Actual source code: ex20.c

  1: /*$Id: ex20.c,v 1.19 2001/08/07 21:30:50 bsmith Exp $*/

  3: static char help[] = "This example solves a linear system in parallel with KSP.  The matrix\n\
  4: uses simple bilinear elements on the unit square.  To test the parallel\n\
  5: matrix assembly,the matrix is intentionally laid out across processors\n\
  6: differently from the way it is assembled.  Input arguments are:\n\
  7:   -m <size> : problem size\n\n";

 9:  #include petscksp.h

 13: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
 14: {
 15:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 16:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 17:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 18:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 19:   return 0;
 20: }

 24: int main(int argc,char **args)
 25: {
 26:   Mat          C;
 27:   int          i,m = 5,rank,size,N,start,end,M;
 28:   int          ierr,idx[4];
 29:   PetscTruth   flg;
 30:   PetscScalar  zero = 0.0,Ke[16], one = 1.0;
 31:   PetscReal    h;
 32:   Vec          u,b;
 33:   KSP          ksp;
 34:   MatNullSpace nullsp;
 35:   PC           pc;

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

 45:   /* Create stiffness matrix */
 46:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&C);
 47:   MatSetFromOptions(C);
 48:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 49:   end   = start + M/size + ((M%size) > rank);

 51:   /* Assemble matrix */
 52:   FormElementStiffness(h*h,Ke);   /* element stiffness for Laplacian */
 53:   for (i=start; i<end; i++) {
 54:      /* location of lower left corner of element */
 55:      /* node numbers for the four corners of element */
 56:      idx[0] = (m+1)*(i/m) + (i % m);
 57:      idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 58:      MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 59:   }
 60:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 61:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 63:   /* Create right-hand-side and solution vectors */
 64:   VecCreate(PETSC_COMM_WORLD,&u);
 65:   VecSetSizes(u,PETSC_DECIDE,N);
 66:   VecSetFromOptions(u);
 67:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 68:   VecDuplicate(u,&b);
 69:   PetscObjectSetName((PetscObject)b,"Right hand side");

 71:   VecSet(&one,u);
 72:   MatMult(C,u,b);
 73:   VecSet(&zero,u);

 75:   /* Solve linear system */
 76:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 77:   KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
 78:   KSPSetFromOptions(ksp);
 79:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);

 81:   PetscOptionsHasName(PETSC_NULL,"-fixnullspace",&flg);
 82:   if (flg) {
 83:     KSPGetPC(ksp,&pc);
 84:     MatNullSpaceCreate(PETSC_COMM_WORLD,1,0,PETSC_NULL,&nullsp);
 85:     PCNullSpaceAttach(pc,nullsp);
 86:     MatNullSpaceDestroy(nullsp);
 87:   }

 89:   KSPSetRhs(ksp,b);
 90:   KSPSetSolution(ksp,u);
 91:   KSPSolve(ksp);


 94:   /* Free work space */
 95:   KSPDestroy(ksp);
 96:   VecDestroy(u);
 97:   VecDestroy(b);
 98:   MatDestroy(C);
 99:   PetscFinalize();
100:   return 0;
101: }