Date: 2022-03-04T17:39:25+00:00

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*/

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

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

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

     24:     with boundary conditions

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

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

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

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

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

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

     44:   ------------------------------------------------------------------------- */

     46: /*
     47:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     48:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     49: */
     50: #include <petscdm.h>
     51: #include <petscdmda.h>
     52: #include <petscsnes.h>
     53: #include <petscmatlab.h>
     54: #include <petsc/private/snesimpl.h>

     56: /*
     57:    User-defined application context - contains data needed by the
     58:    application-provided call-back routines, FormJacobianLocal() and
     59:    FormFunctionLocal().
     60: */
     61: typedef struct AppCtx AppCtx;
     62: struct AppCtx {
     63:   PetscReal param;          /* test problem parameter */
     64:   PetscInt  m,n;            /* MMS3 parameters */
     65:   PetscErrorCode (*mms_solution)(AppCtx*,const DMDACoor2d*,PetscScalar*);
     66:   PetscErrorCode (*mms_forcing)(AppCtx*,const DMDACoor2d*,PetscScalar*);
     67: };

     69: /*
     70:    User-defined routines
     71: */
     72: extern PetscErrorCode FormInitialGuess(DM,AppCtx*,Vec);
     73: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
     74: extern PetscErrorCode FormExactSolution(DM,AppCtx*,Vec);
     75: extern PetscErrorCode ZeroBCSolution(AppCtx*,const DMDACoor2d*,PetscScalar*);
     76: extern PetscErrorCode MMSSolution1(AppCtx*,const DMDACoor2d*,PetscScalar*);
     77: extern PetscErrorCode MMSForcing1(AppCtx*,const DMDACoor2d*,PetscScalar*);
     78: extern PetscErrorCode MMSSolution2(AppCtx*,const DMDACoor2d*,PetscScalar*);
     79: extern PetscErrorCode MMSForcing2(AppCtx*,const DMDACoor2d*,PetscScalar*);
     80: extern PetscErrorCode MMSSolution3(AppCtx*,const DMDACoor2d*,PetscScalar*);
     81: extern PetscErrorCode MMSForcing3(AppCtx*,const DMDACoor2d*,PetscScalar*);
     82: extern PetscErrorCode MMSSolution4(AppCtx*,const DMDACoor2d*,PetscScalar*);
     83: extern PetscErrorCode MMSForcing4(AppCtx*,const DMDACoor2d*,PetscScalar*);
     84: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,Mat,AppCtx*);
     85: extern PetscErrorCode FormObjectiveLocal(DMDALocalInfo*,PetscScalar**,PetscReal*,AppCtx*);
     86: extern PetscErrorCode FormFunctionMatlab(SNES,Vec,Vec,void*);
     87: extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*);

     89: int main(int argc,char **argv)
     90: {
     91:   SNES           snes;                         /* nonlinear solver */
     92:   Vec            x;                            /* solution vector */
     93:   AppCtx         user;                         /* user-defined work context */
     94:   PetscInt       its;                          /* iterations for convergence */
     96:   PetscReal      bratu_lambda_max = 6.81;
     97:   PetscReal      bratu_lambda_min = 0.;
     98:   PetscInt       MMS              = 0;
     99:   PetscBool      flg              = PETSC_FALSE;
    100:   DM             da;
    101:   Vec            r               = NULL;
    102:   KSP            ksp;
    103:   PetscInt       lits,slits;

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:      Initialize program
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:      Initialize problem parameters
    113:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    114:   user.param = 6.0;
    115:   PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);
    116:   if (user.param > bratu_lambda_max || user.param < bratu_lambda_min) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Lambda, %g, is out of range, [%g, %g]", user.param, bratu_lambda_min, bratu_lambda_max);
    117:   PetscOptionsGetInt(NULL,NULL,"-mms",&MMS,NULL);
    118:   if (MMS == 3) {
    119:     PetscInt mPar = 2, nPar = 1;
    120:     PetscOptionsGetInt(NULL,NULL,"-m_par",&mPar,NULL);
    121:     PetscOptionsGetInt(NULL,NULL,"-n_par",&nPar,NULL);
    122:     user.m = PetscPowInt(2,mPar);
    123:     user.n = PetscPowInt(2,nPar);
    124:   }

    126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    127:      Create nonlinear solver context
    128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    129:   SNESCreate(PETSC_COMM_WORLD,&snes);
    130:   SNESSetCountersReset(snes,PETSC_FALSE);
    131:   SNESSetNGS(snes, NonlinearGS, NULL);

