Actual source code: ex4.c

  2: static char help[] = "Solves a linear system with KSP.  The matrix uses simple\n\
  3: bilinear elements on the unit square. Input arguments are:\n\
  4:   -m <size> : problem size\n\n";

 6:  #include petscksp.h

 10: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
 11: {
 12:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 13:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 14:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 15:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 16:   return 0;
 17: }
 20: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
 21: {
 22:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
 23:   return 0;
 24: }

 28: int main(int argc,char **args)
 29: {
 30:   Mat            C;
 32:   PetscInt       i,m = 2,N,M,its,idx[4],count,*rows;
 33:   PetscScalar    val,Ke[16],r[4];
 34:   PetscReal      x,y,h,norm;
 35:   Vec            u,ustar,b;
 36:   KSP            ksp;

 38:   PetscInitialize(&argc,&args,(char *)0,help);
 39:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 40:   N = (m+1)*(m+1); /* dimension of matrix */
 41:   M = m*m; /* number of elements */
 42:   h = 1.0/m;       /* mesh width */

 44:   /* create stiffness matrix */
 45:   MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,PETSC_NULL,&C);

 47:   /* forms the element stiffness for the Laplacian */
 48:   FormElementStiffness(h*h,Ke);
 49:   for (i=0; i<M; i++) {
 50:      /* location of lower left corner of element */
 51:      x = h*(i % m); y = h*(i/m);
 52:      /* node numbers for the four corners of element */
 53:      idx[0] = (m+1)*(i/m) + (i % m);
 54:      idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 55:      MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 56:   }
 57:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 58:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

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

 62:   VecCreateSeq(PETSC_COMM_SELF,N,&u);
 63:   VecDuplicate(u,&b);
 64:   VecDuplicate(b,&ustar);
 65:   VecSet(u,0.0);
 66:   VecSet(b,0.0);

 68:   for (i=0; i<M; i++) {
 69:      /* location of lower left corner of element */
 70:      x = h*(i % m); y = h*(i/m);
 71:      /* node numbers for the four corners of element */
 72:      idx[0] = (m+1)*(i/m) + (i % m);
 73:      idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 74:      FormElementRhs(x,y,h*h,r);
 75:      VecSetValues(b,4,idx,r,ADD_VALUES);
 76:   }
 77:   VecAssemblyBegin(b);
 78:   VecAssemblyEnd(b);

 80:   /* modify matrix and rhs for Dirichlet boundary conditions */
 81:   PetscMalloc((4*m+1)*sizeof(PetscInt),&rows);
 82:   for (i=0; i<m+1; i++) {
 83:     rows[i] = i; /* bottom */
 84:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
 85:   }
 86:   count = m+1; /* left side */
 87:   for (i=m+1; i<m*(m+1); i+= m+1) {
 88:     rows[count++] = i;
 89:   }
 90:   count = 2*m; /* left side */
 91:   for (i=2*m+1; i<m*(m+1); i+= m+1) {
 92:     rows[count++] = i;
 93:   }
 94:   for (i=0; i<4*m; i++) {
 95:      x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
 96:      val = y;
 97:      VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
 98:      VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
 99:   }
100:   MatZeroRows(C,4*m,rows,1.0);

102:   PetscFree(rows);
103:   VecAssemblyBegin(u);
104:   VecAssemblyEnd(u);
105:   VecAssemblyBegin(b);
106:   VecAssemblyEnd(b);

108:   /* solve linear system */
109:   KSPCreate(PETSC_COMM_WORLD,&ksp);
110:   KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
111:   KSPSetFromOptions(ksp);
112:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
113:   KSPSolve(ksp,b,u);

115:   /* check error */
116:   for (i=0; i<N; i++) {
117:      x = h*(i % (m+1)); y = h*(i/(m+1));
118:      val = y;
119:      VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
120:   }
121:   VecAssemblyBegin(ustar);
122:   VecAssemblyEnd(ustar);

124:   VecAXPY(u,-1.0,ustar);
125:   VecNorm(u,NORM_2,&norm);
126:   KSPGetIterationNumber(ksp,&its);
127:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %D\n",norm*h,its);

129:   KSPDestroy(ksp);
130:   VecDestroy(ustar);
131:   VecDestroy(u);
132:   VecDestroy(b);
133:   MatDestroy(C);
134:   PetscFinalize();
135:   return 0;
136: }