Actual source code: ex3.c

  1: /*$Id: ex3.c,v 1.73 2001/08/07 21:30:50 bsmith Exp $*/

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

 9:  #include petscsles.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: }
 20: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
 21: {
 23:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
 24:   return(0);
 25: }

 27: int main(int argc,char **args)
 28: {
 29:   Mat         C;
 30:   int         i,m = 5,rank,size,N,start,end,M,its;
 31:   PetscScalar val,zero = 0.0,one = 1.0,none = -1.0,Ke[16],r[4];
 32:   PetscReal   x,y,h,norm;
 33:   int         ierr,idx[4],count,*rows;
 34:   Vec         u,ustar,b;
 35:   SLES        sles;
 36:   KSP         ksp;
 37:   IS          is;

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

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

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

 66:   /* Create right-hand-side and solution vectors */
 67:   VecCreate(PETSC_COMM_WORLD,&u);
 68:   VecSetSizes(u,PETSC_DECIDE,N);
 69:   VecSetFromOptions(u);
 70:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 71:   VecDuplicate(u,&b);
 72:   PetscObjectSetName((PetscObject)b,"Right hand side");
 73:   VecDuplicate(b,&ustar);
 74:   VecSet(&zero,u);
 75:   VecSet(&zero,b);

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

 90:   /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
 91:   PetscMalloc(4*m*sizeof(int),&rows);
 92:   for (i=0; i<m+1; i++) {
 93:     rows[i] = i; /* bottom */
 94:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
 95:   }
 96:   count = m+1; /* left side */
 97:   for (i=m+1; i<m*(m+1); i+= m+1) {
 98:     rows[count++] = i;
 99:   }
100:   count = 2*m; /* left side */
101:   for (i=2*m+1; i<m*(m+1); i+= m+1) {
102:     rows[count++] = i;
103:   }
104:   ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
105:   for (i=0; i<4*m; i++) {
106:      x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
107:      val = y;
108:      VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
109:      VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
110:   }
111:   PetscFree(rows);
112:   VecAssemblyBegin(u);
113:   VecAssemblyEnd(u);
114:   VecAssemblyBegin(b);
115:   VecAssemblyEnd(b);

117:   MatZeroRows(C,is,&one);
118:   ISDestroy(is);


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

128:   /* Solve linear system */
129:   SLESCreate(PETSC_COMM_WORLD,&sles);
130:   SLESSetOperators(sles,C,C,DIFFERENT_NONZERO_PATTERN);
131:   SLESSetFromOptions(sles);
132:   SLESGetKSP(sles,&ksp);
133:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
134:   SLESSolve(sles,b,u,&its);

136:   /* Check error */
137:   VecGetOwnershipRange(ustar,&start,&end);
138:   for (i=start; i<end; i++) {
139:      x = h*(i % (m+1)); y = h*(i/(m+1));
140:      val = y;
141:      VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
142:   }
143:   VecAssemblyBegin(ustar);
144:   VecAssemblyEnd(ustar);
145:   VecAXPY(&none,ustar,u);
146:   VecNorm(u,NORM_2,&norm);
147:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %dn",norm*h,its);

149:   /* Free work space */
150:   SLESDestroy(sles);
151:   VecDestroy(ustar);
152:   VecDestroy(u);
153:   VecDestroy(b);
154:   MatDestroy(C);
155:   PetscFinalize();
156:   return 0;
157: }