    133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    134:      Create distributed array (DMDA) to manage parallel grid and vectors
    135:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    136:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
    137:   DMSetFromOptions(da);
    138:   DMSetUp(da);
    139:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
    140:   DMSetApplicationContext(da,&user);
    141:   SNESSetDM(snes,da);
    142:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:      Extract global vectors from DMDA; then duplicate for remaining
    144:      vectors that are the same types
    145:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    146:   DMCreateGlobalVector(da,&x);

    148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    149:      Set local function evaluation routine
    150:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    151:   user.mms_solution = ZeroBCSolution;
    152:   switch (MMS) {
    153:   case 0: user.mms_solution = NULL; user.mms_forcing = NULL;
    154:   case 1: user.mms_solution = MMSSolution1; user.mms_forcing = MMSForcing1; break;
    155:   case 2: user.mms_solution = MMSSolution2; user.mms_forcing = MMSForcing2; break;
    156:   case 3: user.mms_solution = MMSSolution3; user.mms_forcing = MMSForcing3; break;
    157:   case 4: user.mms_solution = MMSSolution4; user.mms_forcing = MMSForcing4; break;
    158:   default: SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_USER,"Unknown MMS type %d",MMS);
    159:   }
    160:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(DMDASNESFunction)FormFunctionLocal,&user);
    161:   PetscOptionsGetBool(NULL,NULL,"-fd",&flg,NULL);
    162:   if (!flg) {
    163:     DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);
    164:   }

    166:   PetscOptionsGetBool(NULL,NULL,"-obj",&flg,NULL);
    167:   if (flg) {
    168:     DMDASNESSetObjectiveLocal(da,(DMDASNESObjective)FormObjectiveLocal,&user);
    169:   }

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

    180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    181:      Customize nonlinear solver; set runtime options
    182:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    183:   SNESSetFromOptions(snes);

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

    187:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    188:      Solve nonlinear system
    189:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    190:   SNESSolve(snes,NULL,x);
    191:   SNESGetIterationNumber(snes,&its);

    193:   SNESGetLinearSolveIterations(snes,&slits);
    194:   SNESGetKSP(snes,&ksp);
    195:   KSPGetTotalIterations(ksp,&lits);
    196:   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);
    197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    198:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    201:      If using MMS, check the l_2 error
    202:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    203:   if (MMS) {
    204:     Vec       e;
    205:     PetscReal errorl2, errorinf;
    206:     PetscInt  N;

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

    223:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    224:      Free work space.  All PETSc objects should be destroyed when they
    225:      are no longer needed.
    226:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    227:   VecDestroy(&r);
    228:   VecDestroy(&x);
    229:   SNESDestroy(&snes);
    230:   DMDestroy(&da);
    231:   PetscFinalize();
    232:   return ierr;
    233: }
    234: /* ------------------------------------------------------------------- */
    235: /*
    236:    FormInitialGuess - Forms initial approximation.

    238:    Input Parameters:
    239:    da - The DM
    240:    user - user-defined application context

    242:    Output Parameter:
    243:    X - vector
    244:  */
    245: PetscErrorCode FormInitialGuess(DM da,AppCtx *user,Vec X)
    246: {
    247:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
    249:   PetscReal      lambda,temp1,temp,hx,hy;
    250:   PetscScalar    **x;

    253:   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);

    255:   lambda = user->param;
    256:   hx     = 1.0/(PetscReal)(Mx-1);
    257:   hy     = 1.0/(PetscReal)(My-1);
    258:   temp1  = lambda/(lambda + 1.0);

    260:   /*
    261:      Get a pointer to vector data.
    262:        - For default PETSc vectors, VecGetArray() returns a pointer to
    263:          the data array.  Otherwise, the routine is implementation dependent.
    264:        - You MUST call VecRestoreArray() when you no longer need access to
    265:          the array.
    266:   */
    267:   DMDAVecGetArray(da,X,&x);

    269:   /*
    270:      Get local grid boundaries (for 2-dimensional DMDA):
    271:        xs, ys   - starting grid indices (no ghost points)
    272:        xm, ym   - widths of local grid (no ghost points)

    274:   */
    275:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    277:   /*
    278:      Compute initial guess over the locally owned part of the grid
    279:   */
    280:   for (j=ys; j<ys+ym; j++) {
    281:     temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
    282:     for (i=xs; i<xs+xm; i++) {
    283:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    284:         /* boundary conditions are all zero Dirichlet */
    285:         x[j][i] = 0.0;
    286:       } else {
    287:         x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
    288:       }
    289:     }
    290:   }

