Actual source code: ex10.c


  2: static char help[] = "Linear elastiticty with dimensions using 20 node serendipity elements.\n\
  3: This also demonstrates use of  block\n\
  4: diagonal data structure.  Input arguments are:\n\
  5:   -m : problem size\n\n";

  7: #include <petscksp.h>

  9: /* This code is not intended as an efficient implementation, it is only
 10:    here to produce an interesting sparse matrix quickly.

 12:    PLEASE DO NOT BASE ANY OF YOUR CODES ON CODE LIKE THIS, THERE ARE MUCH
 13:    BETTER WAYS TO DO THIS. */

 15: extern PetscErrorCode GetElasticityMatrix(PetscInt,Mat*);
 16: extern PetscErrorCode Elastic20Stiff(PetscReal**);
 17: extern PetscErrorCode AddElement(Mat,PetscInt,PetscInt,PetscReal**,PetscInt,PetscInt);
 18: extern PetscErrorCode paulsetup20(void);
 19: extern PetscErrorCode paulintegrate20(PetscReal K[60][60]);

 21: int main(int argc,char **args)
 22: {
 23:   Mat            mat;
 24:   PetscInt       i,its,m = 3,rdim,cdim,rstart,rend;
 25:   PetscMPIInt    rank,size;
 26:   PetscScalar    v,neg1 = -1.0;
 27:   Vec            u,x,b;
 28:   KSP            ksp;
 29:   PetscReal      norm;

 31:   PetscInitialize(&argc,&args,(char*)0,help);
 32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 33:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 36:   /* Form matrix */
 37:   GetElasticityMatrix(m,&mat);

 39:   /* Generate vectors */
 40:   MatGetSize(mat,&rdim,&cdim);
 41:   MatGetOwnershipRange(mat,&rstart,&rend);
 42:   VecCreate(PETSC_COMM_WORLD,&u);
 43:   VecSetSizes(u,PETSC_DECIDE,rdim);
 44:   VecSetFromOptions(u);
 45:   VecDuplicate(u,&b);
 46:   VecDuplicate(b,&x);
 47:   for (i=rstart; i<rend; i++) {
 48:     v    = (PetscScalar)(i-rstart + 100*rank);
 49:     VecSetValues(u,1,&i,&v,INSERT_VALUES);
 50:   }
 51:   VecAssemblyBegin(u);
 52:   VecAssemblyEnd(u);

 54:   /* Compute right-hand-side */
 55:   MatMult(mat,u,b);

 57:   /* Solve linear system */
 58:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 59:   KSPSetOperators(ksp,mat,mat);
 60:   KSPSetFromOptions(ksp);
 61:   KSPSolve(ksp,b,x);
 62:   KSPGetIterationNumber(ksp,&its);
 63:   /* Check error */
 64:   VecAXPY(x,neg1,u);
 65:   VecNorm(x,NORM_2,&norm);

 67:   PetscPrintf(PETSC_COMM_WORLD,"Norm of residual %g Number of iterations %D\n",(double)norm,its);

 69:   /* Free work space */
 70:   KSPDestroy(&ksp);
 71:   VecDestroy(&u);
 72:   VecDestroy(&x);
 73:   VecDestroy(&b);
 74:   MatDestroy(&mat);

 76:   PetscFinalize();
 77:   return 0;
 78: }
 79: /* -------------------------------------------------------------------- */
 80: /*
 81:   GetElasticityMatrix - Forms 3D linear elasticity matrix.
 82:  */
 83: PetscErrorCode GetElasticityMatrix(PetscInt m,Mat *newmat)
 84: {
 85:   PetscInt       i,j,k,i1,i2,j_1,j2,k1,k2,h1,h2,shiftx,shifty,shiftz;
 86:   PetscInt       ict,nz,base,r1,r2,N,*rowkeep,nstart;
 87:   IS             iskeep;
 88:   PetscReal      **K,norm;
 89:   Mat            mat,submat = 0,*submatb;
 90:   MatType        type = MATSEQBAIJ;

 92:   m   /= 2; /* This is done just to be consistent with the old example */
 93:   N    = 3*(2*m+1)*(2*m+1)*(2*m+1);
 94:   PetscPrintf(PETSC_COMM_SELF,"m = %D, N=%D\n",m,N);
 95:   MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,80,NULL,&mat);

