test:
    902:      suffix: 5_newton_asm_dmda
    903:      nsize: 4
    904:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type newtonls -pc_type asm -pc_asm_dm_subdomains -malloc_dump
    905:      requires: !single

    907:    test:
    908:      suffix: 5_newton_gasm_dmda
    909:      nsize: 4
    910:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type newtonls -pc_type gasm -malloc_dump
    911:      requires: !single

    913:    test:
    914:      suffix: 5_ngmres
    915:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -snes_ngmres_m 10

    917:    test:
    918:      suffix: 5_ngmres_fas
    919:      args: -snes_rtol 1.e-4 -snes_type ngmres -npc_fas_coarse_snes_max_it 1 -npc_fas_coarse_snes_type newtonls -npc_fas_coarse_pc_type lu -npc_fas_coarse_ksp_type preonly -snes_ngmres_m 10 -snes_monitor_short -npc_snes_max_it 1 -npc_snes_type fas -npc_fas_coarse_ksp_type richardson -da_refine 6

    921:    test:
    922:      suffix: 5_ngmres_ngs
    923:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -npc_snes_type ngs -npc_snes_max_it 1

    925:    test:
    926:      suffix: 5_ngmres_nrichardson
    927:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -snes_ngmres_m 10 -npc_snes_type nrichardson -npc_snes_max_it 3
    928:      output_file: output/ex5_5_ngmres_richardson.out

    930:    test:
    931:      suffix: 5_nrichardson
    932:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type nrichardson

    934:    test:
    935:      suffix: 5_qn
    936:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type qn -snes_linesearch_type cp -snes_qn_m 10

    938:    test:
    939:      suffix: 6
    940:      nsize: 4
    941:      args: -snes_converged_reason -ksp_converged_reason -da_grid_x 129 -da_grid_y 129 -pc_type mg -pc_mg_levels 8 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.5,0,1.1 -mg_levels_ksp_max_it 2

    943:    test:
    944:      requires: complex !single
    945:      suffix: complex
    946:      args: -snes_mf_operator -mat_mffd_complex -snes_monitor

    948: TEST*/