Actual source code: ex49.c

petsc-master 2018-05-21
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  1: static char help[] =  "   Solves the compressible plane strain elasticity equations in 2d on the unit domain using Q1 finite elements. \n\
  2:    Material properties E (Youngs modulus) and nu (Poisson ratio) may vary as a function of space. \n\
  3:    The model utilises boundary conditions which produce compression in the x direction. \n\
  4: Options: \n"
  5: "\
  6:      -mx : number of elements in x-direction \n\
  7:      -my : number of elements in y-direction \n\
  8:      -c_str : indicates the structure of the coefficients to use. \n"
  9: "\
 10:           -c_str 0 => Setup for an isotropic material with constant coefficients. \n\
 11:                          Parameters: \n\
 12:                              -iso_E  : Youngs modulus \n\
 13:                              -iso_nu : Poisson ratio \n\
 14:           -c_str 1 => Setup for a step function in the material properties in x. \n\
 15:                          Parameters: \n\
 16:                               -step_E0  : Youngs modulus to the left of the step \n\
 17:                               -step_nu0 : Poisson ratio to the left of the step \n\
 18:                               -step_E1  : Youngs modulus to the right of the step \n\
 19:                               -step_n1  : Poisson ratio to the right of the step \n\
 20:                               -step_xc  : x coordinate of the step \n"
 21: "\
 22:           -c_str 2 => Setup for a checkerboard material with alternating properties. \n\
 23:                       Repeats the following pattern throughout the domain. For example with 4 materials specified, we would heve \n\
 24:                       -------------------------\n\
 25:                       |  D  |  A  |  B  |  C  |\n\
 26:                       ------|-----|-----|------\n\
 27:                       |  C  |  D  |  A  |  B  |\n\
 28:                       ------|-----|-----|------\n\
 29:                       |  B  |  C  |  D  |  A  |\n\
 30:                       ------|-----|-----|------\n\
 31:                       |  A  |  B  |  C  |  D  |\n\
 32:                       -------------------------\n\
 33:                       \n\
 34:                          Parameters: \n\
 35:                               -brick_E    : a comma separated list of Young's modulii \n\
 36:                               -brick_nu   : a comma separated list of Poisson ratios  \n\
 37:                               -brick_span : the number of elements in x and y each brick will span \n\
 38:           -c_str 3 => Setup for a sponge-like material with alternating properties. \n\
 39:                       Repeats the following pattern throughout the domain \n"
 40: "\
 41:                       -----------------------------\n\
 42:                       |       [background]        |\n\
 43:                       |          E0,nu0           |\n\
 44:                       |     -----------------     |\n\
 45:                       |     |  [inclusion]  |     |\n\
 46:                       |     |    E1,nu1     |     |\n\
 47:                       |     |               |     |\n\
 48:                       |     | <---- w ----> |     |\n\
 49:                       |     |               |     |\n\
 50:                       |     |               |     |\n\
 51:                       |     -----------------     |\n\
 52:                       |                           |\n\
 53:                       |                           |\n\
 54:                       -----------------------------\n\
 55:                       <--------  t + w + t ------->\n\
 56:                       \n\
 57:                          Parameters: \n\
 58:                               -sponge_E0  : Youngs modulus of the surrounding material \n\
 59:                               -sponge_E1  : Youngs modulus of the inclusion \n\
 60:                               -sponge_nu0 : Poisson ratio of the surrounding material \n\
 61:                               -sponge_nu1 : Poisson ratio of the inclusion \n\
 62:                               -sponge_t   : the number of elements defining the border around each inclusion \n\
 63:                               -sponge_w   : the number of elements in x and y each inclusion will span\n\
 64:      -use_gp_coords : Evaluate the Youngs modulus, Poisson ratio and the body force at the global coordinates of the quadrature points.\n\
 65:      By default, E, nu and the body force are evaulated at the element center and applied as a constant over the entire element.\n\
 66:      -use_nonsymbc : Option to use non-symmetric boundary condition imposition. This choice will use less memory.";

 68: /* Contributed by Dave May */

 70:  #include <petscksp.h>
 71:  #include <petscdm.h>
 72:  #include <petscdmda.h>

 74: static PetscErrorCode DMDABCApplyCompression(DM,Mat,Vec);
 75: static PetscErrorCode DMDABCApplySymmetricCompression(DM elas_da,Mat A,Vec f,IS *dofs,Mat *AA,Vec *ff);


 78: #define NSD            2 /* number of spatial dimensions */
 79: #define NODES_PER_EL   4 /* nodes per element */
 80: #define U_DOFS         2 /* degrees of freedom per displacement node */
 81: #define GAUSS_POINTS   4

 83: /* cell based evaluation */
 84: typedef struct {
 85:   PetscScalar E,nu,fx,fy;
 86: } Coefficients;

 88: /* Gauss point based evaluation 8+4+4+4 = 20 */
 89: typedef struct {
 90:   PetscScalar gp_coords[2*GAUSS_POINTS];
 91:   PetscScalar E[GAUSS_POINTS];
 92:   PetscScalar nu[GAUSS_POINTS];
 93:   PetscScalar fx[GAUSS_POINTS];
 94:   PetscScalar fy[GAUSS_POINTS];
 95: } GaussPointCoefficients;

 97: typedef struct {
 98:   PetscScalar ux_dof;
 99:   PetscScalar uy_dof;
100: } ElasticityDOF;


103: /*

105:  D = E/((1+nu)(1-2nu)) * [ 1-nu   nu        0     ]
106:                          [  nu   1-nu       0     ]
107:                          [  0     0   0.5*(1-2nu) ]

109:  B = [ d_dx   0   ]
110:      [  0    d_dy ]
111:      [ d_dy  d_dx ]

113:  */

115: /* FEM routines */
116: /*
117:  Element: Local basis function ordering
118:  1-----2
119:  |     |
120:  |     |
121:  0-----3
122:  */
123: static void ConstructQ12D_Ni(PetscScalar _xi[],PetscScalar Ni[])
124: {
125:   PetscScalar xi  = _xi[0];
126:   PetscScalar eta = _xi[1];

128:   Ni[0] = 0.25*(1.0-xi)*(1.0-eta);
129:   Ni[1] = 0.25*(1.0-xi)*(1.0+eta);
130:   Ni[2] = 0.25*(1.0+xi)*(1.0+eta);
131:   Ni[3] = 0.25*(1.0+xi)*(1.0-eta);
132: }

134: static void ConstructQ12D_GNi(PetscScalar _xi[],PetscScalar GNi[][NODES_PER_EL])
135: {
136:   PetscScalar xi  = _xi[0];
137:   PetscScalar eta = _xi[1];

139:   GNi[0][0] = -0.25*(1.0-eta);
140:   GNi[0][1] = -0.25*(1.0+eta);
141:   GNi[0][2] =   0.25*(1.0+eta);
142:   GNi[0][3] =   0.25*(1.0-eta);

144:   GNi[1][0] = -0.25*(1.0-xi);
145:   GNi[1][1] =   0.25*(1.0-xi);
146:   GNi[1][2] =   0.25*(1.0+xi);
147:   GNi[1][3] = -0.25*(1.0+xi);
148: }

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

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

161:     J00 = J00+GNi[0][i]*cx;      /* J_xx = dx/dxi */
162:     J01 = J01+GNi[0][i]*cy;      /* J_xy = dy/dxi */
163:     J10 = J10+GNi[1][i]*cx;      /* J_yx = dx/deta */
164:     J11 = J11+GNi[1][i]*cy;      /* J_yy = dy/deta */
165:   }
166:   J = (J00*J11)-(J01*J10);