 97:   /* Form stiffness for element */
 98:   PetscMalloc1(81,&K);
 99:   for (i=0; i<81; i++) {
100:     PetscMalloc1(81,&K[i]);
101:   }
102:   Elastic20Stiff(K);

104:   /* Loop over elements and add contribution to stiffness */
105:   shiftx = 3; shifty = 3*(2*m+1); shiftz = 3*(2*m+1)*(2*m+1);
106:   for (k=0; k<m; k++) {
107:     for (j=0; j<m; j++) {
108:       for (i=0; i<m; i++) {
109:         h1   = 0;
110:         base = 2*k*shiftz + 2*j*shifty + 2*i*shiftx;
111:         for (k1=0; k1<3; k1++) {
112:           for (j_1=0; j_1<3; j_1++) {
113:             for (i1=0; i1<3; i1++) {
114:               h2 = 0;
115:               r1 = base + i1*shiftx + j_1*shifty + k1*shiftz;
116:               for (k2=0; k2<3; k2++) {
117:                 for (j2=0; j2<3; j2++) {
118:                   for (i2=0; i2<3; i2++) {
119:                     r2   = base + i2*shiftx + j2*shifty + k2*shiftz;
120:                     AddElement(mat,r1,r2,K,h1,h2);
121:                     h2  += 3;
122:                   }
123:                 }
124:               }
125:               h1 += 3;
126:             }
127:           }
128:         }
129:       }
130:     }
131:   }

133:   for (i=0; i<81; i++) {
134:     PetscFree(K[i]);
135:   }
136:   PetscFree(K);

138:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
139:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);

141:   /* Exclude any superfluous rows and columns */
142:   nstart = 3*(2*m+1)*(2*m+1);
143:   ict    = 0;
144:   PetscMalloc1(N-nstart,&rowkeep);
145:   for (i=nstart; i<N; i++) {
146:     MatGetRow(mat,i,&nz,0,0);
147:     if (nz) rowkeep[ict++] = i;
148:     MatRestoreRow(mat,i,&nz,0,0);
149:   }
150:   ISCreateGeneral(PETSC_COMM_SELF,ict,rowkeep,PETSC_COPY_VALUES,&iskeep);
151:   MatCreateSubMatrices(mat,1,&iskeep,&iskeep,MAT_INITIAL_MATRIX,&submatb);
152:   submat = *submatb;
153:   PetscFree(submatb);
154:   PetscFree(rowkeep);
155:   ISDestroy(&iskeep);
156:   MatDestroy(&mat);

158:   /* Convert storage formats -- just to demonstrate conversion to various
159:      formats (in particular, block diagonal storage).  This is NOT the
160:      recommended means to solve such a problem.  */
161:   MatConvert(submat,type,MAT_INITIAL_MATRIX,newmat);
162:   MatDestroy(&submat);

164:   MatNorm(*newmat,NORM_1,&norm);
165:   PetscPrintf(PETSC_COMM_WORLD,"matrix 1 norm = %g\n",(double)norm);

167:   return 0;
168: }
169: /* -------------------------------------------------------------------- */
170: PetscErrorCode AddElement(Mat mat,PetscInt r1,PetscInt r2,PetscReal **K,PetscInt h1,PetscInt h2)
171: {
172:   PetscScalar    val;
173:   PetscInt       l1,l2,row,col;

