Actual source code: ex43.c

petsc-3.10.2 2018-10-09
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  1: static char help[] = "Solves the incompressible, variable viscosity Stokes equation in 2d on the unit domain \n\
  2: using Q1Q1 elements, stabilized with Bochev's polynomial projection method. \n\
  3: The models defined utilise free slip boundary conditions on all sides. \n\
  4: Options: \n"
  5: "\
  6:      -mx : Number of elements in the x-direction \n\
  7:      -my : Number of elements in the y-direction \n\
  8:      -o : Specify output filename for solution (will be petsc binary format or paraview format if the extension is .vts) \n\
  9:      -gnuplot : Output Gauss point coordinates, coefficients and u,p solution in gnuplot format \n\
 10:      -glvis : Visualizes coefficients and u,p solution through GLVIs (use -viewer_glvis_dmda_bs 2,1 to visualize velocity as a vector)\n\
 11:      -c_str : Indicates the structure of the coefficients to use \n"
 12: "\
 13:           -c_str 0 => Coefficient definition for an analytic solution with a vertical jump in viscosity at x = xc \n\
 14:                       This problem is driven by the forcing function f(x,y) = (0, sin(nz pi y)cos(pi x) \n\
 15:                          Parameters: \n\
 16:                               -solcx_eta0  : Viscosity to the left of the interface \n\
 17:                               -solcx_eta1  : Viscosity to the right of the interface \n\
 18:                               -solcx_xc    : Location of the interface \n\
 19:                               -solcx_nz    : Wavenumber in the y direction \n"
 20: "\
 21:           -c_str 1 => Coefficient definition for a dense rectangular blob located at the center of the domain \n\
 22:                          Parameters: \n\
 23:                               -sinker_eta0 : Viscosity of the background fluid \n\
 24:                               -sinker_eta1 : Viscosity of the blob \n\
 25:                               -sinker_dx   : Width of the blob \n\
 26:                               -sinker_dy   : Height of the blob \n"
 27: "\
 28:           -c_str 2 => Coefficient definition for a dense circular blob located at the center of the domain \n\
 29:                          Parameters: \n\
 30:                               -sinker_eta0 : Viscosity of the background fluid \n\
 31:                               -sinker_eta1 : Viscosity of the blob \n\
 32:                               -sinker_r    : Radius of the blob \n"
 33: "\
 34:           -c_str 3 => Coefficient definition for a dense circular and rectangular inclusion (located at the center of the domain) \n\
 35:                               -sinker_eta0 : Viscosity of the background fluid \n\
 36:                               -sinker_eta1 : Viscosity of the two inclusions \n\
 37:                               -sinker_r    : Radius of the circular inclusion \n\
 38:                               -sinker_c0x  : Origin (x-coord) of the circular inclusion \n\
 39:                               -sinker_c0y  : Origin (y-coord) of the circular inclusion \n\
 40:                               -sinker_dx   : Width of the rectangular inclusion \n\
 41:                               -sinker_dy   : Height of the rectangular inclusion \n\
 42:                               -sinker_phi  : Rotation angle of the rectangular inclusion \n"
 43: "\
 44:           -c_str 4 => Coefficient definition for checkerboard jumps aligned with the domain decomposition \n\
 45:                               -jump_eta0      : Viscosity for black subdomains \n\
 46:                               -jump_magnitude : Magnitude of jumps. White subdomains will have eta = eta0*10^magnitude \n\
 47:                               -jump_nz        : Wavenumber in the y direction for rhs \n"
 48: "\
 49:      -use_gp_coords : Evaluate the viscosity and force term at the global coordinates of each quadrature point \n\
 50:                       By default, the viscosity and force term are evaulated at the element center and applied as a constant over the entire element \n";

 52: /* Contributed by Dave May */

 54:  #include <petscksp.h>
 55:  #include <petscdm.h>
 56:  #include <petscdmda.h>

 58: /* A Maple-generated exact solution created by Mirko Velic (mirko.velic@sci.monash.edu.au) */
 59: #include "ex43-solcx.h"

 61: static PetscErrorCode DMDABCApplyFreeSlip(DM,Mat,Vec);


 64: #define NSD            2 /* number of spatial dimensions */
 65: #define NODES_PER_EL   4 /* nodes per element */
 66: #define U_DOFS         2 /* degrees of freedom per velocity node */
 67: #define P_DOFS         1 /* degrees of freedom per pressure node */
 68: #define GAUSS_POINTS   4

 70: /* Gauss point based evaluation 8+4+4+4 = 20 */
 71: typedef struct {
 72:   PetscScalar gp_coords[2*GAUSS_POINTS];
 73:   PetscScalar eta[GAUSS_POINTS];
 74:   PetscScalar fx[GAUSS_POINTS];
 75:   PetscScalar fy[GAUSS_POINTS];
 76: } GaussPointCoefficients;

 78: typedef struct {
 79:   PetscScalar u_dof;
 80:   PetscScalar v_dof;
 81:   PetscScalar p_dof;
 82: } StokesDOF;

 84: static PetscErrorCode glvis_extract_eta(PetscObject oV,PetscInt nf, PetscObject oVf[], void *ctx)
 85: {
 86:   DM                     properties_da = (DM)(ctx),stokes_da;
 87:   Vec                    V = (Vec)oV, *Vf = (Vec*)oVf;
 88:   GaussPointCoefficients **props;
 89:   PetscInt               sex,sey,mx,my;
 90:   PetscInt               ei,ej,p,cum;
 91:   PetscScalar            *array;
 92:   PetscErrorCode         ierr;

 95:   VecGetDM(Vf[0],&stokes_da);
 96:   DMDAVecGetArrayRead(properties_da,V,&props);
 97:   DMDAGetElementsCorners(stokes_da,&sex,&sey,NULL);
 98:   DMDAGetElementsSizes(stokes_da,&mx,&my,NULL);
 99:   VecGetArray(Vf[0],&array);
100:   cum  = 0;
101:   for (ej = sey; ej < sey+my; ej++) {
102:     for (ei = sex; ei < sex+mx; ei++) {
103:       for (p = 0; p < GAUSS_POINTS; p++) {
104:         array[cum++] = props[ej][ei].eta[p];
105:       }
106:     }
107:   }
108:   VecRestoreArray(Vf[0],&array);
109:   DMDAVecRestoreArrayRead(properties_da,V,&props);
110:   return(0);
111: }

113: /*
114:  Element: Local basis function ordering
115:  1-----2
116:  |     |
117:  |     |
118:  0-----3
119:  */
120: static void ConstructQ12D_Ni(PetscScalar _xi[],PetscScalar Ni[])
121: {
122:   PetscScalar xi  = _xi[0];
123:   PetscScalar eta = _xi[1];

125:   Ni[0] = 0.25*(1.0-xi)*(1.0-eta);
126:   Ni[1] = 0.25*(1.0-xi)*(1.0+eta);
127:   Ni[2] = 0.25*(1.0+xi)*(1.0+eta);
128:   Ni[3] = 0.25*(1.0+xi)*(1.0-eta);
129: }

131: static void ConstructQ12D_GNi(PetscScalar _xi[],PetscScalar GNi[][NODES_PER_EL])
132: {
133:   PetscScalar xi  = _xi[0];
134:   PetscScalar eta = _xi[1];

136:   GNi[0][0] = -0.25*(1.0-eta);
137:   GNi[0][1] = -0.25*(1.0+eta);
138:   GNi[0][2] =   0.25*(1.0+eta);
139:   GNi[0][3] =   0.25*(1.0-eta);

141:   GNi[1][0] = -0.25*(1.0-xi);
142:   GNi[1][1] =   0.25*(1.0-xi);
143:   GNi[1][2] =   0.25*(1.0+xi);
144:   GNi[1][3] = -0.25*(1.0+xi);
145: }

147: static void ConstructQ12D_GNx(PetscScalar GNi[][NODES_PER_EL],PetscScalar GNx[][NODES_PER_EL],PetscScalar coords[],PetscScalar *det_J)
148: {
149:   PetscScalar J00,J01,J10,J11,J;
150:   PetscScalar iJ00,iJ01,iJ10,iJ11;
151:   PetscInt    i;

153:   J00 = J01 = J10 = J11 = 0.0;
154:   for (i = 0; i < NODES_PER_EL; i++) {
155:     PetscScalar cx = coords[2*i];
156:     PetscScalar cy = coords[2*i+1];

158:     J00 = J00+GNi[0][i]*cx;      /* J_xx = dx/dxi */
159:     J01 = J01+GNi[0][i]*cy;      /* J_xy = dy/dxi */
160:     J10 = J10+GNi[1][i]*cx;      /* J_yx = dx/deta */
161:     J11 = J11+GNi[1][i]*cy;      /* J_yy = dy/deta */
162:   }
163:   J = (J00*J11)-(J01*J10);

165:   iJ00 =  J11/J;
166:   iJ01 = -J01/J;
167:   iJ10 = -J10/J;
168:   iJ11 =  J00/J;

170:   for (i = 0; i < NODES_PER_EL; i++) {
171:     GNx[0][i] = GNi[0][i]*iJ00+GNi[1][i]*iJ01;
172:     GNx[1][i] = GNi[0][i]*iJ10+GNi[1][i]*iJ11;
173:   }

175:   if (det_J) *det_J = J;
176: }

178: static void ConstructGaussQuadrature(PetscInt *ngp,PetscScalar gp_xi[][2],PetscScalar gp_weight[])
179: {
180:   *ngp         = 4;
181:   gp_xi[0][0]  = -0.57735026919; gp_xi[0][1] = -0.57735026919;
182:   gp_xi[1][0]  = -0.57735026919; gp_xi[1][1] =  0.57735026919;
183:   gp_xi[2][0]  =  0.57735026919; gp_xi[2][1] =  0.57735026919;
184:   gp_xi[3][0]  =  0.57735026919; gp_xi[3][1] = -0.57735026919;
185:   gp_weight[0] = 1.0;
186:   gp_weight[1] = 1.0;
187:   gp_weight[2] = 1.0;
188:   gp_weight[3] = 1.0;
189: }

191: /*
192: i,j are the element indices
193: The unknown is a vector quantity.
194: The s[].c is used to indicate the degree of freedom.
195: */
196: static PetscErrorCode DMDAGetElementEqnums_up(MatStencil s_u[],MatStencil s_p[],PetscInt i,PetscInt j)
197: {
199:   /* velocity */
200:   /* node 0 */
201:   s_u[0].i = i; s_u[0].j = j; s_u[0].c = 0;       /* Vx0 */
202:   s_u[1].i = i; s_u[1].j = j; s_u[1].c = 1;       /* Vy0 */

204:   /* node 1 */
205:   s_u[2].i = i; s_u[2].j = j+1; s_u[2].c = 0;     /* Vx1 */
206:   s_u[3].i = i; s_u[3].j = j+1; s_u[3].c = 1;     /* Vy1 */

208:   /* node 2 */
209:   s_u[4].i = i+1; s_u[4].j = j+1; s_u[4].c = 0;   /* Vx2 */
210:   s_u[5].i = i+1; s_u[5].j = j+1; s_u[5].c = 1;   /* Vy2 */

212:   /* node 3 */
213:   s_u[6].i = i+1; s_u[6].j = j; s_u[6].c = 0;     /* Vx3 */
214:   s_u[7].i = i+1; s_u[7].j = j; s_u[7].c = 1;     /* Vy3 */

216:   /* pressure */
217:   s_p[0].i = i;   s_p[0].j = j;   s_p[0].c = 2; /* P0 */
218:   s_p[1].i = i;   s_p[1].j = j+1; s_p[1].c = 2; /* P1 */
219:   s_p[2].i = i+1; s_p[2].j = j+1; s_p[2].c = 2; /* P2 */
220:   s_p[3].i = i+1; s_p[3].j = j;   s_p[3].c = 2; /* P3 */
221:   return(0);
222: }

