Actual source code: ex54.c

  2: static char help[] = "Creates a matrix using simple quadirlateral finite elements, and uses it to test GAMG\n\
  3:   -ne <size>       : problem size\n                                      \
  4:   -alpha <v>      : scaling of material coeficient in embedded circle\n\n";

  6: #include <petscksp.h>

 10: int main(int argc,char **args)
 11: {
 12:   Mat            Amat,Pmat;
 14:   PetscInt       i,m,M,its,Istart,Iend,j,Ii,bs,ix,ne=4;
 15:   PetscReal      x,y,h;
 16:   Vec            xx,bb;
 17:   KSP            ksp;
 18:   PetscReal      soft_alpha = 1.e-3;
 19:   MPI_Comm       wcomm;
 20:   PetscMPIInt    npe,mype;
 21:   PC pc;
 22:   PetscScalar DD[4][4],DD2[4][4];
 23: #if defined(PETSC_USE_LOG)
 24:   PetscLogStage  stage;
 25: #endif
 26: #define DIAG_S 0.0
 27:   PetscScalar DD1[4][4] = { {5.0+DIAG_S, -2.0, -1.0, -2.0},
 28:                             {-2.0, 5.0+DIAG_S, -2.0, -1.0},
 29:                             {-1.0, -2.0, 5.0+DIAG_S, -2.0},
 30:                             {-2.0, -1.0, -2.0, 5.0+DIAG_S} };

 32:   PetscInitialize(&argc,&args,(char *)0,help);
 33:   wcomm = PETSC_COMM_WORLD;
 34:   MPI_Comm_rank( wcomm, &mype );
 35:   MPI_Comm_size( wcomm, &npe );
 36:   PetscOptionsGetInt(PETSC_NULL,"-ne",&ne,PETSC_NULL);
 37:   h = 1./ne;
 38:   /* ne*ne; number of global elements */
 39:   PetscOptionsGetReal(PETSC_NULL,"-alpha",&soft_alpha,PETSC_NULL);
 40:   M = (ne+1)*(ne+1); /* global number of nodes */
 41:   /* create stiffness matrix */
 42:   MatCreateMPIAIJ(wcomm,PETSC_DECIDE,PETSC_DECIDE,M,M,
 43:                          18,PETSC_NULL,6,PETSC_NULL,&Amat);
 44:   MatCreateMPIAIJ(wcomm,PETSC_DECIDE,PETSC_DECIDE,M,M,
 45:                          18,PETSC_NULL,6,PETSC_NULL,&Pmat);
 46:   MatGetOwnershipRange(Amat,&Istart,&Iend);
 47:   m = Iend-Istart;
 48:   bs = 1;
 49:   /* Generate vectors */
 50:   VecCreate(wcomm,&xx);
 51:   VecSetSizes(xx,m,M);
 52:   VecSetFromOptions(xx);
 53:   VecDuplicate(xx,&bb);
 54:   VecSet(bb,.0);
 55:   /* generate element matrices */
 56:   {
 57:     FILE *file;
 58:     char fname[] = "elem_2d_therm.txt";
 59:     file = fopen(fname, "r");
 60:     if (file == 0) {
 61:       DD1[0][0] =  0.66666666666666663;
 62:       DD1[0][1] = -0.16666666666666669;
 63:       DD1[0][2] = -0.33333333333333343;
 64:       DD1[0][3] = -0.16666666666666666;
 65:       DD1[1][0] = -0.16666666666666669;
 66:       DD1[1][1] =  0.66666666666666663;
 67:       DD1[1][2] = -0.16666666666666666;
 68:       DD1[1][3] = -0.33333333333333343;
 69:       DD1[2][0] = -0.33333333333333343;
 70:       DD1[2][1] = -0.16666666666666666;
 71:       DD1[2][2] =  0.66666666666666663;
 72:       DD1[2][3] = -0.16666666666666663;
 73:       DD1[3][0] = -0.16666666666666666;
 74:       DD1[3][1] = -0.33333333333333343;
 75:       DD1[3][2] = -0.16666666666666663;
 76:       DD1[3][3] =  0.66666666666666663;
 77:     }
 78:     else {
 79:       for(i=0;i<4;i++)
 80:         for(j=0;j<4;j++)
 81:           fscanf(file, "%le", &DD1[i][j]);
 82:     }
 83:     /* BC version of element */
 84:     for(i=0;i<4;i++)
 85:       for(j=0;j<4;j++)
 86:         if(i<2 || j < 2)
 87:           if(i==j) DD2[i][j] = .1*DD1[i][j];
 88:           else DD2[i][j] = 0.0;
 89:         else DD2[i][j] = DD1[i][j];
 90:   }
 91:   {
 92:     PetscReal coords[2*m];
 93:     /* forms the element stiffness for the Laplacian and coordinates */
 94:     for (Ii=Istart,ix=0; Ii<Iend; Ii++,ix++) {
 95:       j = Ii/(ne+1); i = Ii%(ne+1);
 96:       /* coords */
 97:       x = h*(Ii % (ne+1)); y = h*(Ii/(ne+1));
 98:       coords[2*ix] = x; coords[2*ix+1] = y;
 99:       if( i<ne && j<ne ) {
100:         PetscInt jj,ii,idx[4] = {Ii, Ii+1, Ii + (ne+1) + 1, Ii + (ne+1)};
101:         /* radius */
102:         PetscReal radius = PetscSqrtScalar( (x-.5+h/2)*(x-.5+h/2) + (y-.5+h/2)*(y-.5+h/2) );
103:         PetscReal alpha = 1.0;
104:         if( radius < 0.25 ){
105:           alpha = soft_alpha;
106:         }

