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

 12:             -Laplacian u  = g,  0 < x,y < 1,

 14:     with boundary conditions

 16:              u = 0  for  x = 0, x = 1, y = 0, y = 1.

 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 <petscdm.h>
 25: #include <petscdmda.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:   DM       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

 48: extern PetscErrorCode FormJacobian_Grid(AppCtx*,GridCtx*,Mat*);

 50: /*
 51:       Mm_ratio - ration of grid lines between fine and coarse grids.
 52: */
 53: int main(int argc,char **argv)
 54: {
 55:   AppCtx         user;
 56:   PetscInt       its,N,n,Nx = PETSC_DECIDE,Ny = PETSC_DECIDE,nlocal,Nlocal;
 57:   PetscMPIInt    size;
 58:   KSP            ksp,ksp_fine;
 59:   PC             pc;
 60:   PetscScalar    one = 1.0;

 62:   PetscInitialize(&argc,&argv,NULL,help);
 63:   user.ratio     = 2;
 64:   user.coarse.mx = 5; user.coarse.my = 5;

 66:   PetscOptionsGetInt(NULL,NULL,"-Mx",&user.coarse.mx,NULL);
 67:   PetscOptionsGetInt(NULL,NULL,"-My",&user.coarse.my,NULL);
 68:   PetscOptionsGetInt(NULL,NULL,"-ratio",&user.ratio,NULL);

 70:   user.fine.mx = user.ratio*(user.coarse.mx-1)+1; user.fine.my = user.ratio*(user.coarse.my-1)+1;

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

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

 77:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 78:   PetscOptionsGetInt(NULL,NULL,"-Nx",&Nx,NULL);
 79:   PetscOptionsGetInt(NULL,NULL,"-Ny",&Ny,NULL);

 81:   /* Set up distributed array for fine grid */
 82:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.fine.mx,user.fine.my,Nx,Ny,1,1,NULL,NULL,&user.fine.da);
 83:   DMSetFromOptions(user.fine.da);
 84:   DMSetUp(user.fine.da);
 85:   DMCreateGlobalVector(user.fine.da,&user.fine.x);
 86:   VecDuplicate(user.fine.x,&user.fine.r);
 87:   VecDuplicate(user.fine.x,&user.fine.b);
 88:   VecGetLocalSize(user.fine.x,&nlocal);
 89:   DMCreateLocalVector(user.fine.da,&user.fine.localX);
 90:   VecDuplicate(user.fine.localX,&user.fine.localF);
 91:   MatCreateAIJ(PETSC_COMM_WORLD,nlocal,nlocal,n,n,5,NULL,3,NULL,&user.fine.J);

 93:   /* Set up distributed array for coarse grid */
 94:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.coarse.mx,user.coarse.my,Nx,Ny,1,1,NULL,NULL,&user.coarse.da);
 95:   DMSetFromOptions(user.coarse.da);
 96:   DMSetUp(user.coarse.da);
 97:   DMCreateGlobalVector(user.coarse.da,&user.coarse.x);
 98:   VecDuplicate(user.coarse.x,&user.coarse.b);
 99:   VecGetLocalSize(user.coarse.x,&Nlocal);
100:   DMCreateLocalVector(user.coarse.da,&user.coarse.localX);
101:   VecDuplicate(user.coarse.localX,&user.coarse.localF);
102:   MatCreateAIJ(PETSC_COMM_WORLD,Nlocal,Nlocal,N,N,5,NULL,3,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,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);
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);
129:   PCMGSetR(pc,FINE_LEVEL,user.fine.r);

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

136:   KSPSetOperators(ksp,user.fine.J,user.fine.J);

138:   VecSet(user.fine.b,one);

140:   /* Set options, then solve nonlinear system */
141:   KSPSetFromOptions(ksp);

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

147:   /* Free data structures */
148:   MatDestroy(&user.fine.J);
149:   VecDestroy(&user.fine.x);
150:   VecDestroy(&user.fine.r);
151:   VecDestroy(&user.fine.b);
152:   DMDestroy(&user.fine.da);
153:   VecDestroy(&user.fine.localX);
154:   VecDestroy(&user.fine.localF);

156:   MatDestroy(&user.coarse.J);
157:   VecDestroy(&user.coarse.x);
158:   VecDestroy(&user.coarse.b);
159:   DMDestroy(&user.coarse.da);
160:   VecDestroy(&user.coarse.localX);
161:   VecDestroy(&user.coarse.localF);

163:   KSPDestroy(&ksp);
164:   MatDestroy(&user.Ii);
165:   PetscFinalize();
166:   return 0;
167: }

169: PetscErrorCode FormJacobian_Grid(AppCtx *user,GridCtx *grid,Mat *J)
170: {
171:   Mat                    jac = *J;
172:   PetscInt               i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym,col[5];
173:   PetscInt               grow;
174:   const PetscInt         *ltog;
175:   PetscScalar            two = 2.0,one = 1.0,v[5],hx,hy,hxdhy,hydhx,value;
176:   ISLocalToGlobalMapping ltogm;

178:   mx    = grid->mx;               my = grid->my;
179:   hx    = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
180:   hxdhy = hx/hy;               hydhx = hy/hx;

182:   /* Get ghost points */
183:   DMDAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
184:   DMDAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
185:   DMGetLocalToGlobalMapping(grid->da,&ltogm);
186:   ISLocalToGlobalMappingGetIndices(ltogm,&ltog);

188:   /* Evaluate Jacobian of function */
189:   for (j=ys; j<ys+ym; j++) {
190:     row = (j - Ys)*Xm + xs - Xs - 1;
191:     for (i=xs; i<xs+xm; i++) {
192:       row++;
193:       grow = ltog[row];
194:       if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
195:         v[0] = -hxdhy; col[0] = ltog[row - Xm];
196:         v[1] = -hydhx; col[1] = ltog[row - 1];
197:         v[2] = two*(hydhx + hxdhy); col[2] = grow;
198:         v[3] = -hydhx; col[3] = ltog[row + 1];
199:         v[4] = -hxdhy; col[4] = ltog[row + Xm];
200:         MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
201:       } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)) {
202:         value = .5*two*(hydhx + hxdhy);
203:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
204:       } else {
205:         value = .25*two*(hydhx + hxdhy);
206:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
207:       }
208:     }
209:   }
210:   ISLocalToGlobalMappingRestoreIndices(ltogm,&ltog);
211:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
212:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

214:   return 0;
215: }

217: /*TEST

219:     test:
220:       args: -ksp_gmres_cgs_refinement_type refine_always -pc_type jacobi -ksp_monitor_short -ksp_type gmres

222:     test:
223:       suffix: 2
224:       nsize: 3
225:       args: -ksp_monitor_short

227: TEST*/