Actual source code: ex2.c

petsc-master 2020-11-28
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  1: static char help[] = "Solve a toy 2D problem on a staggered grid\n\n";
  2: /*

  4:   To demonstrate the basic functionality of DMStag, solves an isoviscous
  5:   incompressible Stokes problem on a rectangular 2D domain, using a manufactured
  6:   solution.

  8:   u_xx + u_yy - p_x = f^x
  9:   v_xx + v_yy - p_y = f^y
 10:   u_x + v_y         = g

 12:   g is 0 in the physical case.

 14:   Boundary conditions give prescribed flow perpendicular to the boundaries,
 15:   and zero derivative perpendicular to them (free slip).

 17:   Use the -pinpressure option to fix a pressure node, instead of providing
 18:   a constant-pressure nullspace. This allows use of direct solvers, e.g. to
 19:   use UMFPACK,

 21:      ./ex2 -pinpressure 1 -pc_type lu -pc_factor_mat_solver_type umfpack

 23:   This example demonstrates the use of DMProduct to efficiently store coordinates
 24:   on an orthogonal grid.

 26: */
 27: #include <petscdm.h>
 28: #include <petscksp.h>
 29: #include <petscdmstag.h>

 31: /* Shorter, more convenient names for DMStagStencilLocation entries */
 32: #define DOWN_LEFT  DMSTAG_DOWN_LEFT
 33: #define DOWN       DMSTAG_DOWN
 34: #define DOWN_RIGHT DMSTAG_DOWN_RIGHT
 35: #define LEFT       DMSTAG_LEFT
 36: #define ELEMENT    DMSTAG_ELEMENT
 37: #define RIGHT      DMSTAG_RIGHT
 38: #define UP_LEFT    DMSTAG_UP_LEFT
 39: #define UP         DMSTAG_UP
 40: #define UP_RIGHT   DMSTAG_UP_RIGHT

 42: static PetscErrorCode CreateSystem(DM,Mat*,Vec*,PetscBool);
 43: static PetscErrorCode CreateReferenceSolution(DM,Vec*);
 44: static PetscErrorCode AttachNullspace(DM,Mat);
 45: static PetscErrorCode CheckSolution(Vec,Vec);

 47: /* Manufactured solution. Chosen to be higher order than can be solved exactly,
 48: and to have a zero derivative for flow parallel to the boundaries. That is,
 49: d(ux)/dy = 0 at the top and bottom boundaries, and d(uy)/dx = 0 at the right
 50: and left boundaries. */
 51: static PetscScalar uxRef(PetscScalar x,PetscScalar y){return 0.0*x + y*y - 2.0*y*y*y + y*y*y*y;}      /* no x-dependence  */
 52: static PetscScalar uyRef(PetscScalar x,PetscScalar y) {return x*x - 2.0*x*x*x + x*x*x*x + 0.0*y;}      /* no y-dependence  */
 53: static PetscScalar pRef (PetscScalar x,PetscScalar y) {return -1.0*(x-0.5) + -3.0/2.0*y*y + 0.5;}    /* zero integral    */
 54: static PetscScalar fx   (PetscScalar x,PetscScalar y) {return 0.0*x + 2.0 -12.0*y + 12.0*y*y + 1.0;} /* no x-dependence  */
 55: static PetscScalar fy   (PetscScalar x,PetscScalar y) {return 2.0 -12.0*x + 12.0*x*x + 3.0*y;}
 56: static PetscScalar g    (PetscScalar x,PetscScalar y) {return 0.0*x*y;}                              /* identically zero */

 58: int main(int argc,char **argv)
 59: {
 61:   DM             dmSol;
 62:   Vec            sol,solRef,rhs;
 63:   Mat            A;
 64:   KSP            ksp;
 65:   PC             pc;
 66:   PetscBool      pinPressure;

 68:   /* Initialize PETSc and process command line arguments */
 69:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 70:   pinPressure = PETSC_TRUE;
 71:   PetscOptionsGetBool(NULL,NULL,"-pinpressure",&pinPressure,NULL);

