Actual source code: ex10.c

petsc-3.7.2 2016-06-05
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  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]);

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

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

 39:   /* Form matrix */
 40:   GetElasticityMatrix(m,&mat);

 42:   /* Generate vectors */
 43:   MatGetSize(mat,&rdim,&cdim);
 44:   MatGetOwnershipRange(mat,&rstart,&rend);
 45:   VecCreate(PETSC_COMM_WORLD,&u);
 46:   VecSetSizes(u,PETSC_DECIDE,rdim);
 47:   VecSetFromOptions(u);
 48:   VecDuplicate(u,&b);
 49:   VecDuplicate(b,&x);
 50:   for (i=rstart; i<rend; i++) {
 51:     v    = (PetscScalar)(i-rstart + 100*rank);
 52:     VecSetValues(u,1,&i,&v,INSERT_VALUES);
 53:   }
 54:   VecAssemblyBegin(u);
 55:   VecAssemblyEnd(u);

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

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

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

 72:   /* Free work space */
 73:   KSPDestroy(&ksp);
 74:   VecDestroy(&u);
 75:   VecDestroy(&x);
 76:   VecDestroy(&b);
 77:   MatDestroy(&mat);

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

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

103:   /* Form stiffness for element */
104:   PetscMalloc1(81,&K);
105:   for (i=0; i<81; i++) {
106:     PetscMalloc1(81,&K[i]);
107:   }
108:   Elastic20Stiff(K);

110:   /* Loop over elements and add contribution to stiffness */
111:   shiftx = 3; shifty = 3*(2*m+1); shiftz = 3*(2*m+1)*(2*m+1);
112:   for (k=0; k<m; k++) {
113:     for (j=0; j<m; j++) {
114:       for (i=0; i<m; i++) {
115:         h1   = 0;
116:         base = 2*k*shiftz + 2*j*shifty + 2*i*shiftx;
117:         for (k1=0; k1<3; k1++) {
118:           for (j_1=0; j_1<3; j_1++) {
119:             for (i1=0; i1<3; i1++) {
120:               h2 = 0;
121:               r1 = base + i1*shiftx + j_1*shifty + k1*shiftz;
122:               for (k2=0; k2<3; k2++) {
123:                 for (j2=0; j2<3; j2++) {
124:                   for (i2=0; i2<3; i2++) {
125:                     r2   = base + i2*shiftx + j2*shifty + k2*shiftz;
126:                     AddElement(mat,r1,r2,K,h1,h2);
127:                     h2  += 3;
128:                   }
129:                 }
130:               }
131:               h1 += 3;
132:             }
133:           }
134:         }
135:       }
136:     }
137:   }

139:   for (i=0; i<81; i++) {
140:     PetscFree(K[i]);
141:   }
142:   PetscFree(K);

144:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
145:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);

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

164:   /* Convert storage formats -- just to demonstrate conversion to various
165:      formats (in particular, block diagonal storage).  This is NOT the
166:      recommended means to solve such a problem.  */
167:   MatConvert(submat,type,MAT_INITIAL_MATRIX,newmat);
168:   MatDestroy(&submat);

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

173:   return 0;
174: }
175: /* -------------------------------------------------------------------- */
178: PetscErrorCode AddElement(Mat mat,PetscInt r1,PetscInt r2,PetscReal **K,PetscInt h1,PetscInt h2)
179: {
180:   PetscScalar    val;
181:   PetscInt       l1,l2,row,col;

