Actual source code: ex20.c

petsc-3.8.4 2018-03-24
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  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>

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

 18: int main(int argc,char **args)
 19: {
 20:   Mat          C;
 21:   int          i,m = 5,rank,size,N,start,end,M;
 22:   int          ierr,idx[4];
 23:   PetscScalar  Ke[16];
 24:   PetscReal    h;
 25:   Vec          u,b;
 26:   KSP          ksp;
 27:   MatNullSpace nullsp;

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

 37:   /* Create stiffness matrix */
 38:   MatCreate(PETSC_COMM_WORLD,&C);
 39:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 40:   MatSetFromOptions(C);
 41:   MatSetUp(C);
 42:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 43:   end   = start + M/size + ((M%size) > rank);

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

 57:   /* Create right-hand-side and solution vectors */
 58:   VecCreate(PETSC_COMM_WORLD,&u);
 59:   VecSetSizes(u,PETSC_DECIDE,N);
 60:   VecSetFromOptions(u);
 61:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 62:   VecDuplicate(u,&b);
 63:   PetscObjectSetName((PetscObject)b,"Right hand side");

 65:   VecSet(b,1.0);
 66:   VecSetValue(b,0,1.2,ADD_VALUES);
 67:   VecSet(u,0.0);

 69:   /* Solve linear system */
 70:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 71:   KSPSetOperators(ksp,C,C);
 72:   KSPSetFromOptions(ksp);
 73:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);

 75:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nullsp);
 76:   /*
 77:      The KSP solver will remove this nullspace from the solution at each iteration
 78:   */
 79:   MatSetNullSpace(C,nullsp);
 80:   /*
 81:      The KSP solver will remove from the right hand side any portion in this nullspace, thus making the linear system consistent.
 82:   */
 83:   MatSetTransposeNullSpace(C,nullsp);
 84:   MatNullSpaceDestroy(&nullsp);

 86:   KSPSolve(ksp,b,u);


 89:   /* Free work space */
 90:   KSPDestroy(&ksp);
 91:   VecDestroy(&u);
 92:   VecDestroy(&b);
 93:   MatDestroy(&C);
 94:   PetscFinalize();
 95:   return ierr;
 96: }