108:         for(ii=0;ii<4;ii++)for(jj=0;jj<4;jj++) DD[ii][jj] = alpha*DD1[ii][jj];
109:         MatSetValues(Pmat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
110:         if( j>0 ) {
111:           MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
112:         }
113:         else {
114:           /* a BC */
115:           for(ii=0;ii<4;ii++)for(jj=0;jj<4;jj++) DD[ii][jj] = alpha*DD2[ii][jj];
116:           MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
117:         }
118:       }
119:       if( j>0 ) {
120:         PetscScalar v = h*h;
121:         PetscInt jj = Ii;
122:         VecSetValues(bb,1,&jj,&v,INSERT_VALUES);
123:       }
124:     }
125:     MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);
126:     MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);
127:     MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY);
128:     MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY);
129:     VecAssemblyBegin(bb);
130:     VecAssemblyEnd(bb);

132:     /* Setup solver */
133:     KSPCreate(PETSC_COMM_WORLD,&ksp);
134:     KSPSetOperators( ksp, Amat, Amat, SAME_NONZERO_PATTERN );
135:     KSPSetType( ksp, KSPCG );
136:     KSPGetPC(ksp,&pc);
137:     PCSetType(pc,PCGAMG);
138:     PCSetCoordinates( pc, 2, coords );
139:     KSPSetFromOptions(ksp);
140:   }

142:   if( !PETSC_TRUE ) {
143:     PetscViewer viewer;
144:     PetscViewerASCIIOpen(wcomm, "Amat.m", &viewer);
145:     PetscViewerSetFormat( viewer, PETSC_VIEWER_ASCII_MATLAB);
146:     MatView(Amat,viewer);
147:     PetscViewerDestroy( &viewer );
148:   }

150:   /* solve */
151: #if defined(PETSC_USE_LOG)
152:   PetscLogStageRegister("Solve", &stage);
153:   PetscLogStagePush(stage);
154: #endif
155:   VecSet(xx,.0);
156: 
157:   KSPSolve(ksp,bb,xx);
158: 
159: #if defined(PETSC_USE_LOG)
160:   PetscLogStagePop();
161: #endif

163:   KSPGetIterationNumber(ksp,&its);

165:   if( !PETSC_TRUE ) {
166:     PetscReal norm,norm2;
167:     PetscViewer viewer;
168:     Vec res;
169:     PetscViewerASCIIOpen(wcomm, "rhs.m", &viewer);
170:     PetscViewerSetFormat( viewer, PETSC_VIEWER_ASCII_MATLAB);
171:     VecView(bb,viewer);
172:     PetscViewerDestroy( &viewer );
173:     VecNorm( bb, NORM_2, &norm2 );

175:     PetscViewerASCIIOpen(wcomm, "solution.m", &viewer);
176:     PetscViewerSetFormat( viewer, PETSC_VIEWER_ASCII_MATLAB);
177:     VecView(xx,viewer);
178:     PetscViewerDestroy( &viewer );

180:     VecDuplicate( xx, &res );
181:     MatMult( Amat, xx, res );
182:     VecAXPY( bb, -1.0, res );
183:     VecDestroy( &res );
184:     VecNorm(bb,NORM_2,&norm);
185:     PetscPrintf(PETSC_COMM_WORLD,"[%d]%s |b-Ax|/|b|=%e, |b|=%e\n",0,__FUNCT__,norm/norm2,norm2);

187:     PetscViewerASCIIOpen(wcomm, "residual.m", &viewer);
188:     PetscViewerSetFormat( viewer, PETSC_VIEWER_ASCII_MATLAB);
189:     VecView(bb,viewer);
190:     PetscViewerDestroy( &viewer );
191:   }

193:   /* Free work space */
194:   KSPDestroy(&ksp);
195:   VecDestroy(&xx);
196:   VecDestroy(&bb);
197:   MatDestroy(&Amat);
198:   MatDestroy(&Pmat);

200:   PetscFinalize();
201:   return 0;
202: }