184:   for (l1=0; l1<3; l1++) {
185:     for (l2=0; l2<3; l2++) {
186: /*
187:    NOTE you should never do this! Inserting values 1 at a time is
188:    just too expensive!
189: */
190:       if (K[h1+l1][h2+l2] != 0.0) {
191:         row  = r1+l1; col = r2+l2; val = K[h1+l1][h2+l2];
192:         MatSetValues(mat,1,&row,1,&col,&val,ADD_VALUES);
193:         row  = r2+l2; col = r1+l1;
194:         MatSetValues(mat,1,&row,1,&col,&val,ADD_VALUES);
195:       }
196:     }
197:   }
198:   return 0;
199: }
200: /* -------------------------------------------------------------------- */
201: PetscReal N[20][64];                  /* Interpolation function. */
202: PetscReal part_N[3][20][64];          /* Partials of interpolation function. */
203: PetscReal rst[3][64];                 /* Location of integration pts in (r,s,t) */
204: PetscReal weight[64];                 /* Gaussian quadrature weights. */
205: PetscReal xyz[20][3];                 /* (x,y,z) coordinates of nodes  */
206: PetscReal E,nu;                       /* Physcial constants. */
207: PetscInt  n_int,N_int;                /* N_int = n_int^3, number of int. pts. */
208: /* Ordering of the vertices, (r,s,t) coordinates, of the canonical cell. */
209: PetscReal r2[20] = {-1.0,0.0,1.0,-1.0,1.0,-1.0,0.0,1.0,
210:                     -1.0,1.0,-1.0,1.0,
211:                     -1.0,0.0,1.0,-1.0,1.0,-1.0,0.0,1.0};
212: PetscReal s2[20] = {-1.0,-1.0, -1.0,0.0,0.0,1.0, 1.0, 1.0,
213:                     -1.0,-1.0,1.0,1.0,
214:                     -1.0,-1.0, -1.0,0.0,0.0,1.0, 1.0, 1.0};
215: PetscReal t2[20] = {-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,
216:                     0.0,0.0,0.0,0.0,
217:                     1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0};
218: PetscInt  rmap[20] = {0,1,2,3,5,6,7,8,9,11,15,17,18,19,20,21,23,24,25,26};
219: /* -------------------------------------------------------------------- */
222: /*
223:   Elastic20Stiff - Forms 20 node elastic stiffness for element.
224:  */
225: PetscErrorCode Elastic20Stiff(PetscReal **Ke)
226: {
227:   PetscReal K[60][60],x,y,z,dx,dy,dz,v;
228:   PetscInt  i,j,k,l,Ii,J;

230:   paulsetup20();

232:   x          = -1.0;  y = -1.0; z = -1.0; dx = 2.0; dy = 2.0; dz = 2.0;
233:   xyz[0][0]  = x;          xyz[0][1] = y;          xyz[0][2] = z;
234:   xyz[1][0]  = x + dx;     xyz[1][1] = y;          xyz[1][2] = z;
235:   xyz[2][0]  = x + 2.*dx;  xyz[2][1] = y;          xyz[2][2] = z;
236:   xyz[3][0]  = x;          xyz[3][1] = y + dy;     xyz[3][2] = z;
237:   xyz[4][0]  = x + 2.*dx;  xyz[4][1] = y + dy;     xyz[4][2] = z;
238:   xyz[5][0]  = x;          xyz[5][1] = y + 2.*dy;  xyz[5][2] = z;
239:   xyz[6][0]  = x + dx;     xyz[6][1] = y + 2.*dy;  xyz[6][2] = z;
240:   xyz[7][0]  = x + 2.*dx;  xyz[7][1] = y + 2.*dy;  xyz[7][2] = z;
241:   xyz[8][0]  = x;          xyz[8][1] = y;          xyz[8][2] = z + dz;
242:   xyz[9][0]  = x + 2.*dx;  xyz[9][1] = y;          xyz[9][2] = z + dz;
243:   xyz[10][0] = x;         xyz[10][1] = y + 2.*dy; xyz[10][2] = z + dz;
244:   xyz[11][0] = x + 2.*dx; xyz[11][1] = y + 2.*dy; xyz[11][2] = z + dz;
245:   xyz[12][0] = x;         xyz[12][1] = y;         xyz[12][2] = z + 2.*dz;
246:   xyz[13][0] = x + dx;    xyz[13][1] = y;         xyz[13][2] = z + 2.*dz;
247:   xyz[14][0] = x + 2.*dx; xyz[14][1] = y;         xyz[14][2] = z + 2.*dz;
248:   xyz[15][0] = x;         xyz[15][1] = y + dy;    xyz[15][2] = z + 2.*dz;
249:   xyz[16][0] = x + 2.*dx; xyz[16][1] = y + dy;    xyz[16][2] = z + 2.*dz;
250:   xyz[17][0] = x;         xyz[17][1] = y + 2.*dy; xyz[17][2] = z + 2.*dz;
251:   xyz[18][0] = x + dx;    xyz[18][1] = y + 2.*dy; xyz[18][2] = z + 2.*dz;
252:   xyz[19][0] = x + 2.*dx; xyz[19][1] = y + 2.*dy; xyz[19][2] = z + 2.*dz;
253:   paulintegrate20(K);