175:   for (l1=0; l1<3; l1++) {
176:     for (l2=0; l2<3; l2++) {
177: /*
178:    NOTE you should never do this! Inserting values 1 at a time is
179:    just too expensive!
180: */
181:       if (K[h1+l1][h2+l2] != 0.0) {
182:         row  = r1+l1; col = r2+l2; val = K[h1+l1][h2+l2];
183:         MatSetValues(mat,1,&row,1,&col,&val,ADD_VALUES);
184:         row  = r2+l2; col = r1+l1;
185:         MatSetValues(mat,1,&row,1,&col,&val,ADD_VALUES);
186:       }
187:     }
188:   }
189:   return 0;
190: }
191: /* -------------------------------------------------------------------- */
192: PetscReal N[20][64];                  /* Interpolation function. */
193: PetscReal part_N[3][20][64];          /* Partials of interpolation function. */
194: PetscReal rst[3][64];                 /* Location of integration pts in (r,s,t) */
195: PetscReal weight[64];                 /* Gaussian quadrature weights. */
196: PetscReal xyz[20][3];                 /* (x,y,z) coordinates of nodes  */
197: PetscReal E,nu;                       /* Physcial constants. */
198: PetscInt  n_int,N_int;                /* N_int = n_int^3, number of int. pts. */
199: /* Ordering of the vertices, (r,s,t) coordinates, of the canonical cell. */
200: PetscReal r2[20] = {-1.0,0.0,1.0,-1.0,1.0,-1.0,0.0,1.0,
201:                     -1.0,1.0,-1.0,1.0,
202:                     -1.0,0.0,1.0,-1.0,1.0,-1.0,0.0,1.0};
203: PetscReal s2[20] = {-1.0,-1.0, -1.0,0.0,0.0,1.0, 1.0, 1.0,
204:                     -1.0,-1.0,1.0,1.0,
205:                     -1.0,-1.0, -1.0,0.0,0.0,1.0, 1.0, 1.0};
206: PetscReal t2[20] = {-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,
207:                     0.0,0.0,0.0,0.0,
208:                     1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0};
209: PetscInt  rmap[20] = {0,1,2,3,5,6,7,8,9,11,15,17,18,19,20,21,23,24,25,26};
210: /* -------------------------------------------------------------------- */
211: /*
212:   Elastic20Stiff - Forms 20 node elastic stiffness for element.
213:  */
214: PetscErrorCode Elastic20Stiff(PetscReal **Ke)
215: {
216:   PetscReal K[60][60],x,y,z,dx,dy,dz;
217:   PetscInt  i,j,k,l,Ii,J;

219:   paulsetup20();

221:   x          = -1.0;  y = -1.0; z = -1.0; dx = 2.0; dy = 2.0; dz = 2.0;
222:   xyz[0][0]  = x;          xyz[0][1] = y;          xyz[0][2] = z;
223:   xyz[1][0]  = x + dx;     xyz[1][1] = y;          xyz[1][2] = z;
224:   xyz[2][0]  = x + 2.*dx;  xyz[2][1] = y;          xyz[2][2] = z;
225:   xyz[3][0]  = x;          xyz[3][1] = y + dy;     xyz[3][2] = z;
226:   xyz[4][0]  = x + 2.*dx;  xyz[4][1] = y + dy;     xyz[4][2] = z;
227:   xyz[5][0]  = x;          xyz[5][1] = y + 2.*dy;  xyz[5][2] = z;
228:   xyz[6][0]  = x + dx;     xyz[6][1] = y + 2.*dy;  xyz[6][2] = z;
229:   xyz[7][0]  = x + 2.*dx;  xyz[7][1] = y + 2.*dy;  xyz[7][2] = z;
230:   xyz[8][0]  = x;          xyz[8][1] = y;          xyz[8][2] = z + dz;
231:   xyz[9][0]  = x + 2.*dx;  xyz[9][1] = y;          xyz[9][2] = z + dz;
232:   xyz[10][0] = x;         xyz[10][1] = y + 2.*dy; xyz[10][2] = z + dz;
233:   xyz[11][0] = x + 2.*dx; xyz[11][1] = y + 2.*dy; xyz[11][2] = z + dz;
234:   xyz[12][0] = x;         xyz[12][1] = y;         xyz[12][2] = z + 2.*dz;
235:   xyz[13][0] = x + dx;    xyz[13][1] = y;         xyz[13][2] = z + 2.*dz;
236:   xyz[14][0] = x + 2.*dx; xyz[14][1] = y;         xyz[14][2] = z + 2.*dz;
237:   xyz[15][0] = x;         xyz[15][1] = y + dy;    xyz[15][2] = z + 2.*dz;
238:   xyz[16][0] = x + 2.*dx; xyz[16][1] = y + dy;    xyz[16][2] = z + 2.*dz;
239:   xyz[17][0] = x;         xyz[17][1] = y + 2.*dy; xyz[17][2] = z + 2.*dz;
240:   xyz[18][0] = x + dx;    xyz[18][1] = y + 2.*dy; xyz[18][2] = z + 2.*dz;
241:   xyz[19][0] = x + 2.*dx; xyz[19][1] = y + 2.*dy; xyz[19][2] = z + 2.*dz;
242:   paulintegrate20(K);