    292:   /*
    293:      Restore vector
    294:   */
    295:   DMDAVecRestoreArray(da,X,&x);
    296:   return(0);
    297: }

    299: /*
    300:   FormExactSolution - Forms MMS solution

    302:   Input Parameters:
    303:   da - The DM
    304:   user - user-defined application context

    306:   Output Parameter:
    307:   X - vector
    308:  */
    309: PetscErrorCode FormExactSolution(DM da, AppCtx *user, Vec U)
    310: {
    311:   DM             coordDA;
    312:   Vec            coordinates;
    313:   DMDACoor2d   **coords;
    314:   PetscScalar  **u;
    315:   PetscInt       xs, ys, xm, ym, i, j;

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

    334: PetscErrorCode ZeroBCSolution(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    335: {
    336:   u[0] = 0.;
    337:   return 0;
    338: }

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

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

    344:   such that u(x,y) is an exact solution with f(x,y) as the right hand side forcing term.
    345:  */
    346: PetscErrorCode MMSSolution1(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    347: {
    348:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    349:   u[0] = x*(1 - x)*y*(1 - y);
    350:   PetscLogFlops(5);
    351:   return 0;
    352: }
    353: PetscErrorCode MMSForcing1(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    354: {
    355:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    356:   f[0] = 2*x*(1 - x) + 2*y*(1 - y) - user->param*PetscExpReal(x*(1 - x)*y*(1 - y));
    357:   return 0;
    358: }

    360: PetscErrorCode MMSSolution2(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    361: {
    362:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    363:   u[0] = PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y);
    364:   PetscLogFlops(5);
    365:   return 0;
    366: }
    367: PetscErrorCode MMSForcing2(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    368: {
    369:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    370:   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));
    371:   return 0;
    372: }

    374: PetscErrorCode MMSSolution3(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    375: {
    376:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    377:   u[0] = PetscSinReal(user->m*PETSC_PI*x*(1-y))*PetscSinReal(user->n*PETSC_PI*y*(1-x));
    378:   PetscLogFlops(5);
    379:   return 0;
    380: }
    381: PetscErrorCode MMSForcing3(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    382: {
    383:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    384:   PetscReal m = user->m, n = user->n, lambda = user->param;
    385:   f[0] = (-(PetscExpReal(PetscSinReal(m*PETSC_PI*x*(1 - y))*PetscSinReal(n*PETSC_PI*(1 - x)*y))*lambda)
    386:           + 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)
    387:                                 + (PetscSqr(m)*(PetscSqr(x) + PetscSqr(-1 + y)) + PetscSqr(n)*(PetscSqr(-1 + x) + PetscSqr(y)))
    388:                                 *PetscSinReal(m*PETSC_PI*x*(-1 + y))*PetscSinReal(n*PETSC_PI*(-1 + x)*y)));
    389:   return 0;
    390: }

    392: PetscErrorCode MMSSolution4(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
    393: {
    394:   const PetscReal Lx = 1.,Ly = 1.;
    395:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    396:   u[0] = (PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y));
    397:   PetscLogFlops(9);
    398:   return 0;
    399: }
    400: PetscErrorCode MMSForcing4(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
    401: {
    402:   const PetscReal Lx = 1.,Ly = 1.;
    403:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
    404:   f[0] = (2*PetscSqr(x)*(PetscSqr(x)-PetscSqr(Lx))*(PetscSqr(Ly)-6*PetscSqr(y))
    405:           + 2*PetscSqr(y)*(PetscSqr(Lx)-6*PetscSqr(x))*(PetscSqr(y)-PetscSqr(Ly))
    406:           - user->param*PetscExpReal((PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y))));
    407:   return 0;
    408: }

    410: /* ------------------------------------------------------------------- */
    411: /*
    412:    FormFunctionLocal - Evaluates nonlinear function, F(x) on local process patch

    414:  */
    415: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
    416: {
    418:   PetscInt       i,j;
    419:   PetscReal      lambda,hx,hy,hxdhy,hydhx;
    420:   PetscScalar    u,ue,uw,un,us,uxx,uyy,mms_solution,mms_forcing;
    421:   DMDACoor2d     c;

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

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

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

    464: /* FormObjectiveLocal - Evaluates nonlinear function, F(x) on local process patch */
    465: PetscErrorCode FormObjectiveLocal(DMDALocalInfo *info,PetscScalar **x,PetscReal *obj,AppCtx *user)
    466: {
    468:   PetscInt       i,j;
    469:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc,lobj=0;
    470:   PetscScalar    u,ue,uw,un,us,uxux,uyuy;
    471:   MPI_Comm       comm;