168:   iJ00 =  J11/J;
169:   iJ01 = -J01/J;
170:   iJ10 = -J10/J;
171:   iJ11 =  J00/J;


174:   for (i = 0; i < NODES_PER_EL; i++) {
175:     GNx[0][i] = GNi[0][i]*iJ00+GNi[1][i]*iJ01;
176:     GNx[1][i] = GNi[0][i]*iJ10+GNi[1][i]*iJ11;
177:   }

179:   if (det_J) *det_J = J;
180: }

182: static void ConstructGaussQuadrature(PetscInt *ngp,PetscScalar gp_xi[][2],PetscScalar gp_weight[])
183: {
184:   *ngp         = 4;
185:   gp_xi[0][0]  = -0.57735026919;gp_xi[0][1] = -0.57735026919;
186:   gp_xi[1][0]  = -0.57735026919;gp_xi[1][1] =  0.57735026919;
187:   gp_xi[2][0]  =  0.57735026919;gp_xi[2][1] =  0.57735026919;
188:   gp_xi[3][0]  =  0.57735026919;gp_xi[3][1] = -0.57735026919;
189:   gp_weight[0] = 1.0;
190:   gp_weight[1] = 1.0;
191:   gp_weight[2] = 1.0;
192:   gp_weight[3] = 1.0;
193: }

195: static PetscErrorCode DMDAGetElementOwnershipRanges2d(DM da,PetscInt **_lx,PetscInt **_ly)
196: {
198:   PetscMPIInt    rank;
199:   PetscInt       proc_I,proc_J;
200:   PetscInt       cpu_x,cpu_y;
201:   PetscInt       local_mx,local_my;
202:   Vec            vlx,vly;
203:   PetscInt       *LX,*LY,i;
204:   PetscScalar    *_a;
205:   Vec            V_SEQ;
206:   VecScatter     ctx;

209:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

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

213:   proc_J = rank/cpu_x;
214:   proc_I = rank-cpu_x*proc_J;

216:   PetscMalloc1(cpu_x,&LX);
217:   PetscMalloc1(cpu_y,&LY);

219:   DMDAGetElementsSizes(da,&local_mx,&local_my,NULL);
220:   VecCreate(PETSC_COMM_WORLD,&vlx);
221:   VecSetSizes(vlx,PETSC_DECIDE,cpu_x);
222:   VecSetFromOptions(vlx);

224:   VecCreate(PETSC_COMM_WORLD,&vly);
225:   VecSetSizes(vly,PETSC_DECIDE,cpu_y);
226:   VecSetFromOptions(vly);

228:   VecSetValue(vlx,proc_I,(PetscScalar)(local_mx+1.0e-9),INSERT_VALUES);
229:   VecSetValue(vly,proc_J,(PetscScalar)(local_my+1.0e-9),INSERT_VALUES);
230:   VecAssemblyBegin(vlx);VecAssemblyEnd(vlx);
231:   VecAssemblyBegin(vly);VecAssemblyEnd(vly);

233:   VecScatterCreateToAll(vlx,&ctx,&V_SEQ);
234:   VecScatterBegin(ctx,vlx,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
235:   VecScatterEnd(ctx,vlx,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
236:   VecGetArray(V_SEQ,&_a);
237:   for (i = 0; i < cpu_x; i++) LX[i] = (PetscInt)PetscRealPart(_a[i]);
238:   VecRestoreArray(V_SEQ,&_a);
239:   VecScatterDestroy(&ctx);
240:   VecDestroy(&V_SEQ);

242:   VecScatterCreateToAll(vly,&ctx,&V_SEQ);
243:   VecScatterBegin(ctx,vly,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
244:   VecScatterEnd(ctx,vly,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
245:   VecGetArray(V_SEQ,&_a);
246:   for (i = 0; i < cpu_y; i++) LY[i] = (PetscInt)PetscRealPart(_a[i]);
247:   VecRestoreArray(V_SEQ,&_a);
248:   VecScatterDestroy(&ctx);
249:   VecDestroy(&V_SEQ);

251:   *_lx = LX;
252:   *_ly = LY;

254:   VecDestroy(&vlx);
255:   VecDestroy(&vly);
256:   return(0);
257: }

259: static PetscErrorCode DMDACoordViewGnuplot2d(DM da,const char prefix[])
260: {
261:   DM             cda;
262:   Vec            coords;
263:   DMDACoor2d     **_coords;
264:   PetscInt       si,sj,nx,ny,i,j;
265:   FILE           *fp;
266:   char           fname[PETSC_MAX_PATH_LEN];
267:   PetscMPIInt    rank;

271:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
272:   PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
273:   PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
274:   if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");
275:   PetscFPrintf(PETSC_COMM_SELF,fp,"### Element geometry for processor %1.4d ### \n",rank);

277:   DMGetCoordinateDM(da,&cda);
278:   DMGetCoordinatesLocal(da,&coords);
279:   DMDAVecGetArray(cda,coords,&_coords);
280:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
281:   for (j = sj; j < sj+ny-1; j++) {
282:     for (i = si; i < si+nx-1; i++) {
283:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j][i].x),PetscRealPart(_coords[j][i].y));
284:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j+1][i].x),PetscRealPart(_coords[j+1][i].y));
285:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j+1][i+1].x),PetscRealPart(_coords[j+1][i+1].y));
286:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j][i+1].x),PetscRealPart(_coords[j][i+1].y));
287:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n\n",PetscRealPart(_coords[j][i].x),PetscRealPart(_coords[j][i].y));
288:     }
289:   }
290:   DMDAVecRestoreArray(cda,coords,&_coords);

292:   PetscFClose(PETSC_COMM_SELF,fp);
293:   return(0);
294: }

296: static PetscErrorCode DMDAViewGnuplot2d(DM da,Vec fields,const char comment[],const char prefix[])
297: {
298:   DM             cda;
299:   Vec            coords,local_fields;
300:   DMDACoor2d     **_coords;
301:   FILE           *fp;
302:   char           fname[PETSC_MAX_PATH_LEN];
303:   const char     *field_name;
304:   PetscMPIInt    rank;
305:   PetscInt       si,sj,nx,ny,i,j;
306:   PetscInt       n_dofs,d;
307:   PetscScalar    *_fields;

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

316:   PetscFPrintf(PETSC_COMM_SELF,fp,"### %s (processor %1.4d) ### \n",comment,rank);
317:   DMDAGetInfo(da,0,0,0,0,0,0,0,&n_dofs,0,0,0,0,0);
318:   PetscFPrintf(PETSC_COMM_SELF,fp,"### x y ");
319:   for (d = 0; d < n_dofs; d++) {
320:     DMDAGetFieldName(da,d,&field_name);
321:     PetscFPrintf(PETSC_COMM_SELF,fp,"%s ",field_name);
322:   }
323:   PetscFPrintf(PETSC_COMM_SELF,fp,"###\n");


326:   DMGetCoordinateDM(da,&cda);
327:   DMGetCoordinatesLocal(da,&coords);
328:   DMDAVecGetArray(cda,coords,&_coords);
329:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);

331:   DMCreateLocalVector(da,&local_fields);
332:   DMGlobalToLocalBegin(da,fields,INSERT_VALUES,local_fields);
333:   DMGlobalToLocalEnd(da,fields,INSERT_VALUES,local_fields);
334:   VecGetArray(local_fields,&_fields);

336:   for (j = sj; j < sj+ny; j++) {
337:     for (i = si; i < si+nx; i++) {
338:       PetscScalar coord_x,coord_y;
339:       PetscScalar field_d;