 73:   /* Create 2D DMStag for the solution, and set up. */
 74:   {
 75:     const PetscInt dof0 = 0, dof1 = 1,dof2 = 1; /* 1 dof on each edge and element center */
 76:     const PetscInt stencilWidth = 1;
 77:     DMStagCreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,7,9,PETSC_DECIDE,PETSC_DECIDE,dof0,dof1,dof2,DMSTAG_STENCIL_BOX,stencilWidth,NULL,NULL,&dmSol);
 78:     DMSetFromOptions(dmSol);
 79:     DMSetUp(dmSol);
 80:   }

 82:   /* Define uniform coordinates as a product of 1D arrays */
 83:   DMStagSetUniformCoordinatesProduct(dmSol,0.0,1.0,0.0,1.0,0.0,0.0);

 85:   /* Compute (manufactured) reference solution */
 86:   CreateReferenceSolution(dmSol,&solRef);

 88:   /* Assemble system */
 89:   CreateSystem(dmSol,&A,&rhs,pinPressure);

 91:   /* Attach a constant-pressure nullspace to the operator
 92:   (logically, this should be in CreateSystem, but we separate it here to highlight
 93:    the features of DMStag exposed, in particular DMStagMigrateVec()) */
 94:   if (!pinPressure) {
 95:     AttachNullspace(dmSol,A);
 96:   }

 98:   /* Solve, using the default FieldSplit (Approximate Block Factorization) Preconditioner
 99:      This is not intended to be an example of a good solver!  */
100:   DMCreateGlobalVector(dmSol,&sol);
101:   KSPCreate(PETSC_COMM_WORLD,&ksp);
102:   KSPSetType(ksp,KSPFGMRES);
103:   KSPSetOperators(ksp,A,A);
104:   KSPGetPC(ksp,&pc);
105:   PCSetType(pc,PCFIELDSPLIT);
106:   PCFieldSplitSetDetectSaddlePoint(pc,PETSC_TRUE);
107:   KSPSetFromOptions(ksp);
108:   KSPSolve(ksp,rhs,sol);

110:   /* Check Solution */
111:   CheckSolution(sol,solRef);

113:   /* Clean up and finalize PETSc */
114:   KSPDestroy(&ksp);
115:   VecDestroy(&sol);
116:   VecDestroy(&solRef);
117:   VecDestroy(&rhs);
118:   MatDestroy(&A);
119:   DMDestroy(&dmSol);
120:   PetscFinalize();
121:   return ierr;
122: }

124: /*
125: Note: this system is not well-scaled! Generally one would adjust the equations
126:  to try to get matrix entries to be of comparable order, regardless of grid spacing
127:  or choice of coefficients.
128: */
129: static PetscErrorCode CreateSystem(DM dmSol,Mat *pA,Vec *pRhs, PetscBool pinPressure)
130: {
132:   PetscInt       N[2];
133:   PetscInt       ex,ey,startx,starty,nx,ny;
134:   PetscInt       iprev,icenter,inext;
135:   Mat            A;
136:   Vec            rhs;
137:   PetscReal      hx,hy;
138:   PetscScalar    **cArrX,**cArrY;

140:   /* Here, we showcase two different methods for manipulating local vector entries.
141:      One can use DMStagStencil objects with DMStagVecSetValuesStencil(),
142:      making sure to call VecAssemble[Begin/End]() after all values are set.
143:      Alternately, one can use DMStagVecGetArray[Read]() and DMStagVecRestoreArray[Read]().
144:      The first approach is used to build the rhs, and the second is used to
145:      obtain coordinate values. Working with the array is almost certainly more efficient,
146:      but only allows setting local entries, requires understanding which "slot" to use,
147:      and doesn't correspond as precisely to the matrix assembly process using DMStagStencil objects */