255:   /* copy the stiffness from K into format used by Ke */
256:   for (i=0; i<81; i++) {
257:     for (j=0; j<81; j++) {
258:       Ke[i][j] = 0.0;
259:     }
260:   }
261:   Ii = 0;
262:   for (i=0; i<20; i++) {
263:     J = 0;
264:     for (j=0; j<20; j++) {
265:       for (k=0; k<3; k++) {
266:         for (l=0; l<3; l++) {
267:           Ke[3*rmap[i]+k][3*rmap[j]+l] = v = K[Ii+k][J+l];
268:         }
269:       }
270:       J += 3;
271:     }
272:     Ii += 3;
273:   }

275:   /* force the matrix to be exactly symmetric */
276:   for (i=0; i<81; i++) {
277:     for (j=0; j<i; j++) {
278:       Ke[i][j] = (Ke[i][j] + Ke[j][i])/2.0;
279:     }
280:   }
281:   return 0;
282: }
283: /* -------------------------------------------------------------------- */
286: /*
287:   paulsetup20 - Sets up data structure for forming local elastic stiffness.
288:  */
289: PetscErrorCode paulsetup20(void)
290: {
291:   PetscInt  i,j,k,cnt;
292:   PetscReal x[4],w[4];
293:   PetscReal c;

295:   n_int = 3;
296:   nu    = 0.3;
297:   E     = 1.0;

299:   /* Assign integration points and weights for
300:        Gaussian quadrature formulae. */
301:   if (n_int == 2) {
302:     x[0] = (-0.577350269189626);
303:     x[1] = (0.577350269189626);
304:     w[0] = 1.0000000;
305:     w[1] = 1.0000000;
306:   } else if (n_int == 3) {
307:     x[0] = (-0.774596669241483);
308:     x[1] = 0.0000000;
309:     x[2] = 0.774596669241483;
310:     w[0] = 0.555555555555555;
311:     w[1] = 0.888888888888888;
312:     w[2] = 0.555555555555555;
313:   } else if (n_int == 4) {
314:     x[0] = (-0.861136311594053);
315:     x[1] = (-0.339981043584856);
316:     x[2] = 0.339981043584856;
317:     x[3] = 0.861136311594053;
318:     w[0] = 0.347854845137454;
319:     w[1] = 0.652145154862546;
320:     w[2] = 0.652145154862546;
321:     w[3] = 0.347854845137454;
322:   } else SETERRQ(PETSC_COMM_SELF,1,"Unknown value for n_int");

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

328:   cnt = 0;
329:   for (i=0; i<n_int; i++) {
330:     for (j=0; j<n_int; j++) {
331:       for (k=0; k<n_int; k++) {
332:         rst[0][cnt] =x[i];
333:         rst[1][cnt] =x[j];
334:         rst[2][cnt] =x[k];
335:         weight[cnt] = w[i]*w[j]*w[k];
336:         ++cnt;
337:       }
338:     }
339:   }
340:   N_int = cnt;

342:   /* N[][j] is the interpolation vector, N[][j] .* xyz[] */
343:   /* yields the (x,y,z)  locations of the integration point. */
344:   /*  part_N[][][j] is the partials of the N function */
345:   /*  w.r.t. (r,s,t). */