341:       coord_x = _coords[j][i].x;
342:       coord_y = _coords[j][i].y;

344:       PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e ",PetscRealPart(coord_x),PetscRealPart(coord_y));
345:       for (d = 0; d < n_dofs; d++) {
346:         field_d = _fields[n_dofs*((i-si)+(j-sj)*(nx))+d];
347:         PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e ",PetscRealPart(field_d));
348:       }
349:       PetscFPrintf(PETSC_COMM_SELF,fp,"\n");
350:     }
351:   }
352:   VecRestoreArray(local_fields,&_fields);
353:   VecDestroy(&local_fields);

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

357:   PetscFClose(PETSC_COMM_SELF,fp);
358:   return(0);
359: }

361: static PetscErrorCode DMDAViewCoefficientsGnuplot2d(DM da,Vec fields,const char comment[],const char prefix[])
362: {
363:   DM                     cda;
364:   Vec                    local_fields;
365:   FILE                   *fp;
366:   char                   fname[PETSC_MAX_PATH_LEN];
367:   const char             *field_name;
368:   PetscMPIInt            rank;
369:   PetscInt               si,sj,nx,ny,i,j,p;
370:   PetscInt               n_dofs,d;
371:   GaussPointCoefficients **_coefficients;
372:   PetscErrorCode         ierr;

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

380:   PetscFPrintf(PETSC_COMM_SELF,fp,"### %s (processor %1.4d) ### \n",comment,rank);
381:   DMDAGetInfo(da,0,0,0,0,0,0,0,&n_dofs,0,0,0,0,0);
382:   PetscFPrintf(PETSC_COMM_SELF,fp,"### x y ");
383:   for (d = 0; d < n_dofs; d++) {
384:     DMDAGetFieldName(da,d,&field_name);
385:     PetscFPrintf(PETSC_COMM_SELF,fp,"%s ",field_name);
386:   }
387:   PetscFPrintf(PETSC_COMM_SELF,fp,"###\n");


390:   DMGetCoordinateDM(da,&cda);
391:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);

393:   DMCreateLocalVector(da,&local_fields);
394:   DMGlobalToLocalBegin(da,fields,INSERT_VALUES,local_fields);
395:   DMGlobalToLocalEnd(da,fields,INSERT_VALUES,local_fields);
396:   DMDAVecGetArray(da,local_fields,&_coefficients);

398:   for (j = sj; j < sj+ny; j++) {
399:     for (i = si; i < si+nx; i++) {
400:       PetscScalar coord_x,coord_y;

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

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

408:         PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e %1.6e %1.6e",
409:                             PetscRealPart(_coefficients[j][i].E[p]),PetscRealPart(_coefficients[j][i].nu[p]),
410:                             PetscRealPart(_coefficients[j][i].fx[p]),PetscRealPart(_coefficients[j][i].fy[p]));
411:         PetscFPrintf(PETSC_COMM_SELF,fp,"\n");
412:       }
413:     }
414:   }
415:   DMDAVecRestoreArray(da,local_fields,&_coefficients);
416:   VecDestroy(&local_fields);

418:   PetscFClose(PETSC_COMM_SELF,fp);
419:   return(0);
420: }

422: static void FormStressOperatorQ1(PetscScalar Ke[],PetscScalar coords[],PetscScalar E[],PetscScalar nu[])
423: {
424:   PetscInt    ngp;
425:   PetscScalar gp_xi[GAUSS_POINTS][2];
426:   PetscScalar gp_weight[GAUSS_POINTS];
427:   PetscInt    p,i,j,k,l;
428:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
429:   PetscScalar J_p;
430:   PetscScalar B[3][U_DOFS*NODES_PER_EL];
431:   PetscScalar prop_E,prop_nu,factor,constit_D[3][3];

433:   /* define quadrature rule */
434:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

436:   /* evaluate integral */
437:   for (p = 0; p < ngp; p++) {
438:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
439:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);

441:     for (i = 0; i < NODES_PER_EL; i++) {
442:       PetscScalar d_dx_i = GNx_p[0][i];
443:       PetscScalar d_dy_i = GNx_p[1][i];

445:       B[0][2*i] = d_dx_i;  B[0][2*i+1] = 0.0;
446:       B[1][2*i] = 0.0;     B[1][2*i+1] = d_dy_i;
447:       B[2][2*i] = d_dy_i;  B[2][2*i+1] = d_dx_i;
448:     }

450:     /* form D for the quadrature point */
451:     prop_E          = E[p];
452:     prop_nu         = nu[p];
453:     factor          = prop_E / ((1.0+prop_nu)*(1.0-2.0*prop_nu));
454:     constit_D[0][0] = 1.0-prop_nu;  constit_D[0][1] = prop_nu;      constit_D[0][2] = 0.0;
455:     constit_D[1][0] = prop_nu;      constit_D[1][1] = 1.0-prop_nu;  constit_D[1][2] = 0.0;
456:     constit_D[2][0] = 0.0;          constit_D[2][1] = 0.0;          constit_D[2][2] = 0.5*(1.0-2.0*prop_nu);
457:     for (i = 0; i < 3; i++) {
458:       for (j = 0; j < 3; j++) {
459:         constit_D[i][j] = factor * constit_D[i][j] * gp_weight[p] * J_p;
460:       }
461:     }

463:     /* form Bt tildeD B */
464:     /*
465:      Ke_ij = Bt_ik . D_kl . B_lj
466:      = B_ki . D_kl . B_lj
467:      */
468:     for (i = 0; i < 8; i++) {
469:       for (j = 0; j < 8; j++) {
470:         for (k = 0; k < 3; k++) {
471:           for (l = 0; l < 3; l++) {
472:             Ke[8*i+j] = Ke[8*i+j] + B[k][i] * constit_D[k][l] * B[l][j];
473:           }
474:         }
475:       }
476:     }

478:   } /* end quadrature */
479: }

481: static void FormMomentumRhsQ1(PetscScalar Fe[],PetscScalar coords[],PetscScalar fx[],PetscScalar fy[])
482: {
483:   PetscInt    ngp;
484:   PetscScalar gp_xi[GAUSS_POINTS][2];
485:   PetscScalar gp_weight[GAUSS_POINTS];
486:   PetscInt    p,i;
487:   PetscScalar Ni_p[NODES_PER_EL];
488:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
489:   PetscScalar J_p,fac;

491:   /* define quadrature rule */
492:   ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

494:   /* evaluate integral */
495:   for (p = 0; p < ngp; p++) {
496:     ConstructQ12D_Ni(gp_xi[p],Ni_p);
497:     ConstructQ12D_GNi(gp_xi[p],GNi_p);
498:     ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
499:     fac = gp_weight[p]*J_p;

501:     for (i = 0; i < NODES_PER_EL; i++) {
502:       Fe[NSD*i]   += fac*Ni_p[i]*fx[p];
503:       Fe[NSD*i+1] += fac*Ni_p[i]*fy[p];
504:     }
505:   }
506: }

508: /*
509:  i,j are the element indices
510:  The unknown is a vector quantity.
511:  The s[].c is used to indicate the degree of freedom.
512:  */
513: static PetscErrorCode DMDAGetElementEqnums_u(MatStencil s_u[],PetscInt i,PetscInt j)
514: {
516:   /* displacement */
517:   /* node 0 */
518:   s_u[0].i = i;s_u[0].j = j;s_u[0].c = 0;          /* Ux0 */
519:   s_u[1].i = i;s_u[1].j = j;s_u[1].c = 1;          /* Uy0 */