150:   DMCreateMatrix(dmSol,pA);
151:   A = *pA;
152:   DMCreateGlobalVector(dmSol,pRhs);
153:   rhs = *pRhs;
154:   DMStagGetCorners(dmSol,&startx,&starty,NULL,&nx,&ny,NULL,NULL,NULL,NULL);
155:   DMStagGetGlobalSizes(dmSol,&N[0],&N[1],NULL);
156:   hx = 1.0/N[0]; hy = 1.0/N[1];
157:   DMStagGetProductCoordinateArraysRead(dmSol,&cArrX,&cArrY,NULL);
158:   DMStagGetProductCoordinateLocationSlot(dmSol,ELEMENT,&icenter);
159:   DMStagGetProductCoordinateLocationSlot(dmSol,LEFT,&iprev);
160:   DMStagGetProductCoordinateLocationSlot(dmSol,RIGHT,&inext);

162:   /* Loop over all local elements. Note that it may be more efficient in real
163:      applications to loop over each boundary separately */
164:   for (ey = starty; ey<starty+ny; ++ey) { /* With DMStag, always iterate x fastest, y second fastest, z slowest */
165:     for (ex = startx; ex<startx+nx; ++ex) {

167:       if (ex == N[0]-1) {
168:         /* Right Boundary velocity Dirichlet */
169:         DMStagStencil row;
170:         PetscScalar   valRhs;
171:         const PetscScalar valA = 1.0;
172:         row.i = ex; row.j = ey; row.loc = RIGHT; row.c = 0;
173:         DMStagMatSetValuesStencil(dmSol,A,1,&row,1,&row,&valA,INSERT_VALUES);
174:         valRhs = uxRef(cArrX[ex][inext],cArrY[ey][icenter]);
175:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
176:       }
177:       if (ey == N[1]-1) {
178:         /* Top boundary velocity Dirichlet */
179:         DMStagStencil row;
180:         PetscScalar   valRhs;
181:         const PetscScalar valA = 1.0;
182:         row.i = ex; row.j = ey; row.loc = UP; row.c = 0;
183:         DMStagMatSetValuesStencil(dmSol,A,1,&row,1,&row,&valA,INSERT_VALUES);
184:         valRhs = uyRef(cArrX[ex][icenter],cArrY[ey][inext]);
185:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
186:       }

188:       if (ey == 0) {
189:         /* Bottom boundary velocity Dirichlet */
190:         DMStagStencil row;
191:         PetscScalar   valRhs;
192:         const PetscScalar valA = 1.0;
193:         row.i = ex; row.j = ey; row.loc = DOWN; row.c = 0;
194:         DMStagMatSetValuesStencil(dmSol,A,1,&row,1,&row,&valA,INSERT_VALUES);
195:         valRhs = uyRef(cArrX[ex][icenter],cArrY[ey][iprev]);
196:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
197:       } else {
198:         /* Y-momentum equation : (u_xx + u_yy) - p_y = f^y */
199:         DMStagStencil row,col[7];
200:         PetscScalar   valA[7],valRhs;
201:         PetscInt      nEntries;

