Actual source code: ex5.c

petsc-master 2020-08-10
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  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 Section 1.5 Writing Application Codes with PETSc context - contains data needed by the
 61:    Section 1.5 Writing Application Codes with PETSc-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 Section 1.5 Writing Application Codes with PETSc 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 Section 1.5 Writing Application Codes with PETSc 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*/