Actual source code: ex4.c

petsc-3.12.1 2019-10-22
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  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: }
 15: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
 16: {
 17:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
 18:   return 0;
 19: }

 21: int main(int argc,char **args)
 22: {
 23:   Mat            C;
 25:   PetscInt       i,m = 2,N,M,its,idx[4],count,*rows;
 26:   PetscScalar    val,Ke[16],r[4];
 27:   PetscReal      x,y,h,norm;
 28:   Vec            u,ustar,b;
 29:   KSP            ksp;

 31:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 33:   N    = (m+1)*(m+1); /* dimension of matrix */
 34:   M    = m*m; /* number of elements */
 35:   h    = 1.0/m;    /* mesh width */

 37:   /* create stiffness matrix */
 38:   MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,NULL,&C);
 39:   MatSetUp(C);

 41:   /* forms the element stiffness for the Laplacian */
 42:   FormElementStiffness(h*h,Ke);
 43:   for (i=0; i<M; i++) {
 44:     /* node numbers for the four corners of element */
 45:     idx[0] = (m+1)*(i/m) + (i % m);
 46:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 47:     MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 48:   }
 49:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 50:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 52:   /* create right hand side and solution */

 54:   VecCreateSeq(PETSC_COMM_SELF,N,&u);
 55:   VecDuplicate(u,&b);
 56:   VecDuplicate(b,&ustar);
 57:   VecSet(u,0.0);
 58:   VecSet(b,0.0);

 60:   for (i=0; i<M; i++) {
 61:     /* location of lower left corner of element */
 62:     x = h*(i % m); y = h*(i/m);
 63:     /* node numbers for the four corners of element */
 64:     idx[0] = (m+1)*(i/m) + (i % m);
 65:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 66:     FormElementRhs(x,y,h*h,r);
 67:     VecSetValues(b,4,idx,r,ADD_VALUES);
 68:   }
 69:   VecAssemblyBegin(b);
 70:   VecAssemblyEnd(b);

 72:   /* modify matrix and rhs for Dirichlet boundary conditions */
 73:   PetscMalloc1(4*m+1,&rows);
 74:   for (i=0; i<m+1; i++) {
 75:     rows[i]          = i; /* bottom */
 76:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
 77:   }
 78:   count = m+1; /* left side */
 79:   for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;

 81:   count = 2*m; /* left side */
 82:   for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;

 84:   for (i=0; i<4*m; i++) {
 85:     val = h*(rows[i]/(m+1));
 86:     VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
 87:     VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
 88:   }
 89:   MatZeroRows(C,4*m,rows,1.0,0,0);

 91:   PetscFree(rows);
 92:   VecAssemblyBegin(u);
 93:   VecAssemblyEnd(u);
 94:   VecAssemblyBegin(b);
 95:   VecAssemblyEnd(b);

 97:   /* solve linear system */
 98:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 99:   KSPSetOperators(ksp,C,C);
100:   KSPSetFromOptions(ksp);
101:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
102:   KSPSolve(ksp,b,u);

104:   /* check error */
105:   for (i=0; i<N; i++) {
106:     val  = h*(i/(m+1));
107:     VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
108:   }
109:   VecAssemblyBegin(ustar);
110:   VecAssemblyEnd(ustar);

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

117:   KSPDestroy(&ksp);
118:   VecDestroy(&ustar);
119:   VecDestroy(&u);
120:   VecDestroy(&b);
121:   MatDestroy(&C);
122:   PetscFinalize();
123:   return ierr;
124: }

126: /*TEST

128:     test:
129:       args: -ksp_monitor_short -m 5 -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always

131:     test:
132:       suffix: 3
133:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always

135:     test:
136:       suffix: 5
137:       args: -pc_type eisenstat -ksp_monitor_short -m 5        -ksp_gmres_cgs_refinement_type refine_always

139: TEST*/