203:         row.i    = ex  ; row.j    = ey  ; row.loc    = DOWN;    row.c     = 0;
204:         if (ex == 0) {
205:           nEntries = 6;
206:           col[0].i = ex  ; col[0].j = ey  ; col[0].loc = DOWN;    col[0].c  = 0; valA[0] = -1.0 / (hx*hx) -2.0 / (hy*hy);
207:           col[1].i = ex  ; col[1].j = ey-1; col[1].loc = DOWN;    col[1].c  = 0; valA[1] =  1.0 / (hy*hy);
208:           col[2].i = ex  ; col[2].j = ey+1; col[2].loc = DOWN;    col[2].c  = 0; valA[2] =  1.0 / (hy*hy);
209:           /* Missing left element */
210:           col[3].i = ex+1; col[3].j = ey  ; col[3].loc = DOWN;    col[3].c  = 0; valA[3] =  1.0 / (hx*hx);
211:           col[4].i = ex  ; col[4].j = ey-1; col[4].loc = ELEMENT; col[4].c  = 0; valA[4] =  1.0 / hy;
212:           col[5].i = ex  ; col[5].j = ey  ; col[5].loc = ELEMENT; col[5].c  = 0; valA[5] = -1.0 / hy;
213:         } else if (ex == N[0]-1) {
214:           /* Right boundary y velocity stencil */
215:           nEntries = 6;
216:           col[0].i = ex  ; col[0].j = ey  ; col[0].loc = DOWN;    col[0].c  = 0; valA[0] = -1.0 / (hx*hx) -2.0 / (hy*hy);
217:           col[1].i = ex  ; col[1].j = ey-1; col[1].loc = DOWN;    col[1].c  = 0; valA[1] =  1.0 / (hy*hy);
218:           col[2].i = ex  ; col[2].j = ey+1; col[2].loc = DOWN;    col[2].c  = 0; valA[2] =  1.0 / (hy*hy);
219:           col[3].i = ex-1; col[3].j = ey  ; col[3].loc = DOWN;    col[3].c  = 0; valA[3] =  1.0 / (hx*hx);
220:           /* Missing right element */
221:           col[4].i = ex  ; col[4].j = ey-1; col[4].loc = ELEMENT; col[4].c  = 0; valA[4] =  1.0 / hy;
222:           col[5].i = ex  ; col[5].j = ey  ; col[5].loc = ELEMENT; col[5].c  = 0; valA[5] = -1.0 / hy;
223:         } else {
224:           nEntries = 7;
225:           col[0].i = ex  ; col[0].j = ey  ; col[0].loc = DOWN;    col[0].c  = 0; valA[0] = -2.0 / (hx*hx) -2.0 / (hy*hy);
226:           col[1].i = ex  ; col[1].j = ey-1; col[1].loc = DOWN;    col[1].c  = 0; valA[1] =  1.0 / (hy*hy);
227:           col[2].i = ex  ; col[2].j = ey+1; col[2].loc = DOWN;    col[2].c  = 0; valA[2] =  1.0 / (hy*hy);
228:           col[3].i = ex-1; col[3].j = ey  ; col[3].loc = DOWN;    col[3].c  = 0; valA[3] =  1.0 / (hx*hx);
229:           col[4].i = ex+1; col[4].j = ey  ; col[4].loc = DOWN;    col[4].c  = 0; valA[4] =  1.0 / (hx*hx);
230:           col[5].i = ex  ; col[5].j = ey-1; col[5].loc = ELEMENT; col[5].c  = 0; valA[5] =  1.0 / hy;
231:           col[6].i = ex  ; col[6].j = ey  ; col[6].loc = ELEMENT; col[6].c  = 0; valA[6] = -1.0 / hy;
232:         }
233:         DMStagMatSetValuesStencil(dmSol,A,1,&row,nEntries,col,valA,INSERT_VALUES);
234:         valRhs = fy(cArrX[ex][icenter],cArrY[ey][iprev]);
235:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
236:       }

238:       if (ex == 0) {
239:         /* Left velocity Dirichlet */
240:         DMStagStencil row;
241:         PetscScalar   valRhs;
242:         const PetscScalar valA = 1.0;
243:         row.i = ex; row.j = ey; row.loc = LEFT; row.c = 0;
244:         DMStagMatSetValuesStencil(dmSol,A,1,&row,1,&row,&valA,INSERT_VALUES);
245:         valRhs = uxRef(cArrX[ex][iprev],cArrY[ey][icenter]);
246:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
247:       } else {
248:         /* X-momentum equation : (u_xx + u_yy) - p_x = f^x */
249:         DMStagStencil row,col[7];
250:         PetscScalar   valA[7],valRhs;
251:         PetscInt      nEntries;
252:         row.i    = ex  ; row.j    = ey  ; row.loc    = LEFT;    row.c     = 0;

