Actual source code: ex4.c


  2: static char help[] = "Bilinear elements on the unit square for the Laplacian. Input arguments are:\n\
  3:   -m <size> : problem size\n\n";

  5: #include <petscksp.h>

  7: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
  8: {
  9:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 10:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 11:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 12:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 13:   return 0;
 14: }

 16: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
 17: {
 18:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
 19:   return 0;
 20: }

 22: /* Note: this code is for testing purposes only. The assembly process is not scalable */
 23: int main(int argc,char **args)
 24: {
 25:   Mat            C;
 27:   PetscInt       i,m = 2,N,M,its,idx[4],count,*rows;
 28:   PetscScalar    val,Ke[16],r[4];
 29:   PetscReal      x,y,h,norm;
 30:   Vec            u,ustar,b;
 31:   KSP            ksp;
 32:   PetscMPIInt    rank;
 33:   PetscBool      usezerorows = PETSC_TRUE;

 35:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 36:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 37:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 38:   PetscOptionsGetBool(NULL,NULL,"-usezerorows",&usezerorows,NULL);
 39:   N    = (m+1)*(m+1); /* dimension of matrix */
 40:   M    = m*m;         /* number of elements */
 41:   h    = 1.0/m;       /* mesh width */

 43:   /* create stiffness matrix */
 44:   MatCreate(PETSC_COMM_WORLD,&C);
 45:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 46:   MatSetFromOptions(C);
 47:   MatMPIAIJSetPreallocation(C,9,NULL,9,NULL);
 48:   MatSeqAIJSetPreallocation(C,9,NULL);
 49: #if defined(PETSC_HAVE_HYPRE)
 50:   MatHYPRESetPreallocation(C,9,NULL,9,NULL);
 51: #endif

 53:   /* forms the element stiffness for the Laplacian */
 54:   FormElementStiffness(h*h,Ke);

 56:   /* assemble the matrix: only process 0 adds the values, not scalable */
 57:   if (!rank) {
 58:     for (i=0; i<M; i++) {
 59:       /* node numbers for the four corners of element */
 60:       idx[0] = (m+1)*(i/m) + (i % m);
 61:       idx[1] = idx[0] + 1;
 62:       idx[2] = idx[1] + m + 1;
 63:       idx[3] = idx[2] - 1;
 64:       if (i == M-1 && !usezerorows) { /* If MatZeroRows not supported -> make it non-singular */
 65:         for (PetscInt ii = 0; ii < 4; ii++) {
 66:           Ke[ 2*4 + ii] = 0.0;
 67:           Ke[ii*4 +  2] = 0.0;
 68:         }
 69:         Ke[10] = 1.0;
 70:       }
 71:       MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 72:     }
 73:   }
 74:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 75:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 77:   /* create right hand side and solution */
 78:   MatCreateVecs(C,&u,&b);
 79:   VecDuplicate(u,&ustar);
 80:   VecSet(u,0.0);
 81:   VecSet(b,0.0);

 83:   /* assemble the right hand side: only process 0 adds the values, not scalable */
 84:   if (!rank) {
 85:     for (i=0; i<M; i++) {
 86:       /* location of lower left corner of element */
 87:       x = h*(i%m);
 88:       y = h*(i/m);
 89:       /* node numbers for the four corners of element */
 90:       idx[0] = (m+1)*(i/m) + (i%m);
 91:       idx[1] = idx[0]+1;
 92:       idx[2] = idx[1]+m+1;
 93:       idx[3] = idx[2]-1;
 94:       FormElementRhs(x,y,h*h,r);
 95:       VecSetValues(b,4,idx,r,ADD_VALUES);
 96:     }
 97:   }
 98:   VecAssemblyBegin(b);
 99:   VecAssemblyEnd(b);

101:   /* modify matrix and rhs for Dirichlet boundary conditions */
102:   if (!rank) {
103:     PetscMalloc1(4*m+1,&rows);
104:     for (i=0; i<m+1; i++) {
105:       rows[i]       = i; /* bottom */
106:       rows[3*m-1+i] = m*(m+1)+i; /* top */
107:     }
108:     count = m+1; /* left side */
109:     for (i=m+1; i<m*(m+1); i+=m+1) rows[count++] = i;

111:     count = 2*m; /* right side */
112:     for (i=2*m+1; i<m*(m+1); i+=m+1) rows[count++] = i;

114:     for (i=0; i<4*m; i++) {
115:       val  = h*(rows[i]/(m+1));
116:       VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
117:       VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
118:     }
119:     if (usezerorows) { MatZeroRows(C,4*m,rows,1.0,0,0); }
120:     PetscFree(rows);
121:   } else {
122:     if (usezerorows) { MatZeroRows(C,0,NULL,1.0,0,0); }
123:   }
124:   VecAssemblyBegin(u);
125:   VecAssemblyEnd(u);
126:   VecAssemblyBegin(b);
127:   VecAssemblyEnd(b);

129:   if (!usezerorows) {
130:     VecSet(ustar,1.0);
131:     MatMult(C,ustar,b);
132:   }

134:   /* solve linear system */
135:   KSPCreate(PETSC_COMM_WORLD,&ksp);
136:   KSPSetOperators(ksp,C,C);
137:   KSPSetFromOptions(ksp);
138:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
139:   KSPSolve(ksp,b,u);

141:   /* check error */
142:   if (usezerorows) {
143:     if (!rank) {
144:       for (i=0; i<N; i++) {
145:         val  = h*(i/(m+1));
146:         VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
147:       }
148:     }
149:     VecAssemblyBegin(ustar);
150:     VecAssemblyEnd(ustar);
151:   }

153:   VecAXPY(u,-1.0,ustar);
154:   VecNorm(u,NORM_2,&norm);
155:   KSPGetIterationNumber(ksp,&its);
156:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)(norm*h),its);

158:   KSPDestroy(&ksp);
159:   VecDestroy(&ustar);
160:   VecDestroy(&u);
161:   VecDestroy(&b);
162:   MatDestroy(&C);
163:   PetscFinalize();
164:   return ierr;
165: }

167: /*TEST

169:     test:
170:       args: -ksp_monitor_short -m 5 -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always

172:     test:
173:       suffix: 3
174:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always

176:     test:
177:       suffix: 5
178:       args: -pc_type eisenstat -ksp_monitor_short -m 5  -ksp_gmres_cgs_refinement_type refine_always

180:     test:
181:       requires: hypre defined(PETSC_HAVE_HYPRE_DEVICE)
182:       suffix: hypre_device_none
183:       output_file: output/ex4_hypre_none.out
184:       nsize: {{1 2}}
185:       args: -usezerorows 0 -mat_type hypre -pc_type none -m 5

187:     test:
188:       requires: hypre defined(PETSC_HAVE_HYPRE_DEVICE)
189:       suffix: hypre_device_amg
190:       nsize: {{1 2}}
191:       args: -usezerorows 0 -mat_type hypre -pc_type hypre -m 25 -ksp_type cg -ksp_norm_type natural

193: TEST*/