Actual source code: ex3.c

petsc-3.7.2 2016-06-05
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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: /* Addendum: piggy-backing on this example to test KSPChebyshev methods */

  9: #include <petscksp.h>

 13: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
 14: {
 16:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 17:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 18:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 19:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 20:   return(0);
 21: }
 24: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
 25: {
 27:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
 28:   return(0);
 29: }

 33: int main(int argc,char **args)
 34: {
 35:   Mat            C;
 36:   PetscMPIInt    rank,size;
 37:   PetscInt       i,m = 5,N,start,end,M,its;
 38:   PetscScalar    val,Ke[16],r[4];
 39:   PetscReal      x,y,h,norm;
 41:   PetscInt       idx[4],count,*rows;
 42:   Vec            u,ustar,b;
 43:   KSP            ksp;
 44:   PetscBool      viewkspest = PETSC_FALSE;

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

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

 63:   /* Assemble matrix */
 64:   FormElementStiffness(h*h,Ke);   /* element stiffness for Laplacian */
 65:   for (i=start; i<end; i++) {
 66:     /* location of lower left corner of element */
 67:     x = h*(i % m); y = h*(i/m);
 68:     /* node numbers for the four corners of element */
 69:     idx[0] = (m+1)*(i/m) + (i % m);
 70:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 71:     MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 72:   }
 73:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 74:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

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

 87:   /* Assemble right-hand-side vector */
 88:   for (i=start; i<end; i++) {
 89:     /* location of lower left corner of element */
 90:     x = h*(i % m); y = h*(i/m);
 91:     /* node numbers for the four corners of element */
 92:     idx[0] = (m+1)*(i/m) + (i % m);
 93:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 94:     FormElementRhs(x,y,h*h,r);
 95:     VecSetValues(b,4,idx,r,ADD_VALUES);
 96:   }
 97:   VecAssemblyBegin(b);
 98:   VecAssemblyEnd(b);

100:   /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
101:   PetscMalloc1(4*m,&rows);
102:   for (i=0; i<m+1; i++) {
103:     rows[i]          = i; /* bottom */
104:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
105:   }
106:   count = m+1; /* left side */
107:   for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;

109:   count = 2*m; /* left side */
110:   for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
111:   for (i=0; i<4*m; i++) {
112:     x    = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
113:     val  = y;
114:     VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
115:     VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
116:   }
117:   MatZeroRows(C,4*m,rows,1.0,0,0);

119:   PetscFree(rows);
120:   VecAssemblyBegin(u);
121:   VecAssemblyEnd(u);
122:   VecAssemblyBegin(b);
123:   VecAssemblyEnd(b);

125:   { Mat A;
126:     MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);
127:     MatDestroy(&C);
128:     MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);
129:     MatDestroy(&A);
130:   }

132:   /* Solve linear system */
133:   KSPCreate(PETSC_COMM_WORLD,&ksp);
134:   KSPSetOperators(ksp,C,C);
135:   KSPSetFromOptions(ksp);
136:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
137:   KSPSolve(ksp,b,u);

139:   if (viewkspest) {
140:     KSP kspest;

142:     KSPChebyshevEstEigGetKSP(ksp,&kspest);
143:     if (kspest) {KSPView(kspest,PETSC_VIEWER_STDOUT_WORLD);}
144:   }

146:   /* Check error */
147:   VecGetOwnershipRange(ustar,&start,&end);
148:   for (i=start; i<end; i++) {
149:     x    = h*(i % (m+1)); y = h*(i/(m+1));
150:     val  = y;
151:     VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
152:   }
153:   VecAssemblyBegin(ustar);
154:   VecAssemblyEnd(ustar);
155:   VecAXPY(u,-1.0,ustar);
156:   VecNorm(u,NORM_2,&norm);
157:   KSPGetIterationNumber(ksp,&its);
158:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)(norm*h),its);

160:   /* Free work space */
161:   KSPDestroy(&ksp);
162:   VecDestroy(&ustar);
163:   VecDestroy(&u);
164:   VecDestroy(&b);
165:   MatDestroy(&C);
166:   PetscFinalize();
167:   return 0;
168: }