244:   /* copy the stiffness from K into format used by Ke */
245:   for (i=0; i<81; i++) {
246:     for (j=0; j<81; j++) {
247:       Ke[i][j] = 0.0;
248:     }
249:   }
250:   Ii = 0;
251:   for (i=0; i<20; i++) {
252:     J = 0;
253:     for (j=0; j<20; j++) {
254:       for (k=0; k<3; k++) {
255:         for (l=0; l<3; l++) {
256:           Ke[3*rmap[i]+k][3*rmap[j]+l] = K[Ii+k][J+l];
257:         }
258:       }
259:       J += 3;
260:     }
261:     Ii += 3;
262:   }

264:   /* force the matrix to be exactly symmetric */
265:   for (i=0; i<81; i++) {
266:     for (j=0; j<i; j++) {
267:       Ke[i][j] = (Ke[i][j] + Ke[j][i])/2.0;
268:     }
269:   }
270:   return 0;
271: }
272: /* -------------------------------------------------------------------- */
273: /*
274:   paulsetup20 - Sets up data structure for forming local elastic stiffness.
275:  */
276: PetscErrorCode paulsetup20(void)
277: {
278:   PetscInt  i,j,k,cnt;
279:   PetscReal x[4],w[4];
280:   PetscReal c;

282:   n_int = 3;
283:   nu    = 0.3;
284:   E     = 1.0;

286:   /* Assign integration points and weights for
287:        Gaussian quadrature formulae. */
288:   if (n_int == 2) {
289:     x[0] = (-0.577350269189626);
290:     x[1] = (0.577350269189626);
291:     w[0] = 1.0000000;
292:     w[1] = 1.0000000;
293:   } else if (n_int == 3) {
294:     x[0] = (-0.774596669241483);
295:     x[1] = 0.0000000;
296:     x[2] = 0.774596669241483;
297:     w[0] = 0.555555555555555;
298:     w[1] = 0.888888888888888;
299:     w[2] = 0.555555555555555;
300:   } else if (n_int == 4) {
301:     x[0] = (-0.861136311594053);
302:     x[1] = (-0.339981043584856);
303:     x[2] = 0.339981043584856;
304:     x[3] = 0.861136311594053;
305:     w[0] = 0.347854845137454;
306:     w[1] = 0.652145154862546;
307:     w[2] = 0.652145154862546;
308:     w[3] = 0.347854845137454;
309:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Value for n_int not supported");

311:   /* rst[][i] contains the location of the i-th integration point
312:       in the canonical (r,s,t) coordinate system.  weight[i] contains
313:       the Gaussian weighting factor. */

315:   cnt = 0;
316:   for (i=0; i<n_int; i++) {
317:     for (j=0; j<n_int; j++) {
318:       for (k=0; k<n_int; k++) {
319:         rst[0][cnt] =x[i];
320:         rst[1][cnt] =x[j];
321:         rst[2][cnt] =x[k];
322:         weight[cnt] = w[i]*w[j]*w[k];
323:         ++cnt;
324:       }
325:     }
326:   }
327:   N_int = cnt;

329:   /* N[][j] is the interpolation vector, N[][j] .* xyz[] */
330:   /* yields the (x,y,z)  locations of the integration point. */
331:   /*  part_N[][][j] is the partials of the N function */
332:   /*  w.r.t. (r,s,t). */