254:         if (ey == 0) {
255:           nEntries = 6;
256:           col[0].i = ex  ; col[0].j = ey  ; col[0].loc = LEFT;    col[0].c  = 0; valA[0] = -2.0 /(hx*hx) -1.0 /(hy*hy);
257:           /* missing term from element below */
258:           col[1].i = ex  ; col[1].j = ey+1; col[1].loc = LEFT;    col[1].c  = 0; valA[1] =  1.0 / (hy*hy);
259:           col[2].i = ex-1; col[2].j = ey  ; col[2].loc = LEFT;    col[2].c  = 0; valA[2] =  1.0 / (hx*hx);
260:           col[3].i = ex+1; col[3].j = ey  ; col[3].loc = LEFT;    col[3].c  = 0; valA[3] =  1.0 / (hx*hx);
261:           col[4].i = ex-1; col[4].j = ey  ; col[4].loc = ELEMENT; col[4].c  = 0; valA[4] =  1.0 / hx;
262:           col[5].i = ex  ; col[5].j = ey  ; col[5].loc = ELEMENT; col[5].c  = 0; valA[5] = -1.0 / hx;
263:         } else if (ey == N[1]-1) {
264:           /* Top boundary x velocity stencil */
265:           nEntries = 6;
266:           row.i    = ex  ; row.j    = ey  ; row.loc    = LEFT;    row.c     = 0;
267:           col[0].i = ex  ; col[0].j = ey  ; col[0].loc = LEFT;    col[0].c  = 0; valA[0] = -2.0 / (hx*hx) -1.0 / (hy*hy);
268:           col[1].i = ex  ; col[1].j = ey-1; col[1].loc = LEFT;    col[1].c  = 0; valA[1] =  1.0 / (hy*hy);
269:           /* Missing element above term */
270:           col[2].i = ex-1; col[2].j = ey  ; col[2].loc = LEFT;    col[2].c  = 0; valA[2] =  1.0 / (hx*hx);
271:           col[3].i = ex+1; col[3].j = ey  ; col[3].loc = LEFT;    col[3].c  = 0; valA[3] =  1.0 / (hx*hx);
272:           col[4].i = ex-1; col[4].j = ey  ; col[4].loc = ELEMENT; col[4].c  = 0; valA[4] =  1.0 / hx;
273:           col[5].i = ex  ; col[5].j = ey  ; col[5].loc = ELEMENT; col[5].c  = 0; valA[5] = -1.0 / hx;
274:         } else {
275:           /* Note how this is identical to the stencil for U_y, with "DOWN" replaced by "LEFT" and the pressure derivative in the other direction */
276:           nEntries = 7;
277:           col[0].i = ex  ; col[0].j = ey  ; col[0].loc = LEFT;    col[0].c  = 0; valA[0] = -2.0 / (hx*hx) + -2.0 / (hy*hy);
278:           col[1].i = ex  ; col[1].j = ey-1; col[1].loc = LEFT;    col[1].c  = 0; valA[1] =  1.0 / (hy*hy);
279:           col[2].i = ex  ; col[2].j = ey+1; col[2].loc = LEFT;    col[2].c  = 0; valA[2] =  1.0 / (hy*hy);
280:           col[3].i = ex-1; col[3].j = ey  ; col[3].loc = LEFT;    col[3].c  = 0; valA[3] =  1.0 / (hx*hx);
281:           col[4].i = ex+1; col[4].j = ey  ; col[4].loc = LEFT;    col[4].c  = 0; valA[4] =  1.0 / (hx*hx);
282:           col[5].i = ex-1; col[5].j = ey  ; col[5].loc = ELEMENT; col[5].c  = 0; valA[5] =  1.0 / hx;
283:           col[6].i = ex  ; col[6].j = ey  ; col[6].loc = ELEMENT; col[6].c  = 0; valA[6] = -1.0 / hx;