521:   /* node 1 */
522:   s_u[2].i = i;s_u[2].j = j+1;s_u[2].c = 0;        /* Ux1 */
523:   s_u[3].i = i;s_u[3].j = j+1;s_u[3].c = 1;        /* Uy1 */

525:   /* node 2 */
526:   s_u[4].i = i+1;s_u[4].j = j+1;s_u[4].c = 0;      /* Ux2 */
527:   s_u[5].i = i+1;s_u[5].j = j+1;s_u[5].c = 1;      /* Uy2 */

529:   /* node 3 */
530:   s_u[6].i = i+1;s_u[6].j = j;s_u[6].c = 0;        /* Ux3 */
531:   s_u[7].i = i+1;s_u[7].j = j;s_u[7].c = 1;        /* Uy3 */
532:   return(0);
533: }

535: static PetscErrorCode GetElementCoords(DMDACoor2d **_coords,PetscInt ei,PetscInt ej,PetscScalar el_coords[])
536: {
538:   /* get coords for the element */
539:   el_coords[NSD*0+0] = _coords[ej][ei].x;      el_coords[NSD*0+1] = _coords[ej][ei].y;
540:   el_coords[NSD*1+0] = _coords[ej+1][ei].x;    el_coords[NSD*1+1] = _coords[ej+1][ei].y;
541:   el_coords[NSD*2+0] = _coords[ej+1][ei+1].x;  el_coords[NSD*2+1] = _coords[ej+1][ei+1].y;
542:   el_coords[NSD*3+0] = _coords[ej][ei+1].x;    el_coords[NSD*3+1] = _coords[ej][ei+1].y;
543:   return(0);
544: }

546: static PetscErrorCode AssembleA_Elasticity(Mat A,DM elas_da,DM properties_da,Vec properties)
547: {
548:   DM                     cda;
549:   Vec                    coords;
550:   DMDACoor2d             **_coords;
551:   MatStencil             u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
552:   PetscInt               sex,sey,mx,my;
553:   PetscInt               ei,ej;
554:   PetscScalar            Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
555:   PetscScalar            el_coords[NODES_PER_EL*NSD];
556:   Vec                    local_properties;
557:   GaussPointCoefficients **props;
558:   PetscScalar            *prop_E,*prop_nu;
559:   PetscErrorCode         ierr;

562:   /* setup for coords */
563:   DMGetCoordinateDM(elas_da,&cda);
564:   DMGetCoordinatesLocal(elas_da,&coords);
565:   DMDAVecGetArray(cda,coords,&_coords);

567:   /* setup for coefficients */
568:   DMCreateLocalVector(properties_da,&local_properties);
569:   DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
570:   DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
571:   DMDAVecGetArray(properties_da,local_properties,&props);

573:   DMDAGetElementsCorners(elas_da,&sex,&sey,0);
574:   DMDAGetElementsSizes(elas_da,&mx,&my,0);
575:   for (ej = sey; ej < sey+my; ej++) {
576:     for (ei = sex; ei < sex+mx; ei++) {
577:       /* get coords for the element */
578:       GetElementCoords(_coords,ei,ej,el_coords);

580:       /* get coefficients for the element */
581:       prop_E  = props[ej][ei].E;
582:       prop_nu = props[ej][ei].nu;

584:       /* initialise element stiffness matrix */
585:       PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);

587:       /* form element stiffness matrix */
588:       FormStressOperatorQ1(Ae,el_coords,prop_E,prop_nu);

590:       /* insert element matrix into global matrix */
591:       DMDAGetElementEqnums_u(u_eqn,ei,ej);
592:       MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
593:     }
594:   }
595:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
596:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

600:   DMDAVecRestoreArray(properties_da,local_properties,&props);
601:   VecDestroy(&local_properties);
602:   return(0);
603: }


606: static PetscErrorCode DMDASetValuesLocalStencil_ADD_VALUES(ElasticityDOF **fields_F,MatStencil u_eqn[],PetscScalar Fe_u[])
607: {
608:   PetscInt n;

611:   for (n = 0; n < 4; n++) {
612:     fields_F[u_eqn[2*n].j][u_eqn[2*n].i].ux_dof     = fields_F[u_eqn[2*n].j][u_eqn[2*n].i].ux_dof+Fe_u[2*n];
613:     fields_F[u_eqn[2*n+1].j][u_eqn[2*n+1].i].uy_dof = fields_F[u_eqn[2*n+1].j][u_eqn[2*n+1].i].uy_dof+Fe_u[2*n+1];
614:   }
615:   return(0);
616: }

618: static PetscErrorCode AssembleF_Elasticity(Vec F,DM elas_da,DM properties_da,Vec properties)
619: {
620:   DM                     cda;
621:   Vec                    coords;
622:   DMDACoor2d             **_coords;
623:   MatStencil             u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
624:   PetscInt               sex,sey,mx,my;
625:   PetscInt               ei,ej;
626:   PetscScalar            Fe[NODES_PER_EL*U_DOFS];
627:   PetscScalar            el_coords[NODES_PER_EL*NSD];
628:   Vec                    local_properties;
629:   GaussPointCoefficients **props;
630:   PetscScalar            *prop_fx,*prop_fy;
631:   Vec                    local_F;
632:   ElasticityDOF          **ff;
633:   PetscErrorCode         ierr;

636:   /* setup for coords */
637:   DMGetCoordinateDM(elas_da,&cda);
638:   DMGetCoordinatesLocal(elas_da,&coords);
639:   DMDAVecGetArray(cda,coords,&_coords);

641:   /* setup for coefficients */
642:   DMGetLocalVector(properties_da,&local_properties);
643:   DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
644:   DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
645:   DMDAVecGetArray(properties_da,local_properties,&props);

647:   /* get acces to the vector */
648:   DMGetLocalVector(elas_da,&local_F);
649:   VecZeroEntries(local_F);
650:   DMDAVecGetArray(elas_da,local_F,&ff);

652:   DMDAGetElementsCorners(elas_da,&sex,&sey,0);
653:   DMDAGetElementsSizes(elas_da,&mx,&my,0);
654:   for (ej = sey; ej < sey+my; ej++) {
655:     for (ei = sex; ei < sex+mx; ei++) {
656:       /* get coords for the element */
657:       GetElementCoords(_coords,ei,ej,el_coords);

659:       /* get coefficients for the element */
660:       prop_fx = props[ej][ei].fx;
661:       prop_fy = props[ej][ei].fy;

663:       /* initialise element stiffness matrix */
664:       PetscMemzero(Fe,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS);

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

669:       /* insert element matrix into global matrix */
670:       DMDAGetElementEqnums_u(u_eqn,ei,ej);

672:       DMDASetValuesLocalStencil_ADD_VALUES(ff,u_eqn,Fe);
673:     }
674:   }

676:   DMDAVecRestoreArray(elas_da,local_F,&ff);
677:   DMLocalToGlobalBegin(elas_da,local_F,ADD_VALUES,F);
678:   DMLocalToGlobalEnd(elas_da,local_F,ADD_VALUES,F);
679:   DMRestoreLocalVector(elas_da,&local_F);

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

683:   DMDAVecRestoreArray(properties_da,local_properties,&props);
684:   DMRestoreLocalVector(properties_da,&local_properties);
685:   return(0);
686: }