224: static PetscErrorCode DMDAGetElementOwnershipRanges2d(DM da,PetscInt **_lx,PetscInt **_ly)
225: {
227:   PetscMPIInt    rank;
228:   PetscInt       proc_I,proc_J;
229:   PetscInt       cpu_x,cpu_y;
230:   PetscInt       local_mx,local_my;
231:   Vec            vlx,vly;
232:   PetscInt       *LX,*LY,i;
233:   PetscScalar    *_a;
234:   Vec            V_SEQ;
235:   VecScatter     ctx;

238:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

240:   DMDAGetInfo(da,0,0,0,0,&cpu_x,&cpu_y,0,0,0,0,0,0,0);

242:   proc_J = rank/cpu_x;
243:   proc_I = rank-cpu_x*proc_J;

245:   PetscMalloc1(cpu_x,&LX);
246:   PetscMalloc1(cpu_y,&LY);

248:   DMDAGetElementsSizes(da,&local_mx,&local_my,NULL);
249:   VecCreate(PETSC_COMM_WORLD,&vlx);
250:   VecSetSizes(vlx,PETSC_DECIDE,cpu_x);
251:   VecSetFromOptions(vlx);

253:   VecCreate(PETSC_COMM_WORLD,&vly);
254:   VecSetSizes(vly,PETSC_DECIDE,cpu_y);
255:   VecSetFromOptions(vly);

257:   VecSetValue(vlx,proc_I,(PetscScalar)(local_mx+1.0e-9),INSERT_VALUES);
258:   VecSetValue(vly,proc_J,(PetscScalar)(local_my+1.0e-9),INSERT_VALUES);
259:   VecAssemblyBegin(vlx);VecAssemblyEnd(vlx);
260:   VecAssemblyBegin(vly);VecAssemblyEnd(vly);

262:   VecScatterCreateToAll(vlx,&ctx,&V_SEQ);
263:   VecScatterBegin(ctx,vlx,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
264:   VecScatterEnd(ctx,vlx,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
265:   VecGetArray(V_SEQ,&_a);
266:   for (i = 0; i < cpu_x; i++) LX[i] = (PetscInt)PetscRealPart(_a[i]);
267:   VecRestoreArray(V_SEQ,&_a);
268:   VecScatterDestroy(&ctx);
269:   VecDestroy(&V_SEQ);

271:   VecScatterCreateToAll(vly,&ctx,&V_SEQ);
272:   VecScatterBegin(ctx,vly,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
273:   VecScatterEnd(ctx,vly,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
274:   VecGetArray(V_SEQ,&_a);
275:   for (i = 0; i < cpu_y; i++) LY[i] = (PetscInt)PetscRealPart(_a[i]);
276:   VecRestoreArray(V_SEQ,&_a);
277:   VecScatterDestroy(&ctx);
278:   VecDestroy(&V_SEQ);

280:   *_lx = LX;
281:   *_ly = LY;

283:   VecDestroy(&vlx);
284:   VecDestroy(&vly);
285:   return(0);
286: }

288: static PetscErrorCode DMDACoordViewGnuplot2d(DM da,const char prefix[])
289: {
290:   DM             cda;
291:   Vec            coords;
292:   DMDACoor2d     **_coords;
293:   PetscInt       si,sj,nx,ny,i,j;
294:   FILE           *fp;
295:   char           fname[PETSC_MAX_PATH_LEN];
296:   PetscMPIInt    rank;

300:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
301:   PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
302:   PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
303:   if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");

305:   PetscFPrintf(PETSC_COMM_SELF,fp,"### Element geometry for processor %1.4d ### \n",rank);

307:   DMGetCoordinateDM(da,&cda);
308:   DMGetCoordinatesLocal(da,&coords);
309:   DMDAVecGetArrayRead(cda,coords,&_coords);
310:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
311:   for (j = sj; j < sj+ny-1; j++) {
312:     for (i = si; i < si+nx-1; i++) {
313:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",(double)PetscRealPart(_coords[j][i].x),(double)PetscRealPart(_coords[j][i].y));
314:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",(double)PetscRealPart(_coords[j+1][i].x),(double)PetscRealPart(_coords[j+1][i].y));
315:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",(double)PetscRealPart(_coords[j+1][i+1].x),(double)PetscRealPart(_coords[j+1][i+1].y));
316:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",(double)PetscRealPart(_coords[j][i+1].x),(double)PetscRealPart(_coords[j][i+1].y));
317:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n\n",(double)PetscRealPart(_coords[j][i].x),(double)PetscRealPart(_coords[j][i].y));
318:     }
319:   }
320:   DMDAVecRestoreArrayRead(cda,coords,&_coords);

322:   PetscFClose(PETSC_COMM_SELF,fp);
323:   return(0);
324: }

326: static PetscErrorCode DMDAViewGnuplot2d(DM da,Vec fields,const char comment[],const char prefix[])
327: {
328:   DM             cda;
329:   Vec            coords,local_fields;
330:   DMDACoor2d     **_coords;
331:   FILE           *fp;
332:   char           fname[PETSC_MAX_PATH_LEN];
333:   PetscMPIInt    rank;
334:   PetscInt       si,sj,nx,ny,i,j;
335:   PetscInt       n_dofs,d;
336:   PetscScalar    *_fields;

340:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
341:   PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
342:   PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
343:   if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");

345:   PetscFPrintf(PETSC_COMM_SELF,fp,"### %s (processor %1.4d) ### \n",comment,rank);
346:   DMDAGetInfo(da,0,0,0,0,0,0,0,&n_dofs,0,0,0,0,0);
347:   PetscFPrintf(PETSC_COMM_SELF,fp,"### x y ");
348:   for (d = 0; d < n_dofs; d++) {
349:     const char *field_name;
350:     DMDAGetFieldName(da,d,&field_name);
351:     PetscFPrintf(PETSC_COMM_SELF,fp,"%s ",field_name);
352:   }
353:   PetscFPrintf(PETSC_COMM_SELF,fp,"###\n");

355:   DMGetCoordinateDM(da,&cda);
356:   DMGetCoordinatesLocal(da,&coords);
357:   DMDAVecGetArray(cda,coords,&_coords);
358:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);

360:   DMCreateLocalVector(da,&local_fields);
361:   DMGlobalToLocalBegin(da,fields,INSERT_VALUES,local_fields);
362:   DMGlobalToLocalEnd(da,fields,INSERT_VALUES,local_fields);
363:   VecGetArray(local_fields,&_fields);

365:   for (j = sj; j < sj+ny; j++) {
366:     for (i = si; i < si+nx; i++) {
367:       PetscScalar coord_x,coord_y;
368:       PetscScalar field_d;

370:       coord_x = _coords[j][i].x;
371:       coord_y = _coords[j][i].y;

373:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e ",(double)PetscRealPart(coord_x),(double)PetscRealPart(coord_y));
374:       for (d = 0; d < n_dofs; d++) {
375:         field_d = _fields[n_dofs*((i-si)+(j-sj)*(nx))+d];
376:         PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e ",(double)PetscRealPart(field_d));
377:       }
378:       PetscFPrintf(PETSC_COMM_SELF,fp,"\n");
379:     }
380:   }
381:   VecRestoreArray(local_fields,&_fields);
382:   VecDestroy(&local_fields);

384:   DMDAVecRestoreArray(cda,coords,&_coords);

386:   PetscFClose(PETSC_COMM_SELF,fp);
387:   return(0);
388: }

390: static PetscErrorCode DMDAViewCoefficientsGnuplot2d(DM da,Vec fields,const char comment[],const char prefix[])
391: {
392:   DM                     cda;
393:   Vec                    local_fields;
394:   FILE                   *fp;
395:   char                   fname[PETSC_MAX_PATH_LEN];
396:   PetscMPIInt            rank;
397:   PetscInt               si,sj,nx,ny,i,j,p;
398:   PetscInt               n_dofs,d;
399:   GaussPointCoefficients **_coefficients;
400:   PetscErrorCode         ierr;

403:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
404:   PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
405:   PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
406:   if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");

408:   PetscFPrintf(PETSC_COMM_SELF,fp,"### %s (processor %1.4d) ### \n",comment,rank);
409:   DMDAGetInfo(da,0,0,0,0,0,0,0,&n_dofs,0,0,0,0,0);
410:   PetscFPrintf(PETSC_COMM_SELF,fp,"### x y ");
411:   for (d = 0; d < n_dofs; d++) {
412:     const char *field_name;
413:     DMDAGetFieldName(da,d,&field_name);
414:     PetscFPrintf(PETSC_COMM_SELF,fp,"%s ",field_name);
415:   }
416:   PetscFPrintf(PETSC_COMM_SELF,fp,"###\n");

418:   DMGetCoordinateDM(da,&cda);
419:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);

421:   DMCreateLocalVector(da,&local_fields);
422:   DMGlobalToLocalBegin(da,fields,INSERT_VALUES,local_fields);
423:   DMGlobalToLocalEnd(da,fields,INSERT_VALUES,local_fields);
424:   DMDAVecGetArray(da,local_fields,&_coefficients);

426:   for (j = sj; j < sj+ny; j++) {
427:     for (i = si; i < si+nx; i++) {
428:       PetscScalar coord_x,coord_y;

430:       for (p = 0; p < GAUSS_POINTS; p++) {
431:         coord_x = _coefficients[j][i].gp_coords[2*p];
432:         coord_y = _coefficients[j][i].gp_coords[2*p+1];

434:         PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e ",(double)PetscRealPart(coord_x),(double)PetscRealPart(coord_y));

436:         PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e %1.6e",(double)PetscRealPart(_coefficients[j][i].eta[p]),(double)PetscRealPart(_coefficients[j][i].fx[p]),(double)PetscRealPart(_coefficients[j][i].fy[p]));
437:         PetscFPrintf(PETSC_COMM_SELF,fp,"\n");
438:       }
439:     }
440:   }
441:   DMDAVecRestoreArray(da,local_fields,&_coefficients);
442:   VecDestroy(&local_fields);

444:   PetscFClose(PETSC_COMM_SELF,fp);
445:   return(0);
446: }

448: static PetscInt ASS_MAP_wIwDI_uJuDJ(PetscInt wi,PetscInt wd,PetscInt w_NPE,PetscInt w_dof,PetscInt ui,PetscInt ud,PetscInt u_NPE,PetscInt u_dof)
449: {
450:   PetscInt ij;
451:   PetscInt r,c,nc;

453:   nc = u_NPE*u_dof;
454:   r = w_dof*wi+wd;
455:   c = u_dof*ui+ud;
456:   ij = r*nc+c;
457:   return ij;
458: }

460: /*
461:  D = [ 2.eta   0   0   ]
462:      [   0   2.eta 0   ]
463:      [   0     0   eta ]

465:  B = [ d_dx   0   ]
466:      [  0    d_dy ]
467:      [ d_dy  d_dx ]
468: */
469: static void FormStressOperatorQ1(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
470: {
471:   PetscInt       ngp;
472:   PetscScalar    gp_xi[GAUSS_POINTS][2];
473:   PetscScalar    gp_weight[GAUSS_POINTS];
474:   PetscInt       p,i,j,k;
475:   PetscScalar    GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
476:   PetscScalar    J_p,tildeD[3];
477:   PetscScalar    B[3][U_DOFS*NODES_PER_EL];

479:   /* define quadrature rule */
480:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

482:   /* evaluate integral */
483:   for (p = 0; p < ngp; p++) {
484:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
485:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);

487:     for (i = 0; i < NODES_PER_EL; i++) {
488:       PetscScalar d_dx_i = GNx_p[0][i];
489:       PetscScalar d_dy_i = GNx_p[1][i];

491:       B[0][2*i] = d_dx_i;B[0][2*i+1] = 0.0;
492:       B[1][2*i] = 0.0;B[1][2*i+1] = d_dy_i;
493:       B[2][2*i] = d_dy_i;B[2][2*i+1] = d_dx_i;
494:     }