347:   c = 1.0/8.0;
348:   for (j=0; j<N_int; j++) {
349:     for (i=0; i<20; i++) {
350:       if (i==0 || i==2 || i==5 || i==7 || i==12 || i==14 || i== 17 || i==19) {
351:         N[i][j] = c*(1.0 + r2[i]*rst[0][j])*
352:                   (1.0 + s2[i]*rst[1][j])*(1.0 + t2[i]*rst[2][j])*
353:                   (-2.0 + r2[i]*rst[0][j] + s2[i]*rst[1][j] + t2[i]*rst[2][j]);
354:         part_N[0][i][j] = c*r2[i]*(1 + s2[i]*rst[1][j])*(1 + t2[i]*rst[2][j])*
355:                           (-1.0 + 2.0*r2[i]*rst[0][j] + s2[i]*rst[1][j] +
356:                            t2[i]*rst[2][j]);
357:         part_N[1][i][j] = c*s2[i]*(1 + r2[i]*rst[0][j])*(1 + t2[i]*rst[2][j])*
358:                           (-1.0 + r2[i]*rst[0][j] + 2.0*s2[i]*rst[1][j] +
359:                            t2[i]*rst[2][j]);
360:         part_N[2][i][j] = c*t2[i]*(1 + r2[i]*rst[0][j])*(1 + s2[i]*rst[1][j])*
361:                           (-1.0 + r2[i]*rst[0][j] + s2[i]*rst[1][j] +
362:                            2.0*t2[i]*rst[2][j]);
363:       } else if (i==1 || i==6 || i==13 || i==18) {
364:         N[i][j] = .25*(1.0 - rst[0][j]*rst[0][j])*
365:                   (1.0 + s2[i]*rst[1][j])*(1.0 + t2[i]*rst[2][j]);
366:         part_N[0][i][j] = -.5*rst[0][j]*(1 + s2[i]*rst[1][j])*
367:                           (1 + t2[i]*rst[2][j]);
368:         part_N[1][i][j] = .25*s2[i]*(1 + t2[i]*rst[2][j])*
369:                           (1.0 - rst[0][j]*rst[0][j]);
370:         part_N[2][i][j] = .25*t2[i]*(1.0 - rst[0][j]*rst[0][j])*
371:                           (1 + s2[i]*rst[1][j]);
372:       } else if (i==3 || i==4 || i==15 || i==16) {
373:         N[i][j] = .25*(1.0 - rst[1][j]*rst[1][j])*
374:                   (1.0 + r2[i]*rst[0][j])*(1.0 + t2[i]*rst[2][j]);
375:         part_N[0][i][j] = .25*r2[i]*(1 + t2[i]*rst[2][j])*
376:                           (1.0 - rst[1][j]*rst[1][j]);
377:         part_N[1][i][j] = -.5*rst[1][j]*(1 + r2[i]*rst[0][j])*
378:                           (1 + t2[i]*rst[2][j]);
379:         part_N[2][i][j] = .25*t2[i]*(1.0 - rst[1][j]*rst[1][j])*
380:                           (1 + r2[i]*rst[0][j]);
381:       } else if (i==8 || i==9 || i==10 || i==11) {
382:         N[i][j] = .25*(1.0 - rst[2][j]*rst[2][j])*
383:                   (1.0 + r2[i]*rst[0][j])*(1.0 + s2[i]*rst[1][j]);
384:         part_N[0][i][j] = .25*r2[i]*(1 + s2[i]*rst[1][j])*
385:                           (1.0 - rst[2][j]*rst[2][j]);
386:         part_N[1][i][j] = .25*s2[i]*(1.0 - rst[2][j]*rst[2][j])*
387:                           (1 + r2[i]*rst[0][j]);
388:         part_N[2][i][j] = -.5*rst[2][j]*(1 + r2[i]*rst[0][j])*
389:                           (1 + s2[i]*rst[1][j]);
390:       }
391:     }
392:   }
393:   return 0;
394: }
395: /* -------------------------------------------------------------------- */
398: /*
399:    paulintegrate20 - Does actual numerical integration on 20 node element.
400:  */
401: PetscErrorCode paulintegrate20(PetscReal K[60][60])
402: {
403:   PetscReal det_jac,jac[3][3],inv_jac[3][3];
404:   PetscReal B[6][60],B_temp[6][60],C[6][6];
405:   PetscReal temp;
406:   PetscInt  i,j,k,step;

408:   /* Zero out K, since we will accumulate the result here */
409:   for (i=0; i<60; i++) {
410:     for (j=0; j<60; j++) {
411:       K[i][j] = 0.0;
412:     }
413:   }

