Actual source code: ex3.c

petsc-3.4.2 2013-07-02
  2: static char help[] = "Bilinear elements on the unit square for Laplacian.  To test the parallel\n\
  3: matrix assembly, the matrix is intentionally laid out across processors\n\
  4: differently from the way it is assembled.  Input arguments are:\n\
  5:   -m <size> : problem size\n\n";

  7: #include <petscksp.h>

 11: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
 12: {
 14:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 15:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 16:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 17:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 18:   return(0);
 19: }
 22: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
 23: {
 25:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
 26:   return(0);
 27: }

 31: int main(int argc,char **args)
 32: {
 33:   Mat            C;
 34:   PetscMPIInt    rank,size;
 35:   PetscInt       i,m = 5,N,start,end,M,its;
 36:   PetscScalar    val,Ke[16],r[4];
 37:   PetscReal      x,y,h,norm,tol=1.e-14;
 39:   PetscInt       idx[4],count,*rows;
 40:   Vec            u,ustar,b;
 41:   KSP            ksp;

 43:   PetscInitialize(&argc,&args,(char*)0,help);
 44:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 45:   N    = (m+1)*(m+1); /* dimension of matrix */
 46:   M    = m*m; /* number of elements */
 47:   h    = 1.0/m;    /* mesh width */
 48:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 49:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 51:   /* Create stiffness matrix */
 52:   MatCreate(PETSC_COMM_WORLD,&C);
 53:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 54:   MatSetFromOptions(C);
 55:   MatSetUp(C);
 56:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 57:   end   = start + M/size + ((M%size) > rank);

 59:   /* Assemble matrix */
 60:   FormElementStiffness(h*h,Ke);   /* element stiffness for Laplacian */
 61:   for (i=start; i<end; i++) {
 62:     /* location of lower left corner of element */
 63:     x = h*(i % m); y = h*(i/m);
 64:     /* node numbers for the four corners of element */
 65:     idx[0] = (m+1)*(i/m) + (i % m);
 66:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 67:     MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 68:   }
 69:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 70:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 72:   /* Create right-hand-side and solution vectors */
 73:   VecCreate(PETSC_COMM_WORLD,&u);
 74:   VecSetSizes(u,PETSC_DECIDE,N);
 75:   VecSetFromOptions(u);
 76:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 77:   VecDuplicate(u,&b);
 78:   PetscObjectSetName((PetscObject)b,"Right hand side");
 79:   VecDuplicate(b,&ustar);
 80:   VecSet(u,0.0);
 81:   VecSet(b,0.0);

 83:   /* Assemble right-hand-side vector */
 84:   for (i=start; i<end; i++) {
 85:     /* location of lower left corner of element */
 86:     x = h*(i % m); y = h*(i/m);
 87:     /* node numbers for the four corners of element */
 88:     idx[0] = (m+1)*(i/m) + (i % m);
 89:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 90:     FormElementRhs(x,y,h*h,r);
 91:     VecSetValues(b,4,idx,r,ADD_VALUES);
 92:   }
 93:   VecAssemblyBegin(b);
 94:   VecAssemblyEnd(b);

 96:   /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
 97:   PetscMalloc(4*m*sizeof(PetscInt),&rows);
 98:   for (i=0; i<m+1; i++) {
 99:     rows[i]          = i; /* bottom */
100:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
101:   }
102:   count = m+1; /* left side */
103:   for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;

105:   count = 2*m; /* left side */
106:   for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
107:   for (i=0; i<4*m; i++) {
108:     x    = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
109:     val  = y;
110:     VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
111:     VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
112:   }
113:   MatZeroRows(C,4*m,rows,1.0,0,0);

115:   PetscFree(rows);
116:   VecAssemblyBegin(u);
117:   VecAssemblyEnd(u);
118:   VecAssemblyBegin(b);
119:   VecAssemblyEnd(b);

121:   { Mat A;
122:     MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);
123:     MatDestroy(&C);
124:     MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);
125:     MatDestroy(&A);
126:   }

128:   /* Solve linear system */
129:   KSPCreate(PETSC_COMM_WORLD,&ksp);
130:   KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
131:   KSPSetFromOptions(ksp);
132:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
133:   KSPSolve(ksp,b,u);

135:   /* Check error */
136:   VecGetOwnershipRange(ustar,&start,&end);
137:   for (i=start; i<end; i++) {
138:     x    = h*(i % (m+1)); y = h*(i/(m+1));
139:     val  = y;
140:     VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
141:   }
142:   VecAssemblyBegin(ustar);
143:   VecAssemblyEnd(ustar);
144:   VecAXPY(u,-1.0,ustar);
145:   VecNorm(u,NORM_2,&norm);
146:   KSPGetIterationNumber(ksp,&its);
147:   if (norm > tol) {
148:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G Iterations %D\n",norm*h,its);
149:   }

151:   /* Free work space */
152:   KSPDestroy(&ksp);
153:   VecDestroy(&ustar);
154:   VecDestroy(&u);
155:   VecDestroy(&b);
156:   MatDestroy(&C);
157:   PetscFinalize();
158:   return 0;
159: }