496:     tildeD[0] = 2.0*gp_weight[p]*J_p*eta[p];
497:     tildeD[1] = 2.0*gp_weight[p]*J_p*eta[p];
498:     tildeD[2] =       gp_weight[p]*J_p*eta[p];

500:     /* form Bt tildeD B */
501:     /*
502:     Ke_ij = Bt_ik . D_kl . B_lj
503:           = B_ki . D_kl . B_lj
504:           = B_ki . D_kk . B_kj
505:     */
506:     for (i = 0; i < 8; i++) {
507:       for (j = 0; j < 8; j++) {
508:         for (k = 0; k < 3; k++) { /* Note D is diagonal for stokes */
509:           Ke[i+8*j] = Ke[i+8*j]+B[k][i]*tildeD[k]*B[k][j];
510:         }
511:       }
512:     }
513:   }
514: }

516: static void FormGradientOperatorQ1(PetscScalar Ke[],PetscScalar coords[])
517: {
518:   PetscInt    ngp;
519:   PetscScalar gp_xi[GAUSS_POINTS][2];
520:   PetscScalar gp_weight[GAUSS_POINTS];
521:   PetscInt    p,i,j,di;
522:   PetscScalar Ni_p[NODES_PER_EL];
523:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
524:   PetscScalar J_p,fac;

526:   /* define quadrature rule */
527:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

529:   /* evaluate integral */
530:   for (p = 0; p < ngp; p++) {
531:     ConstructQ12D_Ni(gp_xi[p],Ni_p);
532:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
533:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
534:     fac = gp_weight[p]*J_p;

536:     for (i = 0; i < NODES_PER_EL; i++) { /* u nodes */
537:       for (di = 0; di < NSD; di++) { /* u dofs */
538:         for (j = 0; j < 4; j++) {  /* p nodes, p dofs = 1 (ie no loop) */
539:           PetscInt IJ;
540:           IJ = ASS_MAP_wIwDI_uJuDJ(i,di,NODES_PER_EL,2,j,0,NODES_PER_EL,1);

542:           Ke[IJ] = Ke[IJ]-GNx_p[di][i]*Ni_p[j]*fac;
543:         }
544:       }
545:     }
546:   }
547: }

549: static void FormDivergenceOperatorQ1(PetscScalar De[],PetscScalar coords[])
550: {
551:   PetscScalar Ge[U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL];
552:   PetscInt    i,j;
553:   PetscInt    nr_g,nc_g;

555:   PetscMemzero(Ge,sizeof(PetscScalar)*U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL);
556:   FormGradientOperatorQ1(Ge,coords);

558:   nr_g = U_DOFS*NODES_PER_EL;
559:   nc_g = P_DOFS*NODES_PER_EL;

561:   for (i = 0; i < nr_g; i++) {
562:     for (j = 0; j < nc_g; j++) {
563:       De[nr_g*j+i] = Ge[nc_g*i+j];
564:     }
565:   }
566: }

568: static void FormStabilisationOperatorQ1(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
569: {
570:   PetscInt    ngp;
571:   PetscScalar gp_xi[GAUSS_POINTS][2];
572:   PetscScalar gp_weight[GAUSS_POINTS];
573:   PetscInt    p,i,j;
574:   PetscScalar Ni_p[NODES_PER_EL];
575:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
576:   PetscScalar J_p,fac,eta_avg;

578:   /* define quadrature rule */
579:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

581:   /* evaluate integral */
582:   for (p = 0; p < ngp; p++) {
583:     ConstructQ12D_Ni(gp_xi[p],Ni_p);
584:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
585:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
586:     fac = gp_weight[p]*J_p;

588:     for (i = 0; i < NODES_PER_EL; i++) {
589:       for (j = 0; j < NODES_PER_EL; j++) {
590:         Ke[NODES_PER_EL*i+j] = Ke[NODES_PER_EL*i+j]-fac*(Ni_p[i]*Ni_p[j]-0.0625);
591:       }
592:     }
593:   }

595:   /* scale */
596:   eta_avg = 0.0;
597:   for (p = 0; p < ngp; p++) eta_avg += eta[p];
598:   eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
599:   fac     = 1.0/eta_avg;
600:   for (i = 0; i < NODES_PER_EL; i++) {
601:     for (j = 0; j < NODES_PER_EL; j++) {
602:       Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
603:     }
604:   }
605: }

607: static void FormScaledMassMatrixOperatorQ1(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
608: {
609:   PetscInt    ngp;
610:   PetscScalar gp_xi[GAUSS_POINTS][2];
611:   PetscScalar gp_weight[GAUSS_POINTS];
612:   PetscInt    p,i,j;
613:   PetscScalar Ni_p[NODES_PER_EL];
614:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
615:   PetscScalar J_p,fac,eta_avg;

617:   /* define quadrature rule */
618:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

620:   /* evaluate integral */
621:   for (p = 0; p < ngp; p++) {
622:     ConstructQ12D_Ni(gp_xi[p],Ni_p);
623:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
624:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
625:     fac = gp_weight[p]*J_p;

627:     for (i = 0; i < NODES_PER_EL; i++) {
628:       for (j = 0; j < NODES_PER_EL; j++) {
629:         Ke[NODES_PER_EL*i+j] = Ke[NODES_PER_EL*i+j]-fac*Ni_p[i]*Ni_p[j];
630:       }
631:     }
632:   }

634:   /* scale */
635:   eta_avg = 0.0;
636:   for (p = 0; p < ngp; p++) eta_avg += eta[p];
637:   eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
638:   fac     = 1.0/eta_avg;
639:   for (i = 0; i < NODES_PER_EL; i++) {
640:     for (j = 0; j < NODES_PER_EL; j++) {
641:       Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
642:     }
643:   }
644: }

646: static void FormMomentumRhsQ1(PetscScalar Fe[],PetscScalar coords[],PetscScalar fx[],PetscScalar fy[])
647: {
648:   PetscInt    ngp;
649:   PetscScalar gp_xi[GAUSS_POINTS][2];
650:   PetscScalar gp_weight[GAUSS_POINTS];
651:   PetscInt    p,i;
652:   PetscScalar Ni_p[NODES_PER_EL];
653:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
654:   PetscScalar J_p,fac;

656:   /* define quadrature rule */
657:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

659:   /* evaluate integral */
660:   for (p = 0; p < ngp; p++) {
661:     ConstructQ12D_Ni(gp_xi[p],Ni_p);
662:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
663:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
664:     fac = gp_weight[p]*J_p;

666:     for (i = 0; i < NODES_PER_EL; i++) {
667:       Fe[NSD*i]   += fac*Ni_p[i]*fx[p];
668:       Fe[NSD*i+1] += fac*Ni_p[i]*fy[p];
669:     }
670:   }
671: }

673: static PetscErrorCode GetElementCoords(DMDACoor2d **_coords,PetscInt ei,PetscInt ej,PetscScalar el_coords[])
674: {
676:   /* get coords for the element */
677:   el_coords[NSD*0] = _coords[ej][ei].x;     el_coords[NSD*0+1] = _coords[ej][ei].y;
678:   el_coords[NSD*1] = _coords[ej+1][ei].x;   el_coords[NSD*1+1] = _coords[ej+1][ei].y;
679:   el_coords[NSD*2] = _coords[ej+1][ei+1].x; el_coords[NSD*2+1] = _coords[ej+1][ei+1].y;
680:   el_coords[NSD*3] = _coords[ej][ei+1].x;   el_coords[NSD*3+1] = _coords[ej][ei+1].y;
681:   return(0);
682: }

684: static PetscErrorCode AssembleA_Stokes(Mat A,DM stokes_da,DM properties_da,Vec properties)
685: {
686:   DM                     cda;
687:   Vec                    coords;
688:   DMDACoor2d             **_coords;
689:   MatStencil             u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
690:   MatStencil             p_eqn[NODES_PER_EL*P_DOFS]; /* 1 degrees of freedom */
691:   PetscInt               sex,sey,mx,my;
692:   PetscInt               ei,ej;
693:   PetscScalar            Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
694:   PetscScalar            Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
695:   PetscScalar            De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
696:   PetscScalar            Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
697:   PetscScalar            el_coords[NODES_PER_EL*NSD];
698:   Vec                    local_properties;
699:   GaussPointCoefficients **props;
700:   PetscScalar            *prop_eta;
701:   PetscErrorCode         ierr;

704:   /* setup for coords */
705:   DMGetCoordinateDM(stokes_da,&cda);
706:   DMGetCoordinatesLocal(stokes_da,&coords);
707:   DMDAVecGetArray(cda,coords,&_coords);

709:   /* setup for coefficients */
710:   DMCreateLocalVector(properties_da,&local_properties);
711:   DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
712:   DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
713:   DMDAVecGetArray(properties_da,local_properties,&props);

715:   DMDAGetElementsCorners(stokes_da,&sex,&sey,NULL);
716:   DMDAGetElementsSizes(stokes_da,&mx,&my,NULL);
717:   for (ej = sey; ej < sey+my; ej++) {
718:     for (ei = sex; ei < sex+mx; ei++) {
719:       /* get coords for the element */
720:       GetElementCoords(_coords,ei,ej,el_coords);

722:       /* get coefficients for the element */
723:       prop_eta = props[ej][ei].eta;

725:       /* initialise element stiffness matrix */
726:       PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);
727:       PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);
728:       PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);
729:       PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);

731:       /* form element stiffness matrix */
732:       FormStressOperatorQ1(Ae,el_coords,prop_eta);
733:       FormGradientOperatorQ1(Ge,el_coords);
734:       FormDivergenceOperatorQ1(De,el_coords);
735:       FormStabilisationOperatorQ1(Ce,el_coords,prop_eta);

737:       /* insert element matrix into global matrix */
738:       DMDAGetElementEqnums_up(u_eqn,p_eqn,ei,ej);
739:       MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
740:       MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
741:       MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);
742:       MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
743:     }
744:   }
745:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
746:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

748:   DMDAVecRestoreArray(cda,coords,&_coords);

750:   DMDAVecRestoreArray(properties_da,local_properties,&props);
751:   VecDestroy(&local_properties);
752:   return(0);
753: }

755: static PetscErrorCode AssembleA_PCStokes(Mat A,DM stokes_da,DM properties_da,Vec properties)
756: {
757:   DM                     cda;
758:   Vec                    coords;
759:   DMDACoor2d             **_coords;
760:   MatStencil             u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
761:   MatStencil             p_eqn[NODES_PER_EL*P_DOFS]; /* 1 degrees of freedom */
762:   PetscInt               sex,sey,mx,my;
763:   PetscInt               ei,ej;
764:   PetscScalar            Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
765:   PetscScalar            Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
766:   PetscScalar            De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
767:   PetscScalar            Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
768:   PetscScalar            el_coords[NODES_PER_EL*NSD];
769:   Vec                    local_properties;
770:   GaussPointCoefficients **props;
771:   PetscScalar            *prop_eta;
772:   PetscErrorCode         ierr;

775:   /* setup for coords */
776:   DMGetCoordinateDM(stokes_da,&cda);
777:   DMGetCoordinatesLocal(stokes_da,&coords);
778:   DMDAVecGetArray(cda,coords,&_coords);

780:   /* setup for coefficients */
781:   DMCreateLocalVector(properties_da,&local_properties);
782:   DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
783:   DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
784:   DMDAVecGetArray(properties_da,local_properties,&props);

786:   DMDAGetElementsCorners(stokes_da,&sex,&sey,NULL);
787:   DMDAGetElementsSizes(stokes_da,&mx,&my,NULL);
788:   for (ej = sey; ej < sey+my; ej++) {
789:     for (ei = sex; ei < sex+mx; ei++) {
790:       /* get coords for the element */
791:       GetElementCoords(_coords,ei,ej,el_coords);

793:       /* get coefficients for the element */
794:       prop_eta = props[ej][ei].eta;

