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 SLES.  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 petscsles.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,its;
 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:   SLES         sles;
 34:   KSP          ksp;
 35:   MatNullSpace nullsp;
 36:   PC           pc;

 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 */
 43:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 44:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

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

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

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

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

 76:   /* Solve linear system */
 77:   SLESCreate(PETSC_COMM_WORLD,&sles);
 78:   SLESSetOperators(sles,C,C,DIFFERENT_NONZERO_PATTERN);
 79:   SLESSetFromOptions(sles);
 80:   SLESGetKSP(sles,&ksp);
 81:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);

 83:   PetscOptionsHasName(PETSC_NULL,"-fixnullspace",&flg);
 84:   if (flg) {
 85:     SLESGetPC(sles,&pc);
 86:     MatNullSpaceCreate(PETSC_COMM_WORLD,1,0,PETSC_NULL,&nullsp);
 87:     PCNullSpaceAttach(pc,nullsp);
 88:     MatNullSpaceDestroy(nullsp);
 89:   }

 91:   SLESSolve(sles,b,u,&its);


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