688: static PetscErrorCode solve_elasticity_2d(PetscInt mx,PetscInt my)
689: {
690:   DM                     elas_da,da_prop;
691:   PetscInt               u_dof,dof,stencil_width;
692:   Mat                    A;
693:   PetscInt               mxl,myl;
694:   DM                     prop_cda,vel_cda;
695:   Vec                    prop_coords,vel_coords;
696:   PetscInt               si,sj,nx,ny,i,j,p;
697:   Vec                    f,X;
698:   PetscInt               prop_dof,prop_stencil_width;
699:   Vec                    properties,l_properties;
700:   MatNullSpace           matnull;
701:   PetscReal              dx,dy;
702:   PetscInt               M,N;
703:   DMDACoor2d             **_prop_coords,**_vel_coords;
704:   GaussPointCoefficients **element_props;
705:   KSP                    ksp_E;
706:   PetscInt               coefficient_structure = 0;
707:   PetscInt               cpu_x,cpu_y,*lx = NULL,*ly = NULL;
708:   PetscBool              use_gp_coords = PETSC_FALSE;
709:   PetscBool              use_nonsymbc  = PETSC_FALSE;
710:   PetscBool              no_view       = PETSC_FALSE;
711:   PetscBool              flg;
712:   PetscErrorCode         ierr;

715:   /* Generate the da for velocity and pressure */
716:   /*
717:    We use Q1 elements for the temperature.
718:    FEM has a 9-point stencil (BOX) or connectivity pattern
719:    Num nodes in each direction is mx+1, my+1
720:    */
721:   u_dof         = U_DOFS; /* Vx, Vy - velocities */
722:   dof           = u_dof;
723:   stencil_width = 1;
724:   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,&elas_da);

726:   DMSetMatType(elas_da,MATAIJ);
727:   DMSetFromOptions(elas_da);
728:   DMSetUp(elas_da);

730:   DMDASetFieldName(elas_da,0,"Ux");
731:   DMDASetFieldName(elas_da,1,"Uy");

733:   /* unit box [0,1] x [0,1] */
734:   DMDASetUniformCoordinates(elas_da,0.0,1.0,0.0,1.0,0.0,1.0);

736:   /* Generate element properties, we will assume all material properties are constant over the element */
737:   /* local number of elements */
738:   DMDAGetElementsSizes(elas_da,&mxl,&myl,NULL);

740:   /* !!! IN PARALLEL WE MUST MAKE SURE THE TWO DMDA's ALIGN !!! */
741:   DMDAGetInfo(elas_da,0,0,0,0,&cpu_x,&cpu_y,0,0,0,0,0,0,0);
742:   DMDAGetElementOwnershipRanges2d(elas_da,&lx,&ly);

744:   prop_dof           = (PetscInt)(sizeof(GaussPointCoefficients)/sizeof(PetscScalar)); /* gauss point setup */
745:   prop_stencil_width = 0;
746:   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);
747:   DMSetFromOptions(da_prop);
748:   DMSetUp(da_prop);

750:   PetscFree(lx);
751:   PetscFree(ly);

753:   /* define centroid positions */
754:   DMDAGetInfo(da_prop,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
755:   dx   = 1.0/((PetscReal)(M));
756:   dy   = 1.0/((PetscReal)(N));

758:   DMDASetUniformCoordinates(da_prop,0.0+0.5*dx,1.0-0.5*dx,0.0+0.5*dy,1.0-0.5*dy,0.0,1.0);

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

763:   DMCreateGlobalVector(da_prop,&properties);
764:   DMCreateLocalVector(da_prop,&l_properties);
765:   DMDAVecGetArray(da_prop,l_properties,&element_props);

767:   DMGetCoordinateDM(da_prop,&prop_cda);
768:   DMGetCoordinatesLocal(da_prop,&prop_coords);
769:   DMDAVecGetArray(prop_cda,prop_coords,&_prop_coords);

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

773:   DMGetCoordinateDM(elas_da,&vel_cda);
774:   DMGetCoordinatesLocal(elas_da,&vel_coords);
775:   DMDAVecGetArray(vel_cda,vel_coords,&_vel_coords);

777:   /* interpolate the coordinates */
778:   for (j = sj; j < sj+ny; j++) {
779:     for (i = si; i < si+nx; i++) {
780:       PetscInt    ngp;
781:       PetscScalar gp_xi[GAUSS_POINTS][2],gp_weight[GAUSS_POINTS];
782:       PetscScalar el_coords[8];

784:       GetElementCoords(_vel_coords,i,j,el_coords);
785:       ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);

787:       for (p = 0; p < GAUSS_POINTS; p++) {
788:         PetscScalar gp_x,gp_y;
789:         PetscInt    n;
790:         PetscScalar xi_p[2],Ni_p[4];

792:         xi_p[0] = gp_xi[p][0];
793:         xi_p[1] = gp_xi[p][1];
794:         ConstructQ12D_Ni(xi_p,Ni_p);

796:         gp_x = 0.0;
797:         gp_y = 0.0;
798:         for (n = 0; n < NODES_PER_EL; n++) {
799:           gp_x = gp_x+Ni_p[n]*el_coords[2*n];
800:           gp_y = gp_y+Ni_p[n]*el_coords[2*n+1];
801:         }
802:         element_props[j][i].gp_coords[2*p]   = gp_x;
803:         element_props[j][i].gp_coords[2*p+1] = gp_y;
804:       }
805:     }
806:   }

808:   /* define the coefficients */
809:   PetscOptionsGetBool(NULL,NULL,"-use_gp_coords",&use_gp_coords,&flg);

811:   for (j = sj; j < sj+ny; j++) {
812:     for (i = si; i < si+nx; i++) {
813:       PetscScalar              centroid_x = _prop_coords[j][i].x; /* centroids of cell */
814:       PetscScalar              centroid_y = _prop_coords[j][i].y;
815:       PETSC_UNUSED PetscScalar coord_x,coord_y;

817:       if (coefficient_structure == 0) { /* isotropic */
818:         PetscScalar opts_E,opts_nu;

820:         opts_E  = 1.0;
821:         opts_nu = 0.33;
822:         PetscOptionsGetScalar(NULL,NULL,"-iso_E",&opts_E,&flg);
823:         PetscOptionsGetScalar(NULL,NULL,"-iso_nu",&opts_nu,&flg);

825:         for (p = 0; p < GAUSS_POINTS; p++) {
826:           element_props[j][i].E[p]  = opts_E;
827:           element_props[j][i].nu[p] = opts_nu;

829:           element_props[j][i].fx[p] = 0.0;
830:           element_props[j][i].fy[p] = 0.0;
831:         }
832:       } else if (coefficient_structure == 1) { /* step */
833:         PetscScalar opts_E0,opts_nu0,opts_xc;
834:         PetscScalar opts_E1,opts_nu1;

836:         opts_E0  = opts_E1  = 1.0;
837:         opts_nu0 = opts_nu1 = 0.333;
838:         opts_xc  = 0.5;
839:         PetscOptionsGetScalar(NULL,NULL,"-step_E0",&opts_E0,&flg);
840:         PetscOptionsGetScalar(NULL,NULL,"-step_nu0",&opts_nu0,&flg);
841:         PetscOptionsGetScalar(NULL,NULL,"-step_E1",&opts_E1,&flg);
842:         PetscOptionsGetScalar(NULL,NULL,"-step_nu1",&opts_nu1,&flg);
843:         PetscOptionsGetScalar(NULL,NULL,"-step_xc",&opts_xc,&flg);

845:         for (p = 0; p < GAUSS_POINTS; p++) {
846:           coord_x = centroid_x;
847:           coord_y = centroid_y;
848:           if (use_gp_coords) {
849:             coord_x = element_props[j][i].gp_coords[2*p];
850:             coord_y = element_props[j][i].gp_coords[2*p+1];
851:           }