334:   c = 1.0/8.0;
335:   for (j=0; j<N_int; j++) {
336:     for (i=0; i<20; i++) {
337:       if (i==0 || i==2 || i==5 || i==7 || i==12 || i==14 || i== 17 || i==19) {
338:         N[i][j] = c*(1.0 + r2[i]*rst[0][j])*
339:                   (1.0 + s2[i]*rst[1][j])*(1.0 + t2[i]*rst[2][j])*
340:                   (-2.0 + r2[i]*rst[0][j] + s2[i]*rst[1][j] + t2[i]*rst[2][j]);
341:         part_N[0][i][j] = c*r2[i]*(1 + s2[i]*rst[1][j])*(1 + t2[i]*rst[2][j])*
342:                           (-1.0 + 2.0*r2[i]*rst[0][j] + s2[i]*rst[1][j] +
343:                            t2[i]*rst[2][j]);
344:         part_N[1][i][j] = c*s2[i]*(1 + r2[i]*rst[0][j])*(1 + t2[i]*rst[2][j])*
345:                           (-1.0 + r2[i]*rst[0][j] + 2.0*s2[i]*rst[1][j] +
346:                            t2[i]*rst[2][j]);
347:         part_N[2][i][j] = c*t2[i]*(1 + r2[i]*rst[0][j])*(1 + s2[i]*rst[1][j])*
348:                           (-1.0 + r2[i]*rst[0][j] + s2[i]*rst[1][j] +
349:                            2.0*t2[i]*rst[2][j]);
350:       } else if (i==1 || i==6 || i==13 || i==18) {
351:         N[i][j] = .25*(1.0 - rst[0][j]*rst[0][j])*
352:                   (1.0 + s2[i]*rst[1][j])*(1.0 + t2[i]*rst[2][j]);
353:         part_N[0][i][j] = -.5*rst[0][j]*(1 + s2[i]*rst[1][j])*
354:                           (1 + t2[i]*rst[2][j]);
355:         part_N[1][i][j] = .25*s2[i]*(1 + t2[i]*rst[2][j])*
356:                           (1.0 - rst[0][j]*rst[0][j]);
357:         part_N[2][i][j] = .25*t2[i]*(1.0 - rst[0][j]*rst[0][j])*
358:                           (1 + s2[i]*rst[1][j]);
359:       } else if (i==3 || i==4 || i==15 || i==16) {
360:         N[i][j] = .25*(1.0 - rst[1][j]*rst[1][j])*
361:                   (1.0 + r2[i]*rst[0][j])*(1.0 + t2[i]*rst[2][j]);
362:         part_N[0][i][j] = .25*r2[i]*(1 + t2[i]*rst[2][j])*
363:                           (1.0 - rst[1][j]*rst[1][j]);
364:         part_N[1][i][j] = -.5*rst[1][j]*(1 + r2[i]*rst[0][j])*
365:                           (1 + t2[i]*rst[2][j]);
366:         part_N[2][i][j] = .25*t2[i]*(1.0 - rst[1][j]*rst[1][j])*
367:                           (1 + r2[i]*rst[0][j]);
368:       } else if (i==8 || i==9 || i==10 || i==11) {
369:         N[i][j] = .25*(1.0 - rst[2][j]*rst[2][j])*
370:                   (1.0 + r2[i]*rst[0][j])*(1.0 + s2[i]*rst[1][j]);
371:         part_N[0][i][j] = .25*r2[i]*(1 + s2[i]*rst[1][j])*
372:                           (1.0 - rst[2][j]*rst[2][j]);
373:         part_N[1][i][j] = .25*s2[i]*(1.0 - rst[2][j]*rst[2][j])*
374:                           (1 + r2[i]*rst[0][j]);
375:         part_N[2][i][j] = -.5*rst[2][j]*(1 + r2[i]*rst[0][j])*
376:                           (1 + s2[i]*rst[1][j]);
377:       }
378:     }
379:   }
380:   return 0;
381: }
382: /* -------------------------------------------------------------------- */
383: /*
384:    paulintegrate20 - Does actual numerical integration on 20 node element.
385:  */
386: PetscErrorCode paulintegrate20(PetscReal K[60][60])
387: {
388:   PetscReal det_jac,jac[3][3],inv_jac[3][3];
389:   PetscReal B[6][60],B_temp[6][60],C[6][6];
390:   PetscReal temp;
391:   PetscInt  i,j,k,step;

393:   /* Zero out K, since we will accumulate the result here */
394:   for (i=0; i<60; i++) {
395:     for (j=0; j<60; j++) {
396:       K[i][j] = 0.0;
397:     }
398:   }

400:   /* Loop over integration points ... */
401:   for (step=0; step<N_int; step++) {