796:       /* initialise element stiffness matrix */
797:       PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);
798:       PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);
799:       PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);
800:       PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);

802:       /* form element stiffness matrix */
803:       FormStressOperatorQ1(Ae,el_coords,prop_eta);
804:       FormGradientOperatorQ1(Ge,el_coords);
805:       FormScaledMassMatrixOperatorQ1(Ce,el_coords,prop_eta);

807:       /* insert element matrix into global matrix */
808:       DMDAGetElementEqnums_up(u_eqn,p_eqn,ei,ej);
809:       MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
810:       MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
811:       MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
812:     }
813:   }
814:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
815:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

817:   DMDAVecRestoreArray(cda,coords,&_coords);

819:   DMDAVecRestoreArray(properties_da,local_properties,&props);
820:   VecDestroy(&local_properties);
821:   return(0);
822: }

824: static PetscErrorCode DMDASetValuesLocalStencil_ADD_VALUES(StokesDOF **fields_F,MatStencil u_eqn[],MatStencil p_eqn[],PetscScalar Fe_u[],PetscScalar Fe_p[])
825: {
826:   PetscInt n;

829:   for (n = 0; n < 4; n++) {
830:     fields_F[u_eqn[2*n].j][u_eqn[2*n].i].u_dof     = fields_F[u_eqn[2*n].j][u_eqn[2*n].i].u_dof+Fe_u[2*n];
831:     fields_F[u_eqn[2*n+1].j][u_eqn[2*n+1].i].v_dof = fields_F[u_eqn[2*n+1].j][u_eqn[2*n+1].i].v_dof+Fe_u[2*n+1];
832:     fields_F[p_eqn[n].j][p_eqn[n].i].p_dof         = fields_F[p_eqn[n].j][p_eqn[n].i].p_dof+Fe_p[n];
833:   }
834:   return(0);
835: }

837: static PetscErrorCode AssembleF_Stokes(Vec F,DM stokes_da,DM properties_da,Vec properties)
838: {
839:   DM                     cda;
840:   Vec                    coords;
841:   DMDACoor2d             **_coords;
842:   MatStencil             u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
843:   MatStencil             p_eqn[NODES_PER_EL*P_DOFS]; /* 1 degrees of freedom */
844:   PetscInt               sex,sey,mx,my;
845:   PetscInt               ei,ej;
846:   PetscScalar            Fe[NODES_PER_EL*U_DOFS];
847:   PetscScalar            He[NODES_PER_EL*P_DOFS];
848:   PetscScalar            el_coords[NODES_PER_EL*NSD];
849:   Vec                    local_properties;
850:   GaussPointCoefficients **props;
851:   PetscScalar            *prop_fx,*prop_fy;
852:   Vec                    local_F;
853:   StokesDOF              **ff;
854:   PetscErrorCode         ierr;

857:   /* setup for coords */
858:   DMGetCoordinateDM(stokes_da,&cda);
859:   DMGetCoordinatesLocal(stokes_da,&coords);
860:   DMDAVecGetArray(cda,coords,&_coords);

862:   /* setup for coefficients */
863:   DMGetLocalVector(properties_da,&local_properties);
864:   DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
865:   DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
866:   DMDAVecGetArray(properties_da,local_properties,&props);

868:   /* get acces to the vector */
869:   DMGetLocalVector(stokes_da,&local_F);
870:   VecZeroEntries(local_F);
871:   DMDAVecGetArray(stokes_da,local_F,&ff);

873:   DMDAGetElementsCorners(stokes_da,&sex,&sey,NULL);
874:   DMDAGetElementsSizes(stokes_da,&mx,&my,NULL);
875:   for (ej = sey; ej < sey+my; ej++) {
876:     for (ei = sex; ei < sex+mx; ei++) {
877:       /* get coords for the element */
878:       GetElementCoords(_coords,ei,ej,el_coords);

880:       /* get coefficients for the element */
881:       prop_fx = props[ej][ei].fx;
882:       prop_fy = props[ej][ei].fy;

884:       /* initialise element stiffness matrix */
885:       PetscMemzero(Fe,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS);
886:       PetscMemzero(He,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS);

888:       /* form element stiffness matrix */
889:       FormMomentumRhsQ1(Fe,el_coords,prop_fx,prop_fy);

891:       /* insert element matrix into global matrix */
892:       DMDAGetElementEqnums_up(u_eqn,p_eqn,ei,ej);

894:       DMDASetValuesLocalStencil_ADD_VALUES(ff,u_eqn,p_eqn,Fe,He);
895:     }
896:   }

898:   DMDAVecRestoreArray(stokes_da,local_F,&ff);
899:   DMLocalToGlobalBegin(stokes_da,local_F,ADD_VALUES,F);
900:   DMLocalToGlobalEnd(stokes_da,local_F,ADD_VALUES,F);
901:   DMRestoreLocalVector(stokes_da,&local_F);

903:   DMDAVecRestoreArray(cda,coords,&_coords);

905:   DMDAVecRestoreArray(properties_da,local_properties,&props);
906:   DMRestoreLocalVector(properties_da,&local_properties);
907:   return(0);
908: }

910: static PetscErrorCode DMDACreateSolCx(PetscReal eta0,PetscReal eta1,PetscReal xc,PetscInt nz,PetscInt mx,PetscInt my,DM *_da,Vec *_X)
911: {
912:   DM             da,cda;
913:   Vec            X;
914:   StokesDOF      **_stokes;
915:   Vec            coords;
916:   DMDACoor2d     **_coords;
917:   PetscInt       si,sj,ei,ej,i,j;

921:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx+1,my+1,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,NULL,&da);
922:   DMSetFromOptions(da);
923:   DMSetUp(da);
924:   DMDASetFieldName(da,0,"anlytic_Vx");
925:   DMDASetFieldName(da,1,"anlytic_Vy");
926:   DMDASetFieldName(da,2,"analytic_P");

928:   DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.,0.);

930:   DMGetCoordinatesLocal(da,&coords);
931:   DMGetCoordinateDM(da,&cda);
932:   DMDAVecGetArray(cda,coords,&_coords);

934:   DMCreateGlobalVector(da,&X);
935:   DMDAVecGetArray(da,X,&_stokes);

937:   DMDAGetCorners(da,&si,&sj,0,&ei,&ej,0);
938:   for (j = sj; j < sj+ej; j++) {
939:     for (i = si; i < si+ei; i++) {
940:       PetscReal pos[2],pressure,vel[2],total_stress[3],strain_rate[3];

942:       pos[0] = PetscRealPart(_coords[j][i].x);
943:       pos[1] = PetscRealPart(_coords[j][i].y);

945:       evaluate_solCx(pos,eta0,eta1,xc,nz,vel,&pressure,total_stress,strain_rate);

947:       _stokes[j][i].u_dof = vel[0];
948:       _stokes[j][i].v_dof = vel[1];
949:       _stokes[j][i].p_dof = pressure;
950:     }
951:   }
952:   DMDAVecRestoreArray(da,X,&_stokes);
953:   DMDAVecRestoreArray(cda,coords,&_coords);

955:   *_da = da;
956:   *_X  = X;
957:   return(0);
958: }

960: static PetscErrorCode StokesDAGetNodalFields(StokesDOF **fields,PetscInt ei,PetscInt ej,StokesDOF nodal_fields[])
961: {
963:   /* get the nodal fields */
964:   nodal_fields[0].u_dof = fields[ej][ei].u_dof;     nodal_fields[0].v_dof = fields[ej][ei].v_dof;     nodal_fields[0].p_dof = fields[ej][ei].p_dof;
965:   nodal_fields[1].u_dof = fields[ej+1][ei].u_dof;   nodal_fields[1].v_dof = fields[ej+1][ei].v_dof;   nodal_fields[1].p_dof = fields[ej+1][ei].p_dof;
966:   nodal_fields[2].u_dof = fields[ej+1][ei+1].u_dof; nodal_fields[2].v_dof = fields[ej+1][ei+1].v_dof; nodal_fields[2].p_dof = fields[ej+1][ei+1].p_dof;
967:   nodal_fields[3].u_dof = fields[ej][ei+1].u_dof;   nodal_fields[3].v_dof = fields[ej][ei+1].v_dof;   nodal_fields[3].p_dof = fields[ej][ei+1].p_dof;
968:   return(0);
969: }

971: static PetscErrorCode DMDAIntegrateErrors(DM stokes_da,Vec X,Vec X_analytic)
972: {
973:   DM             cda;
974:   Vec            coords,X_analytic_local,X_local;
975:   DMDACoor2d     **_coords;
976:   PetscInt       sex,sey,mx,my;
977:   PetscInt       ei,ej;
978:   PetscScalar    el_coords[NODES_PER_EL*NSD];
979:   StokesDOF      **stokes_analytic,**stokes;
980:   StokesDOF      stokes_analytic_e[4],stokes_e[4];

982:   PetscScalar    GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
983:   PetscScalar    Ni_p[NODES_PER_EL];
984:   PetscInt       ngp;
985:   PetscScalar    gp_xi[GAUSS_POINTS][2];
986:   PetscScalar    gp_weight[GAUSS_POINTS];
987:   PetscInt       p,i;
988:   PetscScalar    J_p,fac;
989:   PetscScalar    h,p_e_L2,u_e_L2,u_e_H1,p_L2,u_L2,u_H1,tp_L2,tu_L2,tu_H1;
990:   PetscInt       M;
991:   PetscReal      xymin[2],xymax[2];

995:   /* define quadrature rule */
996:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

998:   /* setup for coords */
999:   DMGetCoordinateDM(stokes_da,&cda);
1000:   DMGetCoordinatesLocal(stokes_da,&coords);
1001:   DMDAVecGetArray(cda,coords,&_coords);

1003:   /* setup for analytic */
1004:   DMCreateLocalVector(stokes_da,&X_analytic_local);
1005:   DMGlobalToLocalBegin(stokes_da,X_analytic,INSERT_VALUES,X_analytic_local);
1006:   DMGlobalToLocalEnd(stokes_da,X_analytic,INSERT_VALUES,X_analytic_local);
1007:   DMDAVecGetArray(stokes_da,X_analytic_local,&stokes_analytic);

1009:   /* setup for solution */
1010:   DMCreateLocalVector(stokes_da,&X_local);
1011:   DMGlobalToLocalBegin(stokes_da,X,INSERT_VALUES,X_local);
1012:   DMGlobalToLocalEnd(stokes_da,X,INSERT_VALUES,X_local);
1013:   DMDAVecGetArray(stokes_da,X_local,&stokes);

1015:   DMDAGetInfo(stokes_da,0,&M,0,0,0,0,0,0,0,0,0,0,0);
1016:   DMDAGetBoundingBox(stokes_da,xymin,xymax);

1018:   h = (xymax[0]-xymin[0])/((PetscReal)M);

1020:   tp_L2 = tu_L2 = tu_H1 = 0.0;

1022:   DMDAGetElementsCorners(stokes_da,&sex,&sey,NULL);
1023:   DMDAGetElementsSizes(stokes_da,&mx,&my,NULL);
1024:   for (ej = sey; ej < sey+my; ej++) {
1025:     for (ei = sex; ei < sex+mx; ei++) {
1026:       /* get coords for the element */
1027:       GetElementCoords(_coords,ei,ej,el_coords);
1028:       StokesDAGetNodalFields(stokes,ei,ej,stokes_e);
1029:       StokesDAGetNodalFields(stokes_analytic,ei,ej,stokes_analytic_e);

1031:       /* evaluate integral */
1032:       p_e_L2 = 0.0;
1033:       u_e_L2 = 0.0;
1034:       u_e_H1 = 0.0;
1035:       for (p = 0; p < ngp; p++) {
1036:         ConstructQ12D_Ni(gp_xi[p],Ni_p);
1037:         ConstructQ12D_GNi(gp_xi[p],GNi_p);
1038:         ConstructQ12D_GNx(GNi_p,GNx_p,el_coords,&J_p);
1039:         fac = gp_weight[p]*J_p;