285:         }
286:         DMStagMatSetValuesStencil(dmSol,A,1,&row,nEntries,col,valA,INSERT_VALUES);
287:         valRhs = fx(cArrX[ex][iprev],cArrY[ey][icenter]);
288:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
289:       }

291:       /* P equation : u_x + v_y = g
292:          Note that this includes an explicit zero on the diagonal. This is only needed for
293:          direct solvers (not required if using an iterative solver and setting the constant-pressure nullspace) */
294:       if (pinPressure && ex == 0 && ey == 0) { /* Pin the first pressure node, if requested */
295:         DMStagStencil row;
296:         PetscScalar valA,valRhs;
297:         row.i = ex; row.j = ey; row.loc  = ELEMENT; row.c = 0;
298:         valA = 1.0;
299:         DMStagMatSetValuesStencil(dmSol,A,1,&row,1,&row,&valA,INSERT_VALUES);
300:         valRhs = pRef(cArrX[ex][icenter],cArrY[ey][icenter]);
301:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
302:       } else {
303:         DMStagStencil row,col[5];
304:         PetscScalar   valA[5],valRhs;

306:         row.i    = ex; row.j    = ey; row.loc    = ELEMENT; row.c    = 0;
307:         col[0].i = ex; col[0].j = ey; col[0].loc = LEFT;    col[0].c = 0; valA[0] = -1.0 / hx;
308:         col[1].i = ex; col[1].j = ey; col[1].loc = RIGHT;   col[1].c = 0; valA[1] =  1.0 / hx;
309:         col[2].i = ex; col[2].j = ey; col[2].loc = DOWN;    col[2].c = 0; valA[2] = -1.0 / hy;
310:         col[3].i = ex; col[3].j = ey; col[3].loc = UP;      col[3].c = 0; valA[3] =  1.0 / hy;
311:         col[4] = row;                                                     valA[4] = 0.0;
312:         DMStagMatSetValuesStencil(dmSol,A,1,&row,5,col,valA,INSERT_VALUES);
313:         valRhs = g(cArrX[ex][icenter],cArrY[ey][icenter]);
314:         DMStagVecSetValuesStencil(dmSol,rhs,1,&row,&valRhs,INSERT_VALUES);
315:       }
316:     }
317:   }
318:   DMStagRestoreProductCoordinateArraysRead(dmSol,&cArrX,&cArrY,NULL);
319:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
320:   VecAssemblyBegin(rhs);
321:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
322:   VecAssemblyEnd(rhs);
323:   return(0);
324: }

326: /* Create a pressure-only DMStag and use it to generate a nullspace vector
327:    - Create a compatible DMStag with one dof per element (and nothing else).
328:    - Create a constant vector and normalize it
329:    - Migrate it to a vector on the original dmSol (making use of the fact
330:    that this will fill in zeros for "extra" dof)
331:    - Set the nullspace for the operator
332:    - Destroy everything (the operator keeps the references it needs) */
333: static PetscErrorCode AttachNullspace(DM dmSol,Mat A)
334: {
336:   DM             dmPressure;
337:   Vec            constantPressure,basis;
338:   PetscReal      nrm;
339:   MatNullSpace   matNullSpace;

342:   DMStagCreateCompatibleDMStag(dmSol,0,0,1,0,&dmPressure);
343:   DMGetGlobalVector(dmPressure,&constantPressure);
344:   VecSet(constantPressure,1.0);
345:   VecNorm(constantPressure,NORM_2,&nrm);
346:   VecScale(constantPressure,1.0/nrm);
347:   DMCreateGlobalVector(dmSol,&basis);
348:   DMStagMigrateVec(dmPressure,constantPressure,dmSol,basis);
349:   MatNullSpaceCreate(PetscObjectComm((PetscObject)dmSol),PETSC_FALSE,1,&basis,&matNullSpace);
350:   VecDestroy(&basis);
351:   VecDestroy(&constantPressure);
352:   MatSetNullSpace(A,matNullSpace);
353:   MatNullSpaceDestroy(&matNullSpace);
354:   return(0);
355: }