403:     /* Compute the Jacobian, its determinant, and inverse. */
404:     for (i=0; i<3; i++) {
405:       for (j=0; j<3; j++) {
406:         jac[i][j] = 0;
407:         for (k=0; k<20; k++) {
408:           jac[i][j] += part_N[i][k][step]*xyz[k][j];
409:         }
410:       }
411:     }
412:     det_jac = jac[0][0]*(jac[1][1]*jac[2][2]-jac[1][2]*jac[2][1])
413:               + jac[0][1]*(jac[1][2]*jac[2][0]-jac[1][0]*jac[2][2])
414:               + jac[0][2]*(jac[1][0]*jac[2][1]-jac[1][1]*jac[2][0]);
415:     inv_jac[0][0] = (jac[1][1]*jac[2][2]-jac[1][2]*jac[2][1])/det_jac;
416:     inv_jac[0][1] = (jac[0][2]*jac[2][1]-jac[0][1]*jac[2][2])/det_jac;
417:     inv_jac[0][2] = (jac[0][1]*jac[1][2]-jac[1][1]*jac[0][2])/det_jac;
418:     inv_jac[1][0] = (jac[1][2]*jac[2][0]-jac[1][0]*jac[2][2])/det_jac;
419:     inv_jac[1][1] = (jac[0][0]*jac[2][2]-jac[2][0]*jac[0][2])/det_jac;
420:     inv_jac[1][2] = (jac[0][2]*jac[1][0]-jac[0][0]*jac[1][2])/det_jac;
421:     inv_jac[2][0] = (jac[1][0]*jac[2][1]-jac[1][1]*jac[2][0])/det_jac;
422:     inv_jac[2][1] = (jac[0][1]*jac[2][0]-jac[0][0]*jac[2][1])/det_jac;
423:     inv_jac[2][2] = (jac[0][0]*jac[1][1]-jac[1][0]*jac[0][1])/det_jac;

425:     /* Compute the B matrix. */
426:     for (i=0; i<3; i++) {
427:       for (j=0; j<20; j++) {
428:         B_temp[i][j] = 0.0;
429:         for (k=0; k<3; k++) {
430:           B_temp[i][j] += inv_jac[i][k]*part_N[k][j][step];
431:         }
432:       }
433:     }
434:     for (i=0; i<6; i++) {
435:       for (j=0; j<60; j++) {
436:         B[i][j] = 0.0;
437:       }
438:     }

440:     /* Put values in correct places in B. */
441:     for (k=0; k<20; k++) {
442:       B[0][3*k]   = B_temp[0][k];
443:       B[1][3*k+1] = B_temp[1][k];
444:       B[2][3*k+2] = B_temp[2][k];
445:       B[3][3*k]   = B_temp[1][k];
446:       B[3][3*k+1] = B_temp[0][k];
447:       B[4][3*k+1] = B_temp[2][k];
448:       B[4][3*k+2] = B_temp[1][k];
449:       B[5][3*k]   = B_temp[2][k];
450:       B[5][3*k+2] = B_temp[0][k];
451:     }

453:     /* Construct the C matrix, uses the constants "nu" and "E". */
454:     for (i=0; i<6; i++) {
455:       for (j=0; j<6; j++) {
456:         C[i][j] = 0.0;
457:       }
458:     }
459:     temp = (1.0 + nu)*(1.0 - 2.0*nu);
460:     temp = E/temp;
461:     C[0][0] = temp*(1.0 - nu);
462:     C[1][1] = C[0][0];
463:     C[2][2] = C[0][0];
464:     C[3][3] = temp*(0.5 - nu);
465:     C[4][4] = C[3][3];
466:     C[5][5] = C[3][3];
467:     C[0][1] = temp*nu;
468:     C[0][2] = C[0][1];
469:     C[1][0] = C[0][1];
470:     C[1][2] = C[0][1];
471:     C[2][0] = C[0][1];
472:     C[2][1] = C[0][1];

474:     for (i=0; i<6; i++) {
475:       for (j=0; j<60; j++) {
476:         B_temp[i][j] = 0.0;
477:         for (k=0; k<6; k++) {
478:           B_temp[i][j] += C[i][k]*B[k][j];
479:         }
480:         B_temp[i][j] *= det_jac;
481:       }
482:     }

484:     /* Accumulate B'*C*B*det(J)*weight, as a function of (r,s,t), in K. */
485:     for (i=0; i<60; i++) {
486:       for (j=0; j<60; j++) {
487:         temp = 0.0;
488:         for (k=0; k<6; k++) {
489:           temp += B[k][i]*B_temp[k][j];
490:         }
491:         K[i][j] += temp*weight[step];
492:       }
493:     }
494:   }  /* end of loop over integration points */
495:   return 0;
496: }

498: /*TEST

500:     test:
501:       args: -matconvert_type seqaij -ksp_monitor_short -ksp_rtol 1.e-2  -pc_type jacobi
502:       requires: x

504: TEST*/