Actual source code: ex19.c

  2: static char help[] ="Solvers Laplacian with multigrid, bad way.\n\
  3:   -mx <xg>, where <xg> = number of grid points in the x-direction\n\
  4:   -my <yg>, where <yg> = number of grid points in the y-direction\n\
  5:   -Nx <npx>, where <npx> = number of processors in the x-direction\n\
  6:   -Ny <npy>, where <npy> = number of processors in the y-direction\n\n";

  8: /*  
  9:     This problem is modeled by
 10:     the partial differential equation
 11:   
 12:             -Laplacian u  = g,  0 < x,y < 1,
 13:   
 14:     with boundary conditions
 15:    
 16:              u = 0  for  x = 0, x = 1, y = 0, y = 1.
 17:   
 18:     A finite difference approximation with the usual 5-point stencil
 19:     is used to discretize the boundary value problem to obtain a nonlinear 
 20:     system of equations.
 21: */

 23:  #include petscksp.h
 24:  #include petscda.h
 25:  #include petscmg.h

 27: /* User-defined application contexts */

 29: typedef struct {
 30:    PetscInt   mx,my;            /* number grid points in x and y direction */
 31:    Vec        localX,localF;    /* local vectors with ghost region */
 32:    DA         da;
 33:    Vec        x,b,r;            /* global vectors */
 34:    Mat        J;                /* Jacobian on grid */
 35: } GridCtx;

 37: typedef struct {
 38:    GridCtx     fine;
 39:    GridCtx     coarse;
 40:    KSP         ksp_coarse;
 41:    PetscInt    ratio;
 42:    Mat         Ii;              /* interpolation from coarse to fine */
 43: } AppCtx;

 45: #define COARSE_LEVEL 0
 46: #define FINE_LEVEL   1


 50: /*
 51:       Mm_ratio - ration of grid lines between fine and coarse grids.
 52: */
 55: int main(int argc,char **argv)
 56: {
 57:   AppCtx         user;
 59:   PetscInt       its,N,n,Nx = PETSC_DECIDE,Ny = PETSC_DECIDE,nlocal,Nlocal;
 60:   PetscMPIInt    size;
 61:   KSP            ksp,ksp_fine;
 62:   PC             pc;
 63:   PetscScalar    one = 1.0;

 65:   PetscInitialize(&argc,&argv,PETSC_NULL,help);

 67:   user.ratio = 2;
 68:   user.coarse.mx = 5; user.coarse.my = 5;
 69:   PetscOptionsGetInt(PETSC_NULL,"-Mx",&user.coarse.mx,PETSC_NULL);
 70:   PetscOptionsGetInt(PETSC_NULL,"-My",&user.coarse.my,PETSC_NULL);
 71:   PetscOptionsGetInt(PETSC_NULL,"-ratio",&user.ratio,PETSC_NULL);
 72:   user.fine.mx = user.ratio*(user.coarse.mx-1)+1; user.fine.my = user.ratio*(user.coarse.my-1)+1;

 74:   PetscPrintf(PETSC_COMM_WORLD,"Coarse grid size %D by %D\n",user.coarse.mx,user.coarse.my);
 75:   PetscPrintf(PETSC_COMM_WORLD,"Fine grid size %D by %D\n",user.fine.mx,user.fine.my);

 77:   n = user.fine.mx*user.fine.my; N = user.coarse.mx*user.coarse.my;

 79:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 80:   PetscOptionsGetInt(PETSC_NULL,"-Nx",&Nx,PETSC_NULL);
 81:   PetscOptionsGetInt(PETSC_NULL,"-Ny",&Ny,PETSC_NULL);

 83:   /* Set up distributed array for fine grid */
 84:   DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,user.fine.mx,
 85:                     user.fine.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.fine.da);
 86:   DACreateGlobalVector(user.fine.da,&user.fine.x);
 87:   VecDuplicate(user.fine.x,&user.fine.r);
 88:   VecDuplicate(user.fine.x,&user.fine.b);
 89:   VecGetLocalSize(user.fine.x,&nlocal);
 90:   DACreateLocalVector(user.fine.da,&user.fine.localX);
 91:   VecDuplicate(user.fine.localX,&user.fine.localF);
 92:   MatCreateMPIAIJ(PETSC_COMM_WORLD,nlocal,nlocal,n,n,5,PETSC_NULL,3,PETSC_NULL,&user.fine.J);

 94:   /* Set up distributed array for coarse grid */
 95:   DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,user.coarse.mx,
 96:                     user.coarse.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.coarse.da);
 97:   DACreateGlobalVector(user.coarse.da,&user.coarse.x);
 98:   VecDuplicate(user.coarse.x,&user.coarse.b);
 99:   VecGetLocalSize(user.coarse.x,&Nlocal);
100:   DACreateLocalVector(user.coarse.da,&user.coarse.localX);
101:   VecDuplicate(user.coarse.localX,&user.coarse.localF);
102:   MatCreateMPIAIJ(PETSC_COMM_WORLD,Nlocal,Nlocal,N,N,5,PETSC_NULL,3,PETSC_NULL,&user.coarse.J);

104:   /* Create linear solver */
105:   KSPCreate(PETSC_COMM_WORLD,&ksp);