1041:         for (i = 0; i < NODES_PER_EL; i++) {
1042:           PetscScalar u_error,v_error;

1044:           p_e_L2 = p_e_L2+fac*Ni_p[i]*(stokes_e[i].p_dof-stokes_analytic_e[i].p_dof)*(stokes_e[i].p_dof-stokes_analytic_e[i].p_dof);

1046:           u_error = stokes_e[i].u_dof-stokes_analytic_e[i].u_dof;
1047:           v_error = stokes_e[i].v_dof-stokes_analytic_e[i].v_dof;
1048:           u_e_L2 += fac*Ni_p[i]*(u_error*u_error+v_error*v_error);

1050:           u_e_H1 = u_e_H1+fac*(GNx_p[0][i]*u_error*GNx_p[0][i]*u_error              /* du/dx */
1051:                                +GNx_p[1][i]*u_error*GNx_p[1][i]*u_error               /* du/dy */
1052:                                +GNx_p[0][i]*v_error*GNx_p[0][i]*v_error               /* dv/dx */
1053:                                +GNx_p[1][i]*v_error*GNx_p[1][i]*v_error);             /* dv/dy */
1054:         }
1055:       }

1057:       tp_L2 += p_e_L2;
1058:       tu_L2 += u_e_L2;
1059:       tu_H1 += u_e_H1;
1060:     }
1061:   }
1062:   MPI_Allreduce(&tp_L2,&p_L2,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1063:   MPI_Allreduce(&tu_L2,&u_L2,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1064:   MPI_Allreduce(&tu_H1,&u_H1,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1065:   p_L2 = PetscSqrtScalar(p_L2);
1066:   u_L2 = PetscSqrtScalar(u_L2);
1067:   u_H1 = PetscSqrtScalar(u_H1);

1069:   PetscPrintf(PETSC_COMM_WORLD,"%1.4e   %1.4e   %1.4e   %1.4e\n",(double)PetscRealPart(h),(double)PetscRealPart(p_L2),(double)PetscRealPart(u_L2),(double)PetscRealPart(u_H1));

1071:   DMDAVecRestoreArray(cda,coords,&_coords);

1073:   DMDAVecRestoreArray(stokes_da,X_analytic_local,&stokes_analytic);
1074:   VecDestroy(&X_analytic_local);
1075:   DMDAVecRestoreArray(stokes_da,X_local,&stokes);
1076:   VecDestroy(&X_local);
1077:   return(0);
1078: }

1080: static PetscErrorCode solve_stokes_2d_coupled(PetscInt mx,PetscInt my)
1081: {
1082:   DM                     da_Stokes,da_prop;
1083:   PetscInt               u_dof,p_dof,dof,stencil_width;
1084:   Mat                    A,B;
1085:   DM                     prop_cda,vel_cda;
1086:   Vec                    prop_coords,vel_coords;
1087:   PetscInt               si,sj,nx,ny,i,j,p;
1088:   Vec                    f,X;
1089:   PetscInt               prop_dof,prop_stencil_width;
1090:   Vec                    properties,l_properties;
1091:   PetscReal              dx,dy;
1092:   PetscInt               M,N;
1093:   DMDACoor2d             **_prop_coords,**_vel_coords;
1094:   GaussPointCoefficients **element_props;
1095:   PetscInt               its;
1096:   KSP                    ksp_S;
1097:   PetscInt               coefficient_structure = 0;
1098:   PetscInt               cpu_x,cpu_y,*lx = NULL,*ly = NULL;
1099:   PetscBool              use_gp_coords = PETSC_FALSE,set,output_gnuplot = PETSC_FALSE,glvis = PETSC_FALSE;
1100:   char                   filename[PETSC_MAX_PATH_LEN];
1101:   PetscErrorCode         ierr;


1105:   PetscOptionsGetBool(NULL,NULL,"-gnuplot",&output_gnuplot,NULL);
1106:   PetscOptionsGetBool(NULL,NULL,"-glvis",&glvis,NULL);

1108:   /* Generate the da for velocity and pressure */
1109:   /*
1110:   We use Q1 elements for the temperature.
1111:   FEM has a 9-point stencil (BOX) or connectivity pattern
1112:   Num nodes in each direction is mx+1, my+1
1113:   */
1114:   u_dof         = U_DOFS; /* Vx, Vy - velocities */
1115:   p_dof         = P_DOFS; /* p - pressure */
1116:   dof           = u_dof+p_dof;
1117:   stencil_width = 1;
1118:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx+1,my+1,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,NULL,NULL,&da_Stokes);

1120:   DMSetMatType(da_Stokes,MATAIJ);
1121:   DMSetFromOptions(da_Stokes);
1122:   DMSetUp(da_Stokes);
1123:   DMDASetFieldName(da_Stokes,0,"Vx");
1124:   DMDASetFieldName(da_Stokes,1,"Vy");
1125:   DMDASetFieldName(da_Stokes,2,"P");

1127:   /* unit box [0,1] x [0,1] */
1128:   DMDASetUniformCoordinates(da_Stokes,0.0,1.0,0.0,1.0,0.,0.);

1130:   /* Generate element properties, we will assume all material properties are constant over the element */
1131:   /* !!! IN PARALLEL WE MUST MAKE SURE THE TWO DMDA's ALIGN !!!  */
1132:   DMDAGetInfo(da_Stokes,0,0,0,0,&cpu_x,&cpu_y,0,0,0,0,0,0,0);
1133:   DMDAGetElementOwnershipRanges2d(da_Stokes,&lx,&ly);

1135:   prop_dof           = (int)(sizeof(GaussPointCoefficients)/sizeof(PetscScalar)); /* gauss point setup */
1136:   prop_stencil_width = 0;
1137:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx,my,cpu_x,cpu_y,prop_dof,prop_stencil_width,lx,ly,&da_prop);
1138:   DMSetFromOptions(da_prop);
1139:   DMSetUp(da_prop);
1140:   PetscFree(lx);
1141:   PetscFree(ly);

1143:   /* define centroid positions */
1144:   DMDAGetInfo(da_prop,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
1145:   dx   = 1.0/((PetscReal)(M));
1146:   dy   = 1.0/((PetscReal)(N));

1148:   DMDASetUniformCoordinates(da_prop,0.0+0.5*dx,1.0-0.5*dx,0.0+0.5*dy,1.0-0.5*dy,0.,0);

1150:   /* define coefficients */
1151:   PetscOptionsGetInt(NULL,NULL,"-c_str",&coefficient_structure,NULL);

1153:   DMCreateGlobalVector(da_prop,&properties);
1154:   DMCreateLocalVector(da_prop,&l_properties);
1155:   DMDAVecGetArray(da_prop,l_properties,&element_props);

1157:   DMGetCoordinateDM(da_prop,&prop_cda);
1158:   DMGetCoordinatesLocal(da_prop,&prop_coords);
1159:   DMDAVecGetArray(prop_cda,prop_coords,&_prop_coords);

1161:   DMDAGetGhostCorners(prop_cda,&si,&sj,0,&nx,&ny,0);

1163:   DMGetCoordinateDM(da_Stokes,&vel_cda);
1164:   DMGetCoordinatesLocal(da_Stokes,&vel_coords);
1165:   DMDAVecGetArray(vel_cda,vel_coords,&_vel_coords);

1167:   /* interpolate the coordinates */
1168:   for (j = sj; j < sj+ny; j++) {
1169:     for (i = si; i < si+nx; i++) {
1170:       PetscInt    ngp;
1171:       PetscScalar gp_xi[GAUSS_POINTS][2],gp_weight[GAUSS_POINTS];
1172:       PetscScalar el_coords[8];

1174:       GetElementCoords(_vel_coords,i,j,el_coords);
1175:       ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

1177:       for (p = 0; p < GAUSS_POINTS; p++) {
1178:         PetscScalar gp_x,gp_y;
1179:         PetscInt    n;
1180:         PetscScalar xi_p[2],Ni_p[4];

1182:         xi_p[0] = gp_xi[p][0];
1183:         xi_p[1] = gp_xi[p][1];
1184:         ConstructQ12D_Ni(xi_p,Ni_p);

1186:         gp_x = 0.0;
1187:         gp_y = 0.0;
1188:         for (n = 0; n < NODES_PER_EL; n++) {
1189:           gp_x = gp_x+Ni_p[n]*el_coords[2*n];
1190:           gp_y = gp_y+Ni_p[n]*el_coords[2*n+1];
1191:         }
1192:         element_props[j][i].gp_coords[2*p]   = gp_x;
1193:         element_props[j][i].gp_coords[2*p+1] = gp_y;
1194:       }
1195:     }
1196:   }

1198:   /* define the coefficients */
1199:   PetscOptionsGetBool(NULL,NULL,"-use_gp_coords",&use_gp_coords,NULL);

1201:   for (j = sj; j < sj+ny; j++) {
1202:     for (i = si; i < si+nx; i++) {
1203:       PetscReal centroid_x = PetscRealPart(_prop_coords[j][i].x); /* centroids of cell */
1204:       PetscReal centroid_y = PetscRealPart(_prop_coords[j][i].y);
1205:       PetscReal coord_x,coord_y;

1207:       if (coefficient_structure == 0) {
1208:         PetscReal opts_eta0,opts_eta1,opts_xc;
1209:         PetscInt  opts_nz;

1211:         opts_eta0 = 1.0;
1212:         opts_eta1 = 1.0;
1213:         opts_xc   = 0.5;
1214:         opts_nz   = 1;

1216:         PetscOptionsGetReal(NULL,NULL,"-solcx_eta0",&opts_eta0,NULL);
1217:         PetscOptionsGetReal(NULL,NULL,"-solcx_eta1",&opts_eta1,NULL);
1218:         PetscOptionsGetReal(NULL,NULL,"-solcx_xc",&opts_xc,NULL);
1219:         PetscOptionsGetInt(NULL,NULL,"-solcx_nz",&opts_nz,NULL);

1221:         for (p = 0; p < GAUSS_POINTS; p++) {
1222:           coord_x = centroid_x;
1223:           coord_y = centroid_y;
1224:           if (use_gp_coords) {
1225:             coord_x = PetscRealPart(element_props[j][i].gp_coords[2*p]);
1226:             coord_y = PetscRealPart(element_props[j][i].gp_coords[2*p+1]);
1227:           }

1229:           element_props[j][i].eta[p] = opts_eta0;
1230:           if (coord_x > opts_xc) element_props[j][i].eta[p] = opts_eta1;

1232:           element_props[j][i].fx[p] = 0.0;
1233:           element_props[j][i].fy[p] = PetscSinReal(opts_nz*PETSC_PI*coord_y)*PetscCosReal(1.0*PETSC_PI*coord_x);
1234:         }
1235:       } else if (coefficient_structure == 1) { /* square sinker */
1236:         PetscReal opts_eta0,opts_eta1,opts_dx,opts_dy;

1238:         opts_eta0 = 1.0;
1239:         opts_eta1 = 1.0;
1240:         opts_dx   = 0.50;
1241:         opts_dy   = 0.50;

1243:         PetscOptionsGetReal(NULL,NULL,"-sinker_eta0",&opts_eta0,NULL);
1244:         PetscOptionsGetReal(NULL,NULL,"-sinker_eta1",&opts_eta1,NULL);
1245:         PetscOptionsGetReal(NULL,NULL,"-sinker_dx",&opts_dx,NULL);
1246:         PetscOptionsGetReal(NULL,NULL,"-sinker_dy",&opts_dy,NULL);

1248:         for (p = 0; p < GAUSS_POINTS; p++) {
1249:           coord_x = centroid_x;
1250:           coord_y = centroid_y;
1251:           if (use_gp_coords) {
1252:             coord_x = PetscRealPart(element_props[j][i].gp_coords[2*p]);
1253:             coord_y = PetscRealPart(element_props[j][i].gp_coords[2*p+1]);
1254:           }