357: /* Create a reference solution.
358:    Here, we use the more direct method of iterating over arrays.  */
359: static PetscErrorCode CreateReferenceSolution(DM dmSol,Vec *pSolRef)
360: {
362:   PetscInt       startx,starty,nx,ny,nExtra[2],ex,ey;
363:   PetscInt       iuy,iux,ip,iprev,icenter;
364:   PetscScalar    ***arrSol,**cArrX,**cArrY;
365:   Vec            solRefLocal;

368:   DMCreateGlobalVector(dmSol,pSolRef);
369:   DMGetLocalVector(dmSol,&solRefLocal);

371:   /* Obtain indices to use in the raw arrays */
372:   DMStagGetLocationSlot(dmSol,DOWN,0,&iuy);
373:   DMStagGetLocationSlot(dmSol,LEFT,0,&iux);
374:   DMStagGetLocationSlot(dmSol,ELEMENT,0,&ip);

376:   /* Use high-level convenience functions to get raw arrays and indices for 1d coordinates */
377:   DMStagGetProductCoordinateArraysRead(dmSol,&cArrX,&cArrY,NULL);
378:   DMStagGetProductCoordinateLocationSlot(dmSol,ELEMENT,&icenter);
379:   DMStagGetProductCoordinateLocationSlot(dmSol,LEFT,&iprev);

381:   DMStagVecGetArray(dmSol,solRefLocal,&arrSol);
382:   DMStagGetCorners(dmSol,&startx,&starty,NULL,&nx,&ny,NULL,&nExtra[0],&nExtra[1],NULL);
383:   for (ey=starty; ey<starty + ny + nExtra[1]; ++ey) {
384:     for (ex=startx; ex<startx + nx + nExtra[0]; ++ex) {
385:       arrSol[ey][ex][iuy] = uyRef(cArrX[ex][icenter],cArrY[ey][iprev]);
386:       arrSol[ey][ex][iux] = uxRef(cArrX[ex][iprev],cArrY[ey][icenter]);
387:       if (ey < starty+ny && ex < startx+nx) { /* Don't fill on the dummy elements (though you could, and these values would just be ignored) */
388:         arrSol[ey][ex][ip]  = pRef(cArrX[ex][icenter],cArrY[ey][icenter]);
389:       }
390:     }
391:   }
392:   DMStagVecRestoreArray(dmSol,solRefLocal,&arrSol);
393:   DMStagRestoreProductCoordinateArraysRead(dmSol,&cArrX,&cArrY,NULL);
394:   DMLocalToGlobal(dmSol,solRefLocal,INSERT_VALUES,*pSolRef);
395:   DMRestoreLocalVector(dmSol,&solRefLocal);
396:   return(0);
397: }

399: static PetscErrorCode CheckSolution(Vec sol,Vec solRef)
400: {
402:   Vec            diff;
403:   PetscReal      normsolRef,errAbs,errRel;

406:   VecDuplicate(sol,&diff);
407:   VecCopy(sol,diff);
408:   VecAXPY(diff,-1.0,solRef);
409:   VecNorm(diff,NORM_2,&errAbs);
410:   VecNorm(solRef,NORM_2,&normsolRef);
411:   errRel = errAbs/normsolRef;
412:   PetscPrintf(PETSC_COMM_WORLD,"Error (abs): %g\nError (rel): %g\n",(double)errAbs,(double)errRel);
413:   VecDestroy(&diff);
414:   return(0);
415: }

417: /*TEST

419:    test:
420:       suffix: 1
421:       nsize: 4
422:       args: -ksp_monitor_short -ksp_converged_reason

424:    test:
425:       suffix: direct_umfpack
426:       requires: suitesparse
427:       nsize: 1
428:       args: -pinpressure 1 -stag_grid_x 8 -stag_grid_y 6 -ksp_monitor_short -pc_type lu -pc_factor_mat_solver_type umfpack

430: TEST*/