107:   /* set two level additive Schwarz preconditioner */
108:   KSPGetPC(ksp,&pc);
109:   PCSetType(pc,PCMG);
110:   PCMGSetLevels(pc,2,PETSC_NULL);
111:   PCMGSetType(pc,PC_MG_ADDITIVE);

113:   FormJacobian_Grid(&user,&user.coarse,&user.coarse.J);
114:   FormJacobian_Grid(&user,&user.fine,&user.fine.J);

116:   /* Create coarse level */
117:   PCMGGetCoarseSolve(pc,&user.ksp_coarse);
118:   KSPSetOptionsPrefix(user.ksp_coarse,"coarse_");
119:   KSPSetFromOptions(user.ksp_coarse);
120:   KSPSetOperators(user.ksp_coarse,user.coarse.J,user.coarse.J,DIFFERENT_NONZERO_PATTERN);
121:   PCMGSetX(pc,COARSE_LEVEL,user.coarse.x);
122:   PCMGSetRhs(pc,COARSE_LEVEL,user.coarse.b);

124:   /* Create fine level */
125:   PCMGGetSmoother(pc,FINE_LEVEL,&ksp_fine);
126:   KSPSetOptionsPrefix(ksp_fine,"fine_");
127:   KSPSetFromOptions(ksp_fine);
128:   KSPSetOperators(ksp_fine,user.fine.J,user.fine.J,DIFFERENT_NONZERO_PATTERN);
129:   PCMGSetR(pc,FINE_LEVEL,user.fine.r);
130:   PCMGSetResidual(pc,FINE_LEVEL,PCMGDefaultResidual,user.fine.J);

132:   /* Create interpolation between the levels */
133:   DAGetInterpolation(user.coarse.da,user.fine.da,&user.Ii,PETSC_NULL);
134:   PCMGSetInterpolation(pc,FINE_LEVEL,user.Ii);
135:   PCMGSetRestriction(pc,FINE_LEVEL,user.Ii);

137:   KSPSetOperators(ksp,user.fine.J,user.fine.J,DIFFERENT_NONZERO_PATTERN);

139:   VecSet(user.fine.b,one);
140:   {
141:     PetscRandom rdm;
142:     PetscRandomCreate(PETSC_COMM_WORLD,&rdm);
143:     PetscRandomSetFromOptions(rdm);
144:     VecSetRandom(user.fine.b,rdm);
145:     PetscRandomDestroy(rdm);
146:   }

148:   /* Set options, then solve nonlinear system */
149:   KSPSetFromOptions(ksp);

151:   KSPSolve(ksp,user.fine.b,user.fine.x);
152:   KSPGetIterationNumber(ksp,&its);
153:   PetscPrintf(PETSC_COMM_WORLD,"Number of iterations = %D\n",its);

155:   /* Free data structures */
156:   MatDestroy(user.fine.J);
157:   VecDestroy(user.fine.x);
158:   VecDestroy(user.fine.r);
159:   VecDestroy(user.fine.b);
160:   DADestroy(user.fine.da);
161:   VecDestroy(user.fine.localX);
162:   VecDestroy(user.fine.localF);

164:   MatDestroy(user.coarse.J);
165:   VecDestroy(user.coarse.x);
166:   VecDestroy(user.coarse.b);
167:   DADestroy(user.coarse.da);
168:   VecDestroy(user.coarse.localX);
169:   VecDestroy(user.coarse.localF);

171:   KSPDestroy(ksp);
172:   MatDestroy(user.Ii);
173:   PetscFinalize();

175:   return 0;
176: }

180: int FormJacobian_Grid(AppCtx *user,GridCtx *grid,Mat *J)
181: {
182:   Mat            jac = *J;
184:   PetscInt       i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym,col[5];
185:   PetscInt       nloc,*ltog,grow;
186:   PetscScalar    two = 2.0,one = 1.0,v[5],hx,hy,hxdhy,hydhx,value;

188:   mx = grid->mx;            my = grid->my;
189:   hx = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
190:   hxdhy = hx/hy;            hydhx = hy/hx;

192:   /* Get ghost points */
193:   DAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
194:   DAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
195:   DAGetGlobalIndices(grid->da,&nloc,&ltog);

197:   /* Evaluate Jacobian of function */
198:   for (j=ys; j<ys+ym; j++) {
199:     row = (j - Ys)*Xm + xs - Xs - 1;
200:     for (i=xs; i<xs+xm; i++) {
201:       row++;
202:       grow = ltog[row];
203:       if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
204:         v[0] = -hxdhy; col[0] = ltog[row - Xm];
205:         v[1] = -hydhx; col[1] = ltog[row - 1];
206:         v[2] = two*(hydhx + hxdhy); col[2] = grow;
207:         v[3] = -hydhx; col[3] = ltog[row + 1];
208:         v[4] = -hxdhy; col[4] = ltog[row + Xm];
209:         MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
210:       } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
211:         value = .5*two*(hydhx + hxdhy);
212:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
213:       } else {
214:         value = .25*two*(hydhx + hxdhy);
215:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
216:       }
217:     }
218:   }
219:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
220:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

222:   return 0;
223: }