1256:           element_props[j][i].eta[p] = opts_eta0;
1257:           element_props[j][i].fx[p]  = 0.0;
1258:           element_props[j][i].fy[p]  = 0.0;

1260:           if ((coord_x > -0.5*opts_dx+0.5) && (coord_x < 0.5*opts_dx+0.5)) {
1261:             if ((coord_y > -0.5*opts_dy+0.5) && (coord_y < 0.5*opts_dy+0.5)) {
1262:               element_props[j][i].eta[p] =  opts_eta1;
1263:               element_props[j][i].fx[p]  =  0.0;
1264:               element_props[j][i].fy[p]  = -1.0;
1265:             }
1266:           }
1267:         }
1268:       } else if (coefficient_structure == 2) { /* circular sinker */
1269:         PetscReal opts_eta0,opts_eta1,opts_r,radius2;

1271:         opts_eta0 = 1.0;
1272:         opts_eta1 = 1.0;
1273:         opts_r    = 0.25;

1275:         PetscOptionsGetReal(NULL,NULL,"-sinker_eta0",&opts_eta0,NULL);
1276:         PetscOptionsGetReal(NULL,NULL,"-sinker_eta1",&opts_eta1,NULL);
1277:         PetscOptionsGetReal(NULL,NULL,"-sinker_r",&opts_r,NULL);

1279:         for (p = 0; p < GAUSS_POINTS; p++) {
1280:           coord_x = centroid_x;
1281:           coord_y = centroid_y;
1282:           if (use_gp_coords) {
1283:             coord_x = PetscRealPart(element_props[j][i].gp_coords[2*p]);
1284:             coord_y = PetscRealPart(element_props[j][i].gp_coords[2*p+1]);
1285:           }

1287:           element_props[j][i].eta[p] = opts_eta0;
1288:           element_props[j][i].fx[p]  = 0.0;
1289:           element_props[j][i].fy[p]  = 0.0;

1291:           radius2 = (coord_x-0.5)*(coord_x-0.5)+(coord_y-0.5)*(coord_y-0.5);
1292:           if (radius2 < opts_r*opts_r) {
1293:             element_props[j][i].eta[p] =  opts_eta1;
1294:             element_props[j][i].fx[p]  =  0.0;
1295:             element_props[j][i].fy[p]  = -1.0;
1296:           }
1297:         }
1298:       } else if (coefficient_structure == 3) { /* circular and rectangular inclusion */
1299:         PetscReal opts_eta0,opts_eta1,opts_r,opts_dx,opts_dy,opts_c0x,opts_c0y,opts_s0x,opts_s0y,opts_phi,radius2;

1301:         opts_eta0 = 1.0;
1302:         opts_eta1 = 1.0;
1303:         opts_r    = 0.25;
1304:         opts_c0x  = 0.35;       /* circle center */
1305:         opts_c0y  = 0.35;
1306:         opts_s0x  = 0.7;       /* square center */
1307:         opts_s0y  = 0.7;
1308:         opts_dx   = 0.25;
1309:         opts_dy   = 0.25;
1310:         opts_phi  = 25;

1312:         PetscOptionsGetReal(NULL,NULL,"-sinker_eta0",&opts_eta0,NULL);
1313:         PetscOptionsGetReal(NULL,NULL,"-sinker_eta1",&opts_eta1,NULL);
1314:         PetscOptionsGetReal(NULL,NULL,"-sinker_r",&opts_r,NULL);
1315:         PetscOptionsGetReal(NULL,NULL,"-sinker_c0x",&opts_c0x,NULL);
1316:         PetscOptionsGetReal(NULL,NULL,"-sinker_c0y",&opts_c0y,NULL);
1317:         PetscOptionsGetReal(NULL,NULL,"-sinker_s0x",&opts_s0x,NULL);
1318:         PetscOptionsGetReal(NULL,NULL,"-sinker_s0y",&opts_s0y,NULL);
1319:         PetscOptionsGetReal(NULL,NULL,"-sinker_dx",&opts_dx,NULL);
1320:         PetscOptionsGetReal(NULL,NULL,"-sinker_dy",&opts_dy,NULL);
1321:         PetscOptionsGetReal(NULL,NULL,"-sinker_phi",&opts_phi,NULL);
1322:         opts_phi *= PETSC_PI / 180;

1324:         for (p = 0; p < GAUSS_POINTS; p++) {
1325:           coord_x = centroid_x;
1326:           coord_y = centroid_y;
1327:           if (use_gp_coords) {
1328:             coord_x = PetscRealPart(element_props[j][i].gp_coords[2*p]);
1329:             coord_y = PetscRealPart(element_props[j][i].gp_coords[2*p+1]);
1330:           }

1332:           element_props[j][i].eta[p] = opts_eta0;
1333:           element_props[j][i].fx[p]  = 0.0;
1334:           element_props[j][i].fy[p]  = -0.2;

1336:           radius2 = PetscSqr(coord_x - opts_c0x) + PetscSqr(coord_y - opts_c0y);
1337:           if (radius2 < opts_r*opts_r
1338:               || (PetscAbs(+(coord_x - opts_s0x)*PetscCosReal(opts_phi) + (coord_y - opts_s0y)*PetscSinReal(opts_phi)) < opts_dx/2
1339:                   && PetscAbs(-(coord_x - opts_s0x)*PetscSinReal(opts_phi) + (coord_y - opts_s0y)*PetscCosReal(opts_phi)) < opts_dy/2)) {
1340:             element_props[j][i].eta[p] =  opts_eta1;
1341:             element_props[j][i].fx[p]  =  0.0;
1342:             element_props[j][i].fy[p]  = -1.0;
1343:           }
1344:         }
1345:       } else if (coefficient_structure == 4) { /* subdomain jump */
1346:         PetscReal opts_mag,opts_eta0;
1347:         PetscInt  opts_nz,px,py;
1348:         PetscBool jump;

1350:         opts_mag  = 1.0;
1351:         opts_eta0 = 1.0;
1352:         opts_nz   = 1;

1354:         PetscOptionsGetReal(NULL,NULL,"-jump_eta0",&opts_eta0,NULL);
1355:         PetscOptionsGetReal(NULL,NULL,"-jump_magnitude",&opts_mag,NULL);
1356:         PetscOptionsGetInt(NULL,NULL,"-jump_nz",&opts_nz,NULL);
1357:         DMDAGetInfo(da_Stokes,NULL,NULL,NULL,NULL,&px,&py,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
1358:         if (px%2) {
1359:           jump = (PetscBool)(PetscGlobalRank%2);
1360:         } else {
1361:           jump = (PetscBool)((PetscGlobalRank/px)%2 ? PetscGlobalRank%2 : !(PetscGlobalRank%2));
1362:         }
1363:         for (p = 0; p < GAUSS_POINTS; p++) {
1364:           coord_x = centroid_x;
1365:           coord_y = centroid_y;
1366:           if (use_gp_coords) {
1367:             coord_x = PetscRealPart(element_props[j][i].gp_coords[2*p]);
1368:             coord_y = PetscRealPart(element_props[j][i].gp_coords[2*p+1]);
1369:           }

1371:           element_props[j][i].eta[p] = jump ? PetscPowReal(10.0,opts_mag) : opts_eta0;
1372:           element_props[j][i].fx[p]  = 0.0;
1373:           element_props[j][i].fy[p]  = PetscSinReal(opts_nz*PETSC_PI*coord_y)*PetscCosReal(1.0*PETSC_PI*coord_x);
1374:         }
1375:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Unknown coefficient_structure");
1376:     }
1377:   }
1378:   DMDAVecRestoreArray(prop_cda,prop_coords,&_prop_coords);

1380:   DMDAVecRestoreArray(vel_cda,vel_coords,&_vel_coords);

1382:   DMDAVecRestoreArray(da_prop,l_properties,&element_props);
1383:   DMLocalToGlobalBegin(da_prop,l_properties,ADD_VALUES,properties);
1384:   DMLocalToGlobalEnd(da_prop,l_properties,ADD_VALUES,properties);

1386:   if (output_gnuplot) {
1387:     DMDACoordViewGnuplot2d(da_Stokes,"mesh");
1388:     DMDAViewCoefficientsGnuplot2d(da_prop,properties,"Coefficients for Stokes eqn.","properties");
1389:   }

1391:   if (glvis) {
1392:     Vec         glv_prop,etaf;
1393:     PetscViewer view;
1394:     PetscInt    dim;
1395:     const char  *fec = {"FiniteElementCollection: L2_2D_P1"};

1397:     DMGetDimension(da_Stokes,&dim);
1398:     VecCreateSeq(PETSC_COMM_SELF,GAUSS_POINTS*mx*mx,&etaf);
1399:     PetscObjectSetName((PetscObject)etaf,"viscosity");
1400:     PetscViewerGLVisOpen(PETSC_COMM_WORLD,PETSC_VIEWER_GLVIS_SOCKET,NULL,PETSC_DECIDE,&view);
1401:     PetscViewerGLVisSetFields(view,1,&fec,&dim,glvis_extract_eta,(PetscObject*)&etaf,da_prop,NULL);
1402:     DMGetLocalVector(da_prop,&glv_prop);
1403:     DMGlobalToLocalBegin(da_prop,properties,INSERT_VALUES,glv_prop);
1404:     DMGlobalToLocalEnd(da_prop,properties,INSERT_VALUES,glv_prop);
1405:     VecSetDM(etaf,da_Stokes);
1406:     VecView(glv_prop,view);
1407:     PetscViewerDestroy(&view);
1408:     DMRestoreLocalVector(da_prop,&glv_prop);
1409:     VecDestroy(&etaf);
1410:   }

1412:   /* Generate a matrix with the correct non-zero pattern of type AIJ. This will work in parallel and serial */
1413:   DMCreateMatrix(da_Stokes,&A);
1414:   DMCreateMatrix(da_Stokes,&B);
1415:   DMCreateGlobalVector(da_Stokes,&f);
1416:   DMCreateGlobalVector(da_Stokes,&X);

1418:   /* assemble A11 */
1419:   MatZeroEntries(A);
1420:   MatZeroEntries(B);
1421:   VecZeroEntries(f);

1423:   AssembleA_Stokes(A,da_Stokes,da_prop,properties);
1424:   AssembleA_PCStokes(B,da_Stokes,da_prop,properties);
1425:   /* build force vector */
1426:   AssembleF_Stokes(f,da_Stokes,da_prop,properties);

1428:   DMDABCApplyFreeSlip(da_Stokes,A,f);
1429:   DMDABCApplyFreeSlip(da_Stokes,B,NULL);

1431:   /* SOLVE */
1432:   KSPCreate(PETSC_COMM_WORLD,&ksp_S);
1433:   KSPSetOptionsPrefix(ksp_S,"stokes_");
1434:   KSPSetDM(ksp_S,da_Stokes);
1435:   KSPSetDMActive(ksp_S,PETSC_FALSE);
1436:   KSPSetOperators(ksp_S,A,B);
1437:   KSPSetFromOptions(ksp_S);
1438:   {
1439:     PC             pc;
1440:     const PetscInt ufields[] = {0,1},pfields[1] = {2};

1442:     KSPGetPC(ksp_S,&pc);
1443:     PCFieldSplitSetBlockSize(pc,3);
1444:     PCFieldSplitSetFields(pc,"u",2,ufields,ufields);
1445:     PCFieldSplitSetFields(pc,"p",1,pfields,pfields);
1446:   }

1448:   {
1449:     PC        pc;
1450:     PetscBool same = PETSC_FALSE;
1451:     KSPGetPC(ksp_S,&pc);
1452:     PetscObjectTypeCompare((PetscObject)pc,PCBDDC,&same);
1453:     if (same) {
1454:       PetscBool usedivmat = PETSC_FALSE;
1455:       KSPSetOperators(ksp_S,A,A);