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

    496:         if (i-1 == 0) uw = 0.;
    497:         if (i+1 == info->mx-1) ue = 0.;
    498:         if (j-1 == 0) un = 0.;
    499:         if (j+1 == info->my-1) us = 0.;

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

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

    506:         lobj += PetscRealPart(0.5*(uxux + uyuy) - sc*PetscExpScalar(u));
    507:       }
    508:     }
    509:   }
    510:   PetscLogFlops(12.0*info->ym*info->xm);
    511:   MPI_Allreduce(&lobj,obj,1,MPIU_REAL,MPIU_SUM,comm);
    512:   return(0);
    513: }

    515: /*
    516:    FormJacobianLocal - Evaluates Jacobian matrix on local process patch
    517: */
    518: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,Mat jacpre,AppCtx *user)
    519: {
    521:   PetscInt       i,j,k;
    522:   MatStencil     col[5],row;
    523:   PetscScalar    lambda,v[5],hx,hy,hxdhy,hydhx,sc;
    524:   DM             coordDA;
    525:   Vec            coordinates;
    526:   DMDACoor2d   **coords;

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

    541:   /*
    542:      Compute entries for the locally owned part of the Jacobian.
    543:       - Currently, all PETSc parallel matrix formats are partitioned by
    544:         contiguous chunks of rows across the processors.
    545:       - Each processor needs to insert only elements that it owns
    546:         locally (but any non-local elements will be sent to the
    547:         appropriate processor during matrix assembly).
    548:       - Here, we set all entries for a particular row at once.
    549:       - We can set matrix entries either using either
    550:         MatSetValuesLocal() or MatSetValues(), as discussed above.
    551:   */
    552:   for (j=info->ys; j<info->ys+info->ym; j++) {
    553:     for (i=info->xs; i<info->xs+info->xm; i++) {
    554:       row.j = j; row.i = i;
    555:       /* boundary points */
    556:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
    557:         v[0] =  2.0*(hydhx + hxdhy);
    558:         MatSetValuesStencil(jacpre,1,&row,1,&row,v,INSERT_VALUES);
    559:       } else {
    560:         k = 0;
    561:         /* interior grid points */
    562:         if (j-1 != 0) {
    563:           v[k]     = -hxdhy;
    564:           col[k].j = j - 1; col[k].i = i;
    565:           k++;
    566:         }
    567:         if (i-1 != 0) {
    568:           v[k]     = -hydhx;
    569:           col[k].j = j;     col[k].i = i-1;
    570:           k++;
    571:         }

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

    575:         if (i+1 != info->mx-1) {
    576:           v[k]     = -hydhx;
    577:           col[k].j = j;     col[k].i = i+1;
    578:           k++;
    579:         }
    580:         if (j+1 != info->mx-1) {
    581:           v[k]     = -hxdhy;
    582:           col[k].j = j + 1; col[k].i = i;
    583:           k++;
    584:         }
    585:         MatSetValuesStencil(jacpre,1,&row,k,col,v,INSERT_VALUES);
    586:       }
    587:     }
    588:   }

    590:   /*
    591:      Assemble matrix, using the 2-step process:
    592:        MatAssemblyBegin(), MatAssemblyEnd().
    593:   */
    594:   MatAssemblyBegin(jacpre,MAT_FINAL_ASSEMBLY);
    595:   MatAssemblyEnd(jacpre,MAT_FINAL_ASSEMBLY);
    596:   /*
    597:      Tell the matrix we will never add a new nonzero location to the
    598:      matrix. If we do, it will generate an error.
    599:   */
    600:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    601:   return(0);
    602: }

    604: PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
    605: {
    606: #if PetscDefined(HAVE_MATLAB_ENGINE)
    607:   AppCtx         *user = (AppCtx*)ptr;
    609:   PetscInt       Mx,My;
    610:   PetscReal      lambda,hx,hy;
    611:   Vec            localX,localF;
    612:   MPI_Comm       comm;
    613:   DM             da;

    616:   SNESGetDM(snes,&da);
    617:   DMGetLocalVector(da,&localX);
    618:   DMGetLocalVector(da,&localF);
    619:   PetscObjectSetName((PetscObject)localX,"localX");
    620:   PetscObjectSetName((PetscObject)localF,"localF");
    621:   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);