853:           element_props[j][i].E[p]  = opts_E0;
854:           element_props[j][i].nu[p] = opts_nu0;
855:           if (PetscRealPart(coord_x) > PetscRealPart(opts_xc)) {
856:             element_props[j][i].E[p]  = opts_E1;
857:             element_props[j][i].nu[p] = opts_nu1;
858:           }

860:           element_props[j][i].fx[p] = 0.0;
861:           element_props[j][i].fy[p] = 0.0;
862:         }
863:       } else if (coefficient_structure == 2) { /* brick */
864:         PetscReal values_E[10];
865:         PetscReal values_nu[10];
866:         PetscInt  nbricks,maxnbricks;
867:         PetscInt  index,span;
868:         PetscInt  jj;

870:         flg        = PETSC_FALSE;
871:         maxnbricks = 10;
872:         PetscOptionsGetRealArray(NULL,NULL, "-brick_E",values_E,&maxnbricks,&flg);
873:         nbricks    = maxnbricks;
874:         if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"User must supply a list of E values for each brick");

876:         flg        = PETSC_FALSE;
877:         maxnbricks = 10;
878:         PetscOptionsGetRealArray(NULL,NULL, "-brick_nu",values_nu,&maxnbricks,&flg);
879:         if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"User must supply a list of nu values for each brick");
880:         if (maxnbricks != nbricks) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"User must supply equal numbers of values for E and nu");

882:         span = 1;
883:         PetscOptionsGetInt(NULL,NULL,"-brick_span",&span,&flg);

885:         /* cycle through the indices so that no two material properties are repeated in lines of x or y */
886:         jj    = (j/span)%nbricks;
887:         index = (jj+i/span)%nbricks;
888:         /*printf("j=%d: index = %d \n", j,index); */

890:         for (p = 0; p < GAUSS_POINTS; p++) {
891:           element_props[j][i].E[p]  = values_E[index];
892:           element_props[j][i].nu[p] = values_nu[index];
893:         }
894:       } else if (coefficient_structure == 3) { /* sponge */
895:         PetscScalar opts_E0,opts_nu0;
896:         PetscScalar opts_E1,opts_nu1;
897:         PetscInt    opts_t,opts_w;
898:         PetscInt    ii,jj,ci,cj;

900:         opts_E0  = opts_E1  = 1.0;
901:         opts_nu0 = opts_nu1 = 0.333;
902:         PetscOptionsGetScalar(NULL,NULL,"-sponge_E0",&opts_E0,&flg);
903:         PetscOptionsGetScalar(NULL,NULL,"-sponge_nu0",&opts_nu0,&flg);
904:         PetscOptionsGetScalar(NULL,NULL,"-sponge_E1",&opts_E1,&flg);
905:         PetscOptionsGetScalar(NULL,NULL,"-sponge_nu1",&opts_nu1,&flg);

907:         opts_t = opts_w = 1;
908:         PetscOptionsGetInt(NULL,NULL,"-sponge_t",&opts_t,&flg);
909:         PetscOptionsGetInt(NULL,NULL,"-sponge_w",&opts_w,&flg);

911:         ii = (i)/(opts_t+opts_w+opts_t);
912:         jj = (j)/(opts_t+opts_w+opts_t);

914:         ci = i - ii*(opts_t+opts_w+opts_t);
915:         cj = j - jj*(opts_t+opts_w+opts_t);

917:         for (p = 0; p < GAUSS_POINTS; p++) {
918:           element_props[j][i].E[p]  = opts_E0;
919:           element_props[j][i].nu[p] = opts_nu0;
920:         }
921:         if ((ci >= opts_t) && (ci < opts_t+opts_w)) {
922:           if ((cj >= opts_t) && (cj < opts_t+opts_w)) {
923:             for (p = 0; p < GAUSS_POINTS; p++) {
924:               element_props[j][i].E[p]  = opts_E1;
925:               element_props[j][i].nu[p] = opts_nu1;
926:             }
927:           }
928:         }
929:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Unknown coefficient_structure");
930:     }
931:   }
932:   DMDAVecRestoreArray(prop_cda,prop_coords,&_prop_coords);

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

936:   DMDAVecRestoreArray(da_prop,l_properties,&element_props);
937:   DMLocalToGlobalBegin(da_prop,l_properties,ADD_VALUES,properties);
938:   DMLocalToGlobalEnd(da_prop,l_properties,ADD_VALUES,properties);

940:   PetscOptionsGetBool(NULL,NULL,"-no_view",&no_view,NULL);
941:   if (!no_view) {
942:     DMDAViewCoefficientsGnuplot2d(da_prop,properties,"Coeffcients for elasticity eqn.","properties");
943:     DMDACoordViewGnuplot2d(elas_da,"mesh");
944:   }

946:   /* Generate a matrix with the correct non-zero pattern of type AIJ. This will work in parallel and serial */
947:   DMCreateMatrix(elas_da,&A);
948:   DMGetCoordinates(elas_da,&vel_coords);
949:   MatNullSpaceCreateRigidBody(vel_coords,&matnull);
950:   MatSetNearNullSpace(A,matnull);
951:   MatNullSpaceDestroy(&matnull);
952:   MatCreateVecs(A,&f,&X);

954:   /* assemble A11 */
955:   MatZeroEntries(A);
956:   VecZeroEntries(f);

958:   AssembleA_Elasticity(A,elas_da,da_prop,properties);
959:   /* build force vector */
960:   AssembleF_Elasticity(f,elas_da,da_prop,properties);

962:   KSPCreate(PETSC_COMM_WORLD,&ksp_E);
963:   KSPSetOptionsPrefix(ksp_E,"elas_");  /* elasticity */

965:   PetscOptionsGetBool(NULL,NULL,"-use_nonsymbc",&use_nonsymbc,&flg);
966:   /* solve */
967:   if (!use_nonsymbc) {
968:     Mat        AA;
969:     Vec        ff,XX;
970:     IS         is;
971:     VecScatter scat;

973:     DMDABCApplySymmetricCompression(elas_da,A,f,&is,&AA,&ff);
974:     VecDuplicate(ff,&XX);

976:     KSPSetOperators(ksp_E,AA,AA);
977:     KSPSetFromOptions(ksp_E);

979:     KSPSolve(ksp_E,ff,XX);

981:     /* push XX back into X */
982:     DMDABCApplyCompression(elas_da,NULL,X);

984:     VecScatterCreate(XX,NULL,X,is,&scat);
985:     VecScatterBegin(scat,XX,X,INSERT_VALUES,SCATTER_FORWARD);
986:     VecScatterEnd(scat,XX,X,INSERT_VALUES,SCATTER_FORWARD);
987:     VecScatterDestroy(&scat);

989:     MatDestroy(&AA);
990:     VecDestroy(&ff);
991:     VecDestroy(&XX);
992:     ISDestroy(&is);
993:   } else {
994:     DMDABCApplyCompression(elas_da,A,f);

996:     KSPSetOperators(ksp_E,A,A);
997:     KSPSetFromOptions(ksp_E);

999:     KSPSolve(ksp_E,f,X);
1000:   }

1002:   if (!no_view) {DMDAViewGnuplot2d(elas_da,X,"Displacement solution for elasticity eqn.","X");}
1003:   KSPDestroy(&ksp_E);

1005:   VecDestroy(&X);
1006:   VecDestroy(&f);
1007:   MatDestroy(&A);

1009:   DMDestroy(&elas_da);
1010:   DMDestroy(&da_prop);

1012:   VecDestroy(&properties);
1013:   VecDestroy(&l_properties);
1014:   return(0);
1015: }