1457:       PetscOptionsGetBool(NULL,NULL,"-stokes_pc_bddc_use_divergence",&usedivmat,NULL);
1458:       if (usedivmat) {
1459:         IS       *fields,vel;
1460:         PetscInt i,nf;

1462:         DMCreateFieldDecomposition(da_Stokes,&nf,NULL,&fields,NULL);
1463:         ISConcatenate(PETSC_COMM_WORLD,2,fields,&vel);
1464:         MatZeroRowsIS(B,fields[2],1.0,NULL,NULL); /* we put 1.0 on the diagonal to pick the pressure average too */
1465:         MatTranspose(B,MAT_INPLACE_MATRIX,&B);
1466:         MatZeroRowsIS(B,vel,0.0,NULL,NULL);
1467:         ISDestroy(&vel);
1468:         PCBDDCSetDivergenceMat(pc,B,PETSC_FALSE,NULL);
1469:         for (i=0;i<nf;i++) {
1470:           ISDestroy(&fields[i]);
1471:         }
1472:         PetscFree(fields);
1473:       }
1474:     }
1475:   }

1477:   {
1478:     PC        pc_S;
1479:     KSP       *sub_ksp,ksp_U;
1480:     PetscInt  nsplits;
1481:     DM        da_U;
1482:     PetscBool is_pcfs;

1484:     KSPSetUp(ksp_S);
1485:     KSPGetPC(ksp_S,&pc_S);

1487:     is_pcfs = PETSC_FALSE;
1488:     PetscObjectTypeCompare((PetscObject)pc_S,PCFIELDSPLIT,&is_pcfs);

1490:     if (is_pcfs) {
1491:       PCFieldSplitGetSubKSP(pc_S,&nsplits,&sub_ksp);
1492:       ksp_U = sub_ksp[0];
1493:       PetscFree(sub_ksp);

1495:       if (nsplits == 2) {
1496:         DMDACreateCompatibleDMDA(da_Stokes,2,&da_U);

1498:         KSPSetDM(ksp_U,da_U);
1499:         KSPSetDMActive(ksp_U,PETSC_FALSE);
1500:         DMDestroy(&da_U);
1501:       }
1502:     }
1503:   }

1505:   KSPSolve(ksp_S,f,X);

1507:   PetscOptionsGetString(NULL,NULL,"-o",filename,sizeof(filename),&set);
1508:   if (set) {
1509:     char        *ext;
1510:     PetscViewer viewer;
1511:     PetscBool   flg;
1512:     PetscViewerCreate(PETSC_COMM_WORLD,&viewer);
1513:     PetscStrrchr(filename,'.',&ext);
1514:     PetscStrcmp("vts",ext,&flg);
1515:     if (flg) {
1516:       PetscViewerSetType(viewer,PETSCVIEWERVTK);
1517:     } else {
1518:       PetscViewerSetType(viewer,PETSCVIEWERBINARY);
1519:     }
1520:     PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
1521:     PetscViewerFileSetName(viewer,filename);
1522:     VecView(X,viewer);
1523:     PetscViewerDestroy(&viewer);
1524:   }
1525:   if (output_gnuplot) {
1526:     DMDAViewGnuplot2d(da_Stokes,X,"Velocity solution for Stokes eqn.","X");
1527:   }

1529:   if (glvis) {
1530:     PetscViewer view;

1532:     PetscViewerCreate(PETSC_COMM_WORLD,&view);
1533:     PetscViewerSetType(view,PETSCVIEWERGLVIS);
1534:     VecView(X,view);
1535:     PetscViewerDestroy(&view);
1536:   }

1538:   KSPGetIterationNumber(ksp_S,&its);

1540:   if (coefficient_structure == 0) {
1541:     PetscReal opts_eta0,opts_eta1,opts_xc;
1542:     PetscInt  opts_nz,N;
1543:     DM        da_Stokes_analytic;
1544:     Vec       X_analytic;
1545:     PetscReal nrm1[3],nrm2[3],nrmI[3];

1547:     opts_eta0 = 1.0;
1548:     opts_eta1 = 1.0;
1549:     opts_xc   = 0.5;
1550:     opts_nz   = 1;

1552:     PetscOptionsGetReal(NULL,NULL,"-solcx_eta0",&opts_eta0,NULL);
1553:     PetscOptionsGetReal(NULL,NULL,"-solcx_eta1",&opts_eta1,NULL);
1554:     PetscOptionsGetReal(NULL,NULL,"-solcx_xc",&opts_xc,NULL);
1555:     PetscOptionsGetInt(NULL,NULL,"-solcx_nz",&opts_nz,NULL);

1557:     DMDACreateSolCx(opts_eta0,opts_eta1,opts_xc,opts_nz,mx,my,&da_Stokes_analytic,&X_analytic);
1558:     if (output_gnuplot) {
1559:       DMDAViewGnuplot2d(da_Stokes_analytic,X_analytic,"Analytic solution for Stokes eqn.","X_analytic");
1560:     }
1561:     DMDAIntegrateErrors(da_Stokes_analytic,X,X_analytic);

1563:     VecAXPY(X_analytic,-1.0,X);
1564:     VecGetSize(X_analytic,&N);
1565:     N    = N/3;

1567:     VecStrideNorm(X_analytic,0,NORM_1,&nrm1[0]);
1568:     VecStrideNorm(X_analytic,0,NORM_2,&nrm2[0]);
1569:     VecStrideNorm(X_analytic,0,NORM_INFINITY,&nrmI[0]);

1571:     VecStrideNorm(X_analytic,1,NORM_1,&nrm1[1]);
1572:     VecStrideNorm(X_analytic,1,NORM_2,&nrm2[1]);
1573:     VecStrideNorm(X_analytic,1,NORM_INFINITY,&nrmI[1]);

1575:     VecStrideNorm(X_analytic,2,NORM_1,&nrm1[2]);
1576:     VecStrideNorm(X_analytic,2,NORM_2,&nrm2[2]);
1577:     VecStrideNorm(X_analytic,2,NORM_INFINITY,&nrmI[2]);

1579:     DMDestroy(&da_Stokes_analytic);
1580:     VecDestroy(&X_analytic);
1581:   }

1583:   KSPDestroy(&ksp_S);
1584:   VecDestroy(&X);
1585:   VecDestroy(&f);
1586:   MatDestroy(&A);
1587:   MatDestroy(&B);

1589:   DMDestroy(&da_Stokes);
1590:   DMDestroy(&da_prop);

1592:   VecDestroy(&properties);
1593:   VecDestroy(&l_properties);
1594:   return(0);
1595: }

1597: int main(int argc,char **args)
1598: {
1600:   PetscInt       mx,my;

1602:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
1603:   mx   = my = 10;
1604:   PetscOptionsGetInt(NULL,NULL,"-mx",&mx,NULL);
1605:   PetscOptionsGetInt(NULL,NULL,"-my",&my,NULL);
1606:   solve_stokes_2d_coupled(mx,my);
1607:   PetscFinalize();
1608:   return ierr;
1609: }

1611: /* -------------------------- helpers for boundary conditions -------------------------------- */
1612: static PetscErrorCode BCApplyZero_EAST(DM da,PetscInt d_idx,Mat A,Vec b)
1613: {
1614:   DM                     cda;
1615:   Vec                    coords;
1616:   PetscInt               si,sj,nx,ny,i,j;
1617:   PetscInt               M,N;
1618:   DMDACoor2d             **_coords;
1619:   const PetscInt         *g_idx;
1620:   PetscInt               *bc_global_ids;
1621:   PetscScalar            *bc_vals;
1622:   PetscInt               nbcs;
1623:   PetscInt               n_dofs;
1624:   PetscErrorCode         ierr;
1625:   ISLocalToGlobalMapping ltogm;

1628:   DMGetLocalToGlobalMapping(da,&ltogm);
1629:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1631:   DMGetCoordinateDM(da,&cda);
1632:   DMGetCoordinatesLocal(da,&coords);
1633:   DMDAVecGetArray(cda,coords,&_coords);
1634:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1635:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1637:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
1638:   PetscMalloc1(ny*n_dofs,&bc_vals);

1640:   /* init the entries to -1 so VecSetValues will ignore them */
1641:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

1643:   i = nx-1;
1644:   for (j = 0; j < ny; j++) {
1645:     PetscInt local_id;

1647:     local_id = i+j*nx;

1649:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

1651:     bc_vals[j] =  0.0;
1652:   }
1653:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1654:   nbcs = 0;
1655:   if ((si+nx) == (M)) nbcs = ny;

1657:   if (b) {
1658:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1659:     VecAssemblyBegin(b);
1660:     VecAssemblyEnd(b);
1661:   }
1662:   if (A) {
1663:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1664:   }

1666:   PetscFree(bc_vals);
1667:   PetscFree(bc_global_ids);

1669:   DMDAVecRestoreArray(cda,coords,&_coords);
1670:   return(0);
1671: }

1673: static PetscErrorCode BCApplyZero_WEST(DM da,PetscInt d_idx,Mat A,Vec b)
1674: {
1675:   DM                     cda;
1676:   Vec                    coords;
1677:   PetscInt               si,sj,nx,ny,i,j;
1678:   PetscInt               M,N;
1679:   DMDACoor2d             **_coords;
1680:   const PetscInt         *g_idx;
1681:   PetscInt               *bc_global_ids;
1682:   PetscScalar            *bc_vals;
1683:   PetscInt               nbcs;
1684:   PetscInt               n_dofs;
1685:   PetscErrorCode         ierr;
1686:   ISLocalToGlobalMapping ltogm;

1689:   DMGetLocalToGlobalMapping(da,&ltogm);
1690:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1692:   DMGetCoordinateDM(da,&cda);
1693:   DMGetCoordinatesLocal(da,&coords);
1694:   DMDAVecGetArray(cda,coords,&_coords);
1695:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1696:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1698:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
1699:   PetscMalloc1(ny*n_dofs,&bc_vals);

1701:   /* init the entries to -1 so VecSetValues will ignore them */
1702:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

1704:   i = 0;
1705:   for (j = 0; j < ny; j++) {
1706:     PetscInt local_id;

1708:     local_id = i+j*nx;

1710:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

1712:     bc_vals[j] =  0.0;
1713:   }
1714:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1715:   nbcs = 0;
1716:   if (si == 0) nbcs = ny;

1718:   if (b) {
1719:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1720:     VecAssemblyBegin(b);
1721:     VecAssemblyEnd(b);
1722:   }

1724:   if (A) {
1725:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1726:   }

1728:   PetscFree(bc_vals);
1729:   PetscFree(bc_global_ids);

1731:   DMDAVecRestoreArray(cda,coords,&_coords);
1732:   return(0);
1733: }

1735: static PetscErrorCode BCApplyZero_NORTH(DM da,PetscInt d_idx,Mat A,Vec b)
1736: {
1737:   DM                     cda;
1738:   Vec                    coords;
1739:   PetscInt               si,sj,nx,ny,i,j;
1740:   PetscInt               M,N;
1741:   DMDACoor2d             **_coords;
1742:   const PetscInt         *g_idx;
1743:   PetscInt               *bc_global_ids;
1744:   PetscScalar            *bc_vals;
1745:   PetscInt               nbcs;
1746:   PetscInt               n_dofs;
1747:   PetscErrorCode         ierr;
1748:   ISLocalToGlobalMapping ltogm;

1751:   DMGetLocalToGlobalMapping(da,&ltogm);
1752:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1754:   DMGetCoordinateDM(da,&cda);
1755:   DMGetCoordinatesLocal(da,&coords);
1756:   DMDAVecGetArray(cda,coords,&_coords);
1757:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1758:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1760:   PetscMalloc1(nx,&bc_global_ids);
1761:   PetscMalloc1(nx,&bc_vals);

1763:   /* init the entries to -1 so VecSetValues will ignore them */
1764:   for (i = 0; i < nx; i++) bc_global_ids[i] = -1;

1766:   j = ny-1;
1767:   for (i = 0; i < nx; i++) {
1768:     PetscInt local_id;