    623:   lambda = user->param;
    624:   hx     = 1.0/(PetscReal)(Mx-1);
    625:   hy     = 1.0/(PetscReal)(My-1);

    627:   PetscObjectGetComm((PetscObject)snes,&comm);
    628:   /*
    629:      Scatter ghost points to local vector,using the 2-step process
    630:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    631:      By placing code between these two statements, computations can be
    632:      done while messages are in transition.
    633:   */
    634:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    635:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
    636:   PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);
    637:   PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);
    638:   PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);

    640:   /*
    641:      Insert values into global vector
    642:   */
    643:   DMLocalToGlobalBegin(da,localF,INSERT_VALUES,F);
    644:   DMLocalToGlobalEnd(da,localF,INSERT_VALUES,F);
    645:   DMRestoreLocalVector(da,&localX);
    646:   DMRestoreLocalVector(da,&localF);
    647:   return(0);
    648: #else
    649:     return 0;                     /* Never called */
    650: #endif
    651: }

    653: /* ------------------------------------------------------------------- */
    654: /*
    655:       Applies some sweeps on nonlinear Gauss-Seidel on each process

    657:  */
    658: PetscErrorCode NonlinearGS(SNES snes,Vec X, Vec B, void *ctx)
    659: {
    660:   PetscInt       i,j,k,Mx,My,xs,ys,xm,ym,its,tot_its,sweeps,l;
    662:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc;
    663:   PetscScalar    **x,**b,bij,F,F0=0,J,u,un,us,ue,eu,uw,uxx,uyy,y;
    664:   PetscReal      atol,rtol,stol;
    665:   DM             da;
    666:   AppCtx         *user;
    667:   Vec            localX,localB;

    670:   tot_its = 0;
    671:   SNESNGSGetSweeps(snes,&sweeps);
    672:   SNESNGSGetTolerances(snes,&atol,&rtol,&stol,&its);
    673:   SNESGetDM(snes,&da);
    674:   DMGetApplicationContext(da,&user);

    676:   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);

    678:   lambda = user->param;
    679:   hx     = 1.0/(PetscReal)(Mx-1);
    680:   hy     = 1.0/(PetscReal)(My-1);
    681:   sc     = hx*hy*lambda;
    682:   hxdhy  = hx/hy;
    683:   hydhx  = hy/hx;

    685:   DMGetLocalVector(da,&localX);
    686:   if (B) {
    687:     DMGetLocalVector(da,&localB);
    688:   }
    689:   for (l=0; l<sweeps; l++) {

    691:     DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    692:     DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
    693:     if (B) {
    694:       DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);
    695:       DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);
    696:     }
    697:     /*
    698:      Get a pointer to vector data.
    699:      - For default PETSc vectors, VecGetArray() returns a pointer to
    700:      the data array.  Otherwise, the routine is implementation dependent.
    701:      - You MUST call VecRestoreArray() when you no longer need access to
    702:      the array.
    703:      */
    704:     DMDAVecGetArray(da,localX,&x);
    705:     if (B) {DMDAVecGetArray(da,localB,&b);}
    706:     /*
    707:      Get local grid boundaries (for 2-dimensional DMDA):
    708:      xs, ys   - starting grid indices (no ghost points)
    709:      xm, ym   - widths of local grid (no ghost points)
    710:      */
    711:     DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    713:     for (j=ys; j<ys+ym; j++) {
    714:       for (i=xs; i<xs+xm; i++) {
    715:         if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    716:           /* boundary conditions are all zero Dirichlet */
    717:           x[j][i] = 0.0;
    718:         } else {
    719:           if (B) bij = b[j][i];
    720:           else   bij = 0.;

    722:           u  = x[j][i];
    723:           un = x[j-1][i];
    724:           us = x[j+1][i];
    725:           ue = x[j][i-1];
    726:           uw = x[j][i+1];

    728:           for (k=0; k<its; k++) {
    729:             eu  = PetscExpScalar(u);
    730:             uxx = (2.0*u - ue - uw)*hydhx;
    731:             uyy = (2.0*u - un - us)*hxdhy;
    732:             F   = uxx + uyy - sc*eu - bij;
    733:             if (k == 0) F0 = F;
    734:             J  = 2.0*(hydhx + hxdhy) - sc*eu;
    735:             y  = F/J;
    736:             u -= y;
    737:             tot_its++;

