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;
 26:   PetscInt       i,m = 2,N,M,its,idx[4],count,*rows;
 27:   PetscScalar    val,Ke[16],r[4];
 28:   PetscReal      x,y,h,norm;
 29:   Vec            u,ustar,b;
 30:   KSP            ksp;
 31:   PetscMPIInt    rank;
 32:   PetscBool      usezerorows = PETSC_TRUE;

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

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

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

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

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

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

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

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

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

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

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

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

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

157:   KSPDestroy(&ksp);
158:   VecDestroy(&ustar);
159:   VecDestroy(&u);
160:   VecDestroy(&b);
161:   MatDestroy(&C);
162:   PetscFinalize();
163:   return 0;
164: }

166: /*TEST

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

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

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

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

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

192: TEST*/