1770:     local_id = i+j*nx;

1772:     bc_global_ids[i] = g_idx[n_dofs*local_id+d_idx];

1774:     bc_vals[i] =  0.0;
1775:   }
1776:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1777:   nbcs = 0;
1778:   if ((sj+ny) == (N)) nbcs = nx;

1780:   if (b) {
1781:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1782:     VecAssemblyBegin(b);
1783:     VecAssemblyEnd(b);
1784:   }
1785:   if (A) {
1786:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1787:   }

1789:   PetscFree(bc_vals);
1790:   PetscFree(bc_global_ids);

1792:   DMDAVecRestoreArray(cda,coords,&_coords);
1793:   return(0);
1794: }

1796: static PetscErrorCode BCApplyZero_SOUTH(DM da,PetscInt d_idx,Mat A,Vec b)
1797: {
1798:   DM                     cda;
1799:   Vec                    coords;
1800:   PetscInt               si,sj,nx,ny,i,j;
1801:   PetscInt               M,N;
1802:   DMDACoor2d             **_coords;
1803:   const PetscInt         *g_idx;
1804:   PetscInt               *bc_global_ids;
1805:   PetscScalar            *bc_vals;
1806:   PetscInt               nbcs;
1807:   PetscInt               n_dofs;
1808:   PetscErrorCode         ierr;
1809:   ISLocalToGlobalMapping ltogm;

1812:   DMGetLocalToGlobalMapping(da,&ltogm);
1813:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1815:   DMGetCoordinateDM(da,&cda);
1816:   DMGetCoordinatesLocal(da,&coords);
1817:   DMDAVecGetArray(cda,coords,&_coords);
1818:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1819:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1821:   PetscMalloc1(nx,&bc_global_ids);
1822:   PetscMalloc1(nx,&bc_vals);

1824:   /* init the entries to -1 so VecSetValues will ignore them */
1825:   for (i = 0; i < nx; i++) bc_global_ids[i] = -1;

1827:   j = 0;
1828:   for (i = 0; i < nx; i++) {
1829:     PetscInt local_id;

1831:     local_id = i+j*nx;

1833:     bc_global_ids[i] = g_idx[n_dofs*local_id+d_idx];

1835:     bc_vals[i] =  0.0;
1836:   }
1837:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1838:   nbcs = 0;
1839:   if (sj == 0) nbcs = nx;

1841:   if (b) {
1842:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1843:     VecAssemblyBegin(b);
1844:     VecAssemblyEnd(b);
1845:   }
1846:   if (A) {
1847:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1848:   }

1850:   PetscFree(bc_vals);
1851:   PetscFree(bc_global_ids);

1853:   DMDAVecRestoreArray(cda,coords,&_coords);
1854:   return(0);
1855: }

1857: /* Impose free slip boundary conditions; u_{i} n_{i} = 0, tau_{ij} t_j = 0 */
1858: static PetscErrorCode DMDABCApplyFreeSlip(DM da_Stokes,Mat A,Vec f)
1859: {

1863:   BCApplyZero_NORTH(da_Stokes,1,A,f);
1864:   BCApplyZero_EAST(da_Stokes,0,A,f);
1865:   BCApplyZero_SOUTH(da_Stokes,1,A,f);
1866:   BCApplyZero_WEST(da_Stokes,0,A,f);
1867:   return(0);
1868: }


1871: /*TEST

1873:    build:
1874:       requires: !complex !single

1876:    test:
1877:       args: -stokes_pc_use_amat -stokes_ksp_type fgmres -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_block_size 3 -stokes_pc_fieldsplit_type SYMMETRIC_MULTIPLICATIVE -stokes_pc_fieldsplit_0_fields 0,1 -stokes_pc_fieldsplit_1_fields 2 -stokes_fieldsplit_0_ksp_type preonly -stokes_fieldsplit_0_pc_type lu -stokes_fieldsplit_1_ksp_type preonly -stokes_fieldsplit_1_pc_type jacobi -c_str 0 -solcx_eta0 1.0 -solcx_eta1 1.0e6 -solcx_xc 0.5 -solcx_nz 2 -mx 20 -my 20 -stokes_ksp_monitor_short

1879:    test:
1880:       suffix: 2
1881:       args: -stokes_pc_use_amat -stokes_ksp_type fgmres -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_block_size 3 -stokes_pc_fieldsplit_type SYMMETRIC_MULTIPLICATIVE -stokes_fieldsplit_u_ksp_type preonly -stokes_fieldsplit_u_pc_type lu -stokes_fieldsplit_p_ksp_type preonly -stokes_fieldsplit_p_pc_type jacobi -c_str 0 -solcx_eta0 1.0 -solcx_eta1 1.0e6 -solcx_xc 0.5 -solcx_nz 2 -mx 20 -my 20 -stokes_ksp_monitor_short
1882:       output_file: output/ex43_1.out

1884:    test:
1885:       suffix: 3
1886:       nsize: 4
1887:       args: -stokes_pc_use_amat -stokes_ksp_type gcr -stokes_ksp_gcr_restart 60 -stokes_ksp_norm_type unpreconditioned -stokes_ksp_rtol 1.e-2 -c_str 3 -sinker_eta0 1.0 -sinker_eta1 100 -sinker_dx 0.4 -sinker_dy 0.3 -mx 128 -my 128 -stokes_ksp_monitor_short -stokes_pc_type mg -stokes_mg_levels_pc_type fieldsplit -stokes_pc_use_amat false -stokes_pc_mg_galerkin pmat -stokes_mg_levels_pc_fieldsplit_block_size 3 -stokes_mg_levels_pc_fieldsplit_0_fields 0,1 -stokes_mg_levels_pc_fieldsplit_1_fields 2 -stokes_mg_levels_fieldsplit_0_pc_type sor -stokes_mg_levels_fieldsplit_1_pc_type sor -stokes_mg_levels_ksp_type chebyshev -stokes_mg_levels_ksp_max_it 1 -stokes_mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.1 -stokes_pc_mg_levels 4 -stokes_ksp_view

1889:    test:
1890:       suffix: 4
1891:       nsize: 4
1892:       args: -stokes_ksp_type pipegcr -stokes_ksp_pipegcr_mmax 60 -stokes_ksp_pipegcr_unroll_w 1 -stokes_ksp_norm_type natural -c_str 3 -sinker_eta0 1.0 -sinker_eta1 100 -sinker_dx 0.4 -sinker_dy 0.3 -mx 128 -my 128 -stokes_ksp_monitor_short -stokes_pc_type mg -stokes_mg_levels_pc_type fieldsplit -stokes_pc_use_amat false -stokes_pc_mg_galerkin pmat -stokes_mg_levels_pc_fieldsplit_block_size 3 -stokes_mg_levels_pc_fieldsplit_0_fields 0,1 -stokes_mg_levels_pc_fieldsplit_1_fields 2 -stokes_mg_levels_fieldsplit_0_pc_type sor -stokes_mg_levels_fieldsplit_1_pc_type sor -stokes_mg_levels_ksp_type chebyshev -stokes_mg_levels_ksp_max_it 1 -stokes_mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.1 -stokes_pc_mg_levels 4 -stokes_ksp_view

1894:    test:
1895:       suffix: 5
1896:       nsize: 4
1897:       args: -stokes_pc_fieldsplit_off_diag_use_amat -stokes_ksp_type pipegcr -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_block_size 3 -stokes_pc_fieldsplit_type SYMMETRIC_MULTIPLICATIVE -stokes_pc_fieldsplit_0_fields 0,1 -stokes_pc_fieldsplit_1_fields 2 -stokes_fieldsplit_0_ksp_type preonly -stokes_fieldsplit_0_pc_type bjacobi -stokes_fieldsplit_1_ksp_type preonly -stokes_fieldsplit_1_pc_type bjacobi -c_str 0 -solcx_eta0 1.0 -solcx_eta1 1.0e6 -solcx_xc 0.5 -solcx_nz 2 -mx 20 -my 20 -stokes_ksp_monitor_short -stokes_ksp_view

1899:    test:
1900:       suffix: 6
1901:       nsize: 8
1902:       args: -stokes_ksp_view -stokes_pc_type mg -stokes_pc_mg_levels 2 -stokes_mg_coarse_pc_type telescope -stokes_mg_coarse_pc_telescope_reduction_factor 2 -stokes_pc_use_amat false -stokes_pc_mg_galerkin pmat -stokes_mg_coarse_pc_telescope_subcomm_type contiguous

1904:    test:
1905:       suffix: bjacobi
1906:       nsize: 4
1907:       args: -stokes_ksp_rtol 1.e-4 -stokes_pc_type bjacobi -stokes_pc_bjacobi_blocks 2 -dm_mat_type aij -stokes_ksp_converged_reason

1909:    test:
1910:       suffix: bjacobi_baij
1911:       nsize: 4
1912:       args: -stokes_ksp_rtol 1.e-4 -stokes_pc_type bjacobi -stokes_pc_bjacobi_blocks 2 -dm_mat_type baij -stokes_ksp_converged_reason
1913:       output_file: output/ex43_bjacobi.out

1915:    test:
1916:       suffix: nested_gmg
1917:       nsize: 4
1918:       args: -stokes_pc_fieldsplit_off_diag_use_amat -mx 16 -my 16 -stokes_ksp_type fgmres -stokes_pc_type fieldsplit -stokes_fieldsplit_u_pc_type mg -stokes_fieldsplit_u_pc_mg_levels 5 -stokes_fieldsplit_u_pc_mg_galerkin pmat -stokes_fieldsplit_u_ksp_type cg -stokes_fieldsplit_u_ksp_rtol 1.0e-4 -stokes_fieldsplit_u_mg_levels_pc_type jacobi -solcx_eta0 1.0e4 -stokes_fieldsplit_u_ksp_converged_reason -stokes_ksp_converged_reason -stokes_fieldsplit_p_sub_pc_factor_zeropivot 1.e-8

1920:    test:
1921:       suffix: fetidp
1922:       nsize: 8
1923:       args: -dm_mat_type is -stokes_ksp_type fetidp -stokes_ksp_fetidp_saddlepoint -stokes_fetidp_ksp_type cg -stokes_ksp_converged_reason -stokes_fetidp_pc_fieldsplit_schur_fact_type diag -stokes_fetidp_fieldsplit_p_pc_type bjacobi -stokes_fetidp_fieldsplit_lag_ksp_type preonly -stokes_fetidp_fieldsplit_p_ksp_type preonly -stokes_ksp_fetidp_pressure_field 2 -stokes_fetidp_pc_fieldsplit_schur_scale -1

1925:    test:
1926:       suffix: fetidp_unsym
1927:       nsize: 8
1928:       args: -dm_mat_type is -stokes_ksp_type fetidp -stokes_ksp_monitor_true_residual -stokes_ksp_converged_reason -stokes_fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd

1930:    test:
1931:       suffix: bddc_stokes_deluxe
1932:       nsize: 8
1933:       args: -stokes_ksp_monitor_short -stokes_ksp_converged_reason -stokes_pc_type bddc -dm_mat_type is -stokes_pc_bddc_coarse_redundant_pc_type svd -stokes_pc_bddc_use_deluxe_scaling -stokes_sub_schurs_posdef 0 -stokes_sub_schurs_symmetric -stokes_sub_schurs_mat_solver_type petsc

1935:    test:
1936:       suffix: bddc_stokes_subdomainjump_deluxe
1937:       nsize: 9
1938:       args: -c_str 4 -jump_magnitude 3 -stokes_ksp_monitor_short -stokes_ksp_converged_reason -stokes_pc_type bddc -dm_mat_type is -stokes_pc_bddc_coarse_redundant_pc_type svd -stokes_pc_bddc_use_deluxe_scaling -stokes_sub_schurs_posdef 0 -stokes_sub_schurs_symmetric -stokes_sub_schurs_mat_solver_type petsc


1941: TEST*/