    739:             if (atol > PetscAbsReal(PetscRealPart(F)) ||
    740:                 rtol*PetscAbsReal(PetscRealPart(F0)) > PetscAbsReal(PetscRealPart(F)) ||
    741:                 stol*PetscAbsReal(PetscRealPart(u)) > PetscAbsReal(PetscRealPart(y))) {
    742:               break;
    743:             }
    744:           }
    745:           x[j][i] = u;
    746:         }
    747:       }
    748:     }
    749:     /*
    750:      Restore vector
    751:      */
    752:     DMDAVecRestoreArray(da,localX,&x);
    753:     DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
    754:     DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
    755:   }
    756:   PetscLogFlops(tot_its*(21.0));
    757:   DMRestoreLocalVector(da,&localX);
    758:   if (B) {
    759:     DMDAVecRestoreArray(da,localB,&b);
    760:     DMRestoreLocalVector(da,&localB);
    761:   }
    762:   return(0);
    763: }

    765: /*TEST

    767:    test:
    768:      suffix: asm_0
    769:      requires: !single
    770:      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

    772:    test:
    773:      suffix: msm_0
    774:      requires: !single
    775:      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

    777:    test:
    778:      suffix: asm_1
    779:      requires: !single
    780:      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

    782:    test:
    783:      suffix: msm_1
    784:      requires: !single
    785:      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

    787:    test:
    788:      suffix: asm_2
    789:      requires: !single
    790:      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

    792:    test:
    793:      suffix: msm_2
    794:      requires: !single
    795:      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

    797:    test:
    798:      suffix: asm_3
    799:      requires: !single
    800:      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

    802:    test:
    803:      suffix: msm_3
    804:      requires: !single
    805:      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

    807:    test:
    808:      suffix: asm_4
    809:      requires: !single
    810:      nsize: 2
    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 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    813:    test:
    814:      suffix: msm_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 multiplicative -sub_pc_type lu -da_grid_x 8

    819:    test:
    820:      suffix: asm_5
    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 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

    825:    test:
    826:      suffix: msm_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 multiplicative -sub_pc_type lu -da_grid_x 8

    831:    test:
    832:      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
    833:      requires: !single

    835:    test:
    836:      suffix: 2
    837:      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.

    839:    test:
    840:      suffix: 3
    841:      nsize: 2
    842:      args: -snes_grid_sequence 2 -snes_mf_operator -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -snes_rtol 1.e-2
    843:      filter: grep -v "otal number of function evaluations"

    845:    test:
    846:      suffix: 4
    847:      nsize: 2
    848:      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

    850:    test:
    851:      suffix: 5_anderson
    852:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type anderson

    854:    test:
    855:      suffix: 5_aspin
    856:      nsize: 4
    857:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type aspin -snes_view

    859:    test:
    860:      suffix: 5_broyden
    861:      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

    863:    test:
    864:      suffix: 5_fas
    865:      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
    866:      requires: !single

    868:    test:
    869:      suffix: 5_fas_additive
    870:      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

    872:    test:
    873:      suffix: 5_fas_monitor
    874:      args: -da_refine 1 -snes_type fas -snes_fas_monitor
    875:      requires: !single

    877:    test:
    878:      suffix: 5_ls
    879:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls

    881:    test:
    882:      suffix: 5_ls_sell_sor
    883:      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
    884:      output_file: output/ex5_5_ls.out

    886:    test:
    887:      suffix: 5_nasm
    888:      nsize: 4
    889:      args: -snes_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type nasm -snes_nasm_type restrict -snes_max_it 10

    891:    test:
    892:      suffix: 5_ncg
    893:      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

    895:    test:
    896:      suffix: 5_newton_asm_dmda
    897:      nsize: 4
    898:      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
    899:      requires: !single

    901:    test:
    902:      suffix: 5_newton_gasm_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 gasm -malloc_dump
    905:      requires: !single

    907:    test:
    908:      suffix: 5_ngmres
    909:      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

    911:    test:
    912:      suffix: 5_ngmres_fas
    913:      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

    915:    test:
    916:      suffix: 5_ngmres_ngs
    917:      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

    919:    test:
    920:      suffix: 5_ngmres_nrichardson
    921:      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
    922:      output_file: output/ex5_5_ngmres_richardson.out

    924:    test:
    925:      suffix: 5_nrichardson
    926:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type nrichardson

    928:    test:
    929:      suffix: 5_qn
    930:      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

    932:    test:
    933:      suffix: 6
    934:      nsize: 4
    935:      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

    937:    test:
    938:      requires: complex !single
    939:      suffix: complex
    940:      args: -snes_mf_operator -mat_mffd_complex -snes_monitor

    942: TEST*/