1017: int main(int argc,char **args)
1018: {
1020:   PetscInt       mx,my;

1022:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
1023:   mx   = my = 10;
1024:   PetscOptionsGetInt(NULL,NULL,"-mx",&mx,NULL);
1025:   PetscOptionsGetInt(NULL,NULL,"-my",&my,NULL);
1026:   solve_elasticity_2d(mx,my);
1027:   PetscFinalize();
1028:   return ierr;
1029: }

1031: /* -------------------------- helpers for boundary conditions -------------------------------- */

1033: static PetscErrorCode BCApply_EAST(DM da,PetscInt d_idx,PetscScalar bc_val,Mat A,Vec b)
1034: {
1035:   DM                     cda;
1036:   Vec                    coords;
1037:   PetscInt               si,sj,nx,ny,i,j;
1038:   PetscInt               M,N;
1039:   DMDACoor2d             **_coords;
1040:   const PetscInt         *g_idx;
1041:   PetscInt               *bc_global_ids;
1042:   PetscScalar            *bc_vals;
1043:   PetscInt               nbcs;
1044:   PetscInt               n_dofs;
1045:   PetscErrorCode         ierr;
1046:   ISLocalToGlobalMapping ltogm;

1049:   /* enforce bc's */
1050:   DMGetLocalToGlobalMapping(da,&ltogm);
1051:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1053:   DMGetCoordinateDM(da,&cda);
1054:   DMGetCoordinatesLocal(da,&coords);
1055:   DMDAVecGetArray(cda,coords,&_coords);
1056:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1057:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1059:   /* --- */

1061:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
1062:   PetscMalloc1(ny*n_dofs,&bc_vals);

1064:   /* init the entries to -1 so VecSetValues will ignore them */
1065:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

1067:   i = nx-1;
1068:   for (j = 0; j < ny; j++) {
1069:     PetscInt                 local_id;
1070:     PETSC_UNUSED PetscScalar coordx,coordy;

1072:     local_id = i+j*nx;

1074:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

1076:     coordx = _coords[j+sj][i+si].x;
1077:     coordy = _coords[j+sj][i+si].y;

1079:     bc_vals[j] =  bc_val;
1080:   }
1081:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1082:   nbcs = 0;
1083:   if ((si+nx) == (M)) nbcs = ny;

1085:   if (b) {
1086:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1087:     VecAssemblyBegin(b);
1088:     VecAssemblyEnd(b);
1089:   }
1090:   if (A) {
1091:     MatZeroRows(A,nbcs,bc_global_ids,1.0,0,0);
1092:   }

1094:   PetscFree(bc_vals);
1095:   PetscFree(bc_global_ids);

1097:   DMDAVecRestoreArray(cda,coords,&_coords);
1098:   return(0);
1099: }

1101: static PetscErrorCode BCApply_WEST(DM da,PetscInt d_idx,PetscScalar bc_val,Mat A,Vec b)
1102: {
1103:   DM                     cda;
1104:   Vec                    coords;
1105:   PetscInt               si,sj,nx,ny,i,j;
1106:   PetscInt               M,N;
1107:   DMDACoor2d             **_coords;
1108:   const PetscInt         *g_idx;
1109:   PetscInt               *bc_global_ids;
1110:   PetscScalar            *bc_vals;
1111:   PetscInt               nbcs;
1112:   PetscInt               n_dofs;
1113:   PetscErrorCode         ierr;
1114:   ISLocalToGlobalMapping ltogm;

1117:   /* enforce bc's */
1118:   DMGetLocalToGlobalMapping(da,&ltogm);
1119:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1121:   DMGetCoordinateDM(da,&cda);
1122:   DMGetCoordinatesLocal(da,&coords);
1123:   DMDAVecGetArray(cda,coords,&_coords);
1124:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1125:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1127:   /* --- */

1129:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
1130:   PetscMalloc1(ny*n_dofs,&bc_vals);

1132:   /* init the entries to -1 so VecSetValues will ignore them */
1133:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

1135:   i = 0;
1136:   for (j = 0; j < ny; j++) {
1137:     PetscInt                 local_id;
1138:     PETSC_UNUSED PetscScalar coordx,coordy;

1140:     local_id = i+j*nx;

1142:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

1144:     coordx = _coords[j+sj][i+si].x;
1145:     coordy = _coords[j+sj][i+si].y;

1147:     bc_vals[j] =  bc_val;
1148:   }
1149:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1150:   nbcs = 0;
1151:   if (si == 0) nbcs = ny;

1153:   if (b) {
1154:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1155:     VecAssemblyBegin(b);
1156:     VecAssemblyEnd(b);
1157:   }
1158:   if (A) {
1159:     MatZeroRows(A,nbcs,bc_global_ids,1.0,0,0);
1160:   }

1162:   PetscFree(bc_vals);
1163:   PetscFree(bc_global_ids);

1165:   DMDAVecRestoreArray(cda,coords,&_coords);
1166:   return(0);
1167: }

1169: static PetscErrorCode DMDABCApplyCompression(DM elas_da,Mat A,Vec f)
1170: {

1174:   BCApply_EAST(elas_da,0,-1.0,A,f);
1175:   BCApply_EAST(elas_da,1, 0.0,A,f);
1176:   BCApply_WEST(elas_da,0,1.0,A,f);
1177:   BCApply_WEST(elas_da,1,0.0,A,f);
1178:   return(0);
1179: }

1181: static PetscErrorCode Orthogonalize(PetscInt n,Vec *vecs)
1182: {
1183:   PetscInt       i,j;
1184:   PetscScalar    dot;

1188:   for (i=0; i<n; i++) {
1189:   VecNormalize(vecs[i],NULL);
1190:      for (j=i+1; j<n; j++) {
1191:        VecDot(vecs[i],vecs[j],&dot);
1192:        VecAXPY(vecs[j],-dot,vecs[i]);
1193:      }
1194:   }
1195:   return(0);
1196: }

1198: static PetscErrorCode DMDABCApplySymmetricCompression(DM elas_da,Mat A,Vec f,IS *dofs,Mat *AA,Vec *ff)
1199: {
1201:   PetscInt       start,end,m;
1202:   PetscInt       *unconstrained;
1203:   PetscInt       cnt,i;
1204:   Vec            x;
1205:   PetscScalar    *_x;
1206:   IS             is;
1207:   VecScatter     scat;

1210:   /* push bc's into f and A */
1211:   VecDuplicate(f,&x);
1212:   BCApply_EAST(elas_da,0,-1.0,A,x);
1213:   BCApply_EAST(elas_da,1, 0.0,A,x);
1214:   BCApply_WEST(elas_da,0,1.0,A,x);
1215:   BCApply_WEST(elas_da,1,0.0,A,x);

1217:   /* define which dofs are not constrained */
1218:   VecGetLocalSize(x,&m);
1219:   PetscMalloc1(m,&unconstrained);
1220:   VecGetOwnershipRange(x,&start,&end);
1221:   VecGetArray(x,&_x);
1222:   cnt  = 0;
1223:   for (i = 0; i < m; i+=2) {
1224:     PetscReal val1,val2;

1226:     val1 = PetscRealPart(_x[i]);
1227:     val2 = PetscRealPart(_x[i+1]);
1228:     if (PetscAbs(val1) < 0.1 && PetscAbs(val2) < 0.1) {
1229:       unconstrained[cnt] = start + i;
1230:       cnt++;
1231:       unconstrained[cnt] = start + i + 1;
1232:       cnt++;
1233:     }
1234:   }
1235:   VecRestoreArray(x,&_x);