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

418:     /* Compute the Jacobian, its determinant, and inverse. */
419:     for (i=0; i<3; i++) {
420:       for (j=0; j<3; j++) {
421:         jac[i][j] = 0;
422:         for (k=0; k<20; k++) {
423:           jac[i][j] += part_N[i][k][step]*xyz[k][j];
424:         }
425:       }
426:     }
427:     det_jac = jac[0][0]*(jac[1][1]*jac[2][2]-jac[1][2]*jac[2][1])
428:               + jac[0][1]*(jac[1][2]*jac[2][0]-jac[1][0]*jac[2][2])
429:               + jac[0][2]*(jac[1][0]*jac[2][1]-jac[1][1]*jac[2][0]);
430:     inv_jac[0][0] = (jac[1][1]*jac[2][2]-jac[1][2]*jac[2][1])/det_jac;
431:     inv_jac[0][1] = (jac[0][2]*jac[2][1]-jac[0][1]*jac[2][2])/det_jac;
432:     inv_jac[0][2] = (jac[0][1]*jac[1][2]-jac[1][1]*jac[0][2])/det_jac;
433:     inv_jac[1][0] = (jac[1][2]*jac[2][0]-jac[1][0]*jac[2][2])/det_jac;
434:     inv_jac[1][1] = (jac[0][0]*jac[2][2]-jac[2][0]*jac[0][2])/det_jac;
435:     inv_jac[1][2] = (jac[0][2]*jac[1][0]-jac[0][0]*jac[1][2])/det_jac;
436:     inv_jac[2][0] = (jac[1][0]*jac[2][1]-jac[1][1]*jac[2][0])/det_jac;
437:     inv_jac[2][1] = (jac[0][1]*jac[2][0]-jac[0][0]*jac[2][1])/det_jac;
438:     inv_jac[2][2] = (jac[0][0]*jac[1][1]-jac[1][0]*jac[0][1])/det_jac;

440:     /* Compute the B matrix. */
441:     for (i=0; i<3; i++) {
442:       for (j=0; j<20; j++) {
443:         B_temp[i][j] = 0.0;
444:         for (k=0; k<3; k++) {
445:           B_temp[i][j] += inv_jac[i][k]*part_N[k][j][step];
446:         }
447:       }
448:     }
449:     for (i=0; i<6; i++) {
450:       for (j=0; j<60; j++) {
451:         B[i][j] = 0.0;
452:       }
453:     }

455:     /* Put values in correct places in B. */
456:     for (k=0; k<20; k++) {
457:       B[0][3*k]   = B_temp[0][k];
458:       B[1][3*k+1] = B_temp[1][k];
459:       B[2][3*k+2] = B_temp[2][k];
460:       B[3][3*k]   = B_temp[1][k];
461:       B[3][3*k+1] = B_temp[0][k];
462:       B[4][3*k+1] = B_temp[2][k];
463:       B[4][3*k+2] = B_temp[1][k];
464:       B[5][3*k]   = B_temp[2][k];
465:       B[5][3*k+2] = B_temp[0][k];
466:     }

468:     /* Construct the C matrix, uses the constants "nu" and "E". */
469:     for (i=0; i<6; i++) {
470:       for (j=0; j<6; j++) {
471:         C[i][j] = 0.0;
472:       }
473:     }
474:     temp = (1.0 + nu)*(1.0 - 2.0*nu);
475:     temp = E/temp;
476:     C[0][0] = temp*(1.0 - nu);
477:     C[1][1] = C[0][0];
478:     C[2][2] = C[0][0];
479:     C[3][3] = temp*(0.5 - nu);
480:     C[4][4] = C[3][3];
481:     C[5][5] = C[3][3];
482:     C[0][1] = temp*nu;
483:     C[0][2] = C[0][1];
484:     C[1][0] = C[0][1];
485:     C[1][2] = C[0][1];
486:     C[2][0] = C[0][1];
487:     C[2][1] = C[0][1];

489:     for (i=0; i<6; i++) {
490:       for (j=0; j<60; j++) {
491:         B_temp[i][j] = 0.0;
492:         for (k=0; k<6; k++) {
493:           B_temp[i][j] += C[i][k]*B[k][j];
494:         }
495:         B_temp[i][j] *= det_jac;
496:       }
497:     }

499:     /* Accumulate B'*C*B*det(J)*weight, as a function of (r,s,t), in K. */
500:     for (i=0; i<60; i++) {
501:       for (j=0; j<60; j++) {
502:         temp = 0.0;
503:         for (k=0; k<6; k++) {
504:           temp += B[k][i]*B_temp[k][j];
505:         }
506:         K[i][j] += temp*weight[step];
507:       }
508:     }
509:   }  /* end of loop over integration points */
510:   return 0;
511: }