1237:   ISCreateGeneral(PETSC_COMM_WORLD,cnt,unconstrained,PETSC_COPY_VALUES,&is);
1238:   PetscFree(unconstrained);
1239:   ISSetBlockSize(is,2);

1241:   /* define correction for dirichlet in the rhs */
1242:   MatMult(A,x,f);
1243:   VecScale(f,-1.0);

1245:   /* get new matrix */
1246:   MatCreateSubMatrix(A,is,is,MAT_INITIAL_MATRIX,AA);
1247:   /* get new vector */
1248:   MatCreateVecs(*AA,NULL,ff);

1250:   VecScatterCreate(f,is,*ff,NULL,&scat);
1251:   VecScatterBegin(scat,f,*ff,INSERT_VALUES,SCATTER_FORWARD);
1252:   VecScatterEnd(scat,f,*ff,INSERT_VALUES,SCATTER_FORWARD);

1254:   {                             /* Constrain near-null space */
1255:     PetscInt     nvecs;
1256:     const        Vec *vecs;
1257:     Vec          *uvecs;
1258:     PetscBool    has_const;
1259:     MatNullSpace mnull,unull;

1261:     MatGetNearNullSpace(A,&mnull);
1262:     MatNullSpaceGetVecs(mnull,&has_const,&nvecs,&vecs);
1263:     VecDuplicateVecs(*ff,nvecs,&uvecs);
1264:     for (i=0; i<nvecs; i++) {
1265:       VecScatterBegin(scat,vecs[i],uvecs[i],INSERT_VALUES,SCATTER_FORWARD);
1266:       VecScatterEnd(scat,vecs[i],uvecs[i],INSERT_VALUES,SCATTER_FORWARD);
1267:     }
1268:     Orthogonalize(nvecs,uvecs);
1269:     MatNullSpaceCreate(PetscObjectComm((PetscObject)A),PETSC_FALSE,nvecs,uvecs,&unull);
1270:     MatSetNearNullSpace(*AA,unull);
1271:     MatNullSpaceDestroy(&unull);
1272:     VecDestroyVecs(nvecs,&uvecs);
1273:   }

1275:   VecScatterDestroy(&scat);

1277:   *dofs = is;
1278:   VecDestroy(&x);
1279:   return(0);
1280: }


1283: /*TEST

1285:    build:
1286:       requires: !complex !single

1288:    test:
1289:       args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_rtol 5e-3 -elas_ksp_view
1290:       output_file: output/ex49_1.out

1292:    test:
1293:       suffix: 2
1294:       nsize: 4
1295:       args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type gcr -elas_pc_type asm -elas_sub_pc_type lu -elas_ksp_rtol 5e-3

1297:    test:
1298:       suffix: 3
1299:       nsize: 4
1300:       args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 2 -brick_E 1,10,1000,100 -brick_nu 0.4,0.2,0.3,0.1 -brick_span 3 -elas_pc_type asm -elas_sub_pc_type lu -elas_ksp_rtol 5e-3

1302:    test:
1303:       suffix: 4
1304:       nsize: 4
1305:       args: -elas_ksp_monitor_short -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type unpreconditioned -mx 40 -my 40 -c_str 2 -brick_E 1,1e-6,1e-2 -brick_nu .3,.2,.4 -brick_span 8 -elas_mg_levels_ksp_type chebyshev -elas_pc_type ml -elas_mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.1 -elas_mg_levels_pc_type pbjacobi -elas_mg_levels_ksp_max_it 2 -use_nonsymbc -elas_pc_ml_nullspace user
1306:       requires: ml

1308:    test:
1309:       suffix: 5
1310:       nsize: 3
1311:       args: -elas_ksp_monitor_short -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -c_str 2 -brick_E 1,1e-6,1e-2 -brick_nu .3,.2,.4 -brick_span 8 -elas_pc_type gamg -elas_mg_levels_ksp_type chebyshev -elas_mg_levels_ksp_max_it 1 -elas_mg_levels_ksp_chebyshev_esteig 0.2,1.1 -elas_mg_levels_pc_type jacobi

1313:    test:
1314:       suffix: 6
1315:       nsize: 4
1316:       args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type pipegcr -elas_pc_type asm -elas_sub_pc_type lu

1318:    test:
1319:       suffix: 7
1320:       nsize: 4
1321:       args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type pipegcr -elas_pc_type asm -elas_sub_pc_type ksp -elas_sub_ksp_ksp_type cg -elas_sub_ksp_ksp_max_it 15

1323:    test:
1324:       suffix: 8
1325:       nsize: 4
1326:       args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type pipefgmres -elas_pc_type asm -elas_sub_pc_type ksp -elas_sub_ksp_ksp_type cg -elas_sub_ksp_ksp_max_it 15

1328:    test:
1329:       suffix: hypre_nullspace
1330:       requires: hypre
1331:       args: -elas_ksp_monitor_short -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -c_str 2 -brick_E 1,1e-6,1e-2 -brick_nu .3,.2,.4 -brick_span 8 -elas_pc_type hypre -elas_pc_hypre_boomeramg_nodal_coarsen 6 -elas_pc_hypre_boomeramg_vec_interp_variant 3 -elas_ksp_view

1333:    test:
1334:       nsize: 4
1335:       suffix: bddc
1336:       args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_pc_type bddc -elas_pc_bddc_monolithic

1338:    test:
1339:       nsize: 4
1340:       suffix: bddc_unsym
1341:       args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_pc_type bddc -elas_pc_bddc_monolithic -use_nonsymbc -elas_pc_bddc_symmetric 0

1343:    test:
1344:       nsize: 4
1345:       suffix: bddc_unsym_deluxe
1346:       args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_pc_type bddc -elas_pc_bddc_monolithic -use_nonsymbc -elas_pc_bddc_symmetric 0 -elas_pc_bddc_use_deluxe_scaling -elas_sub_schurs_symmetric 0

1348:    test:
1349:       nsize: 4
1350:       suffix: fetidp_unsym_deluxe
1351:       args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type fetidp -elas_fetidp_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_fetidp_bddc_pc_bddc_monolithic -use_nonsymbc -elas_fetidp_bddc_pc_bddc_use_deluxe_scaling -elas_fetidp_bddc_sub_schurs_symmetric 0 -elas_fetidp_bddc_pc_bddc_deluxe_singlemat

1353:    test:
1354:       nsize: 4
1355:       suffix: bddc_layerjump
1356:       args: -mx 40 -my 40 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type cg -elas_pc_type bddc -elas_pc_bddc_monolithic -dm_mat_type is -elas_ksp_norm_type natural

1358:    test:
1359:       nsize: 4
1360:       suffix: bddc_subdomainjump
1361:       args: -mx 40 -my 40 -elas_ksp_monitor_short -no_view -c_str 2 -brick_E 1,1000 -brick_nu 0.4,0.2 -brick_span 20  -elas_ksp_type cg -elas_pc_type bddc -elas_pc_bddc_monolithic -dm_mat_type is -elas_pc_is_use_stiffness_scaling -elas_ksp_norm_type natural

1363:    test:
1364:       nsize: 9
1365:       suffix: bddc_subdomainjump_deluxe
1366:       args: -mx 30 -my 30 -elas_ksp_monitor_short -no_view -c_str 2 -brick_E 1,1000 -brick_nu 0.4,0.2 -brick_span 10  -elas_ksp_type cg -elas_pc_type bddc -elas_pc_bddc_monolithic -dm_mat_type is -elas_pc_bddc_use_deluxe_scaling -elas_ksp_norm_type natural -elas_pc_bddc_schur_layers 1
1367: TEST*/