Actual source code: ex26.c

petsc-3.15.0 2021-03-30
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  1: static char help[] ="Solves Laplacian with multigrid. Tests block API for PCMG\n\
  2:   -mx <xg>, where <xg> = number of grid points in the x-direction\n\
  3:   -my <yg>, where <yg> = number of grid points in the y-direction\n\
  4:   -Nx <npx>, where <npx> = number of processors in the x-direction\n\
  5:   -Ny <npy>, where <npy> = number of processors in the y-direction\n\n";

  7: /*  Modified from ~src/ksp/tests/ex19.c. Used for testing ML 6.2 interface.

  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 linear
 20:     system of equations.

 22:     Usage: ./ex26 -ksp_monitor_short -pc_type ml
 23:            -mg_coarse_ksp_max_it 10
 24:            -mg_levels_1_ksp_max_it 10 -mg_levels_2_ksp_max_it 10
 25:            -mg_fine_ksp_max_it 10
 26: */

 28: #include <petscksp.h>
 29: #include <petscdm.h>
 30: #include <petscdmda.h>

 32: /* User-defined application contexts */
 33: typedef struct {
 34:   PetscInt mx,my;              /* number grid points in x and y direction */
 35:   Vec      localX,localF;      /* local vectors with ghost region */
 36:   DM       da;
 37:   Vec      x,b,r;              /* global vectors */
 38:   Mat      J;                  /* Jacobian on grid */
 39:   Mat      A,P,R;
 40:   KSP      ksp;
 41: } GridCtx;

 43: static PetscErrorCode FormJacobian_Grid(GridCtx*,Mat);

 45: int main(int argc,char **argv)
 46: {
 48:   PetscInt       i,its,Nx=PETSC_DECIDE,Ny=PETSC_DECIDE,nlocal,nrhs = 1;
 49:   PetscScalar    one = 1.0;
 50:   Mat            A,B,X;
 51:   GridCtx        fine_ctx;
 52:   KSP            ksp;
 53:   PetscBool      Brand = PETSC_FALSE,flg;

 55:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 56:   /* set up discretization matrix for fine grid */
 57:   fine_ctx.mx = 9;
 58:   fine_ctx.my = 9;
 59:   PetscOptionsGetInt(NULL,NULL,"-mx",&fine_ctx.mx,NULL);
 60:   PetscOptionsGetInt(NULL,NULL,"-my",&fine_ctx.my,NULL);
 61:   PetscOptionsGetInt(NULL,NULL,"-nrhs",&nrhs,NULL);
 62:   PetscOptionsGetInt(NULL,NULL,"-Nx",&Nx,NULL);
 63:   PetscOptionsGetInt(NULL,NULL,"-Ny",&Ny,NULL);
 64:   PetscOptionsGetBool(NULL,NULL,"-rand",&Brand,NULL);
 65:   PetscPrintf(PETSC_COMM_WORLD,"Fine grid size %D by %D\n",fine_ctx.mx,fine_ctx.my);

 67:   /* Set up distributed array for fine grid */
 68:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,fine_ctx.mx,fine_ctx.my,Nx,Ny,1,1,NULL,NULL,&fine_ctx.da);
 69:   DMSetFromOptions(fine_ctx.da);
 70:   DMSetUp(fine_ctx.da);
 71:   DMCreateGlobalVector(fine_ctx.da,&fine_ctx.x);
 72:   VecDuplicate(fine_ctx.x,&fine_ctx.b);
 73:   VecGetLocalSize(fine_ctx.x,&nlocal);
 74:   DMCreateLocalVector(fine_ctx.da,&fine_ctx.localX);
 75:   VecDuplicate(fine_ctx.localX,&fine_ctx.localF);
 76:   DMCreateMatrix(fine_ctx.da,&A);
 77:   FormJacobian_Grid(&fine_ctx,A);

 79:   /* create linear solver */
 80:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 81:   KSPSetDM(ksp,fine_ctx.da);
 82:   KSPSetDMActive(ksp,PETSC_FALSE);

 84:   /* set values for rhs vector */
 85:   VecSet(fine_ctx.b,one);

 87:   /* set options, then solve system */
 88:   KSPSetFromOptions(ksp); /* calls PCSetFromOptions_ML if 'pc_type=ml' */
 89:   KSPSetOperators(ksp,A,A);
 90:   KSPSolve(ksp,fine_ctx.b,fine_ctx.x);
 91:   VecViewFromOptions(fine_ctx.x,NULL,"-debug");
 92:   KSPGetIterationNumber(ksp,&its);
 93:   KSPGetIterationNumber(ksp,&its);
 94:   PetscPrintf(PETSC_COMM_WORLD,"Number of iterations = %D\n",its);

 96:   /* test multiple right-hand side */
 97:   MatCreateDense(PETSC_COMM_WORLD,nlocal,PETSC_DECIDE,fine_ctx.mx*fine_ctx.my,nrhs,NULL,&B);
 98:   MatSetOptionsPrefix(B,"rhs_");
 99:   MatSetFromOptions(B);
100:   MatDuplicate(B,MAT_DO_NOT_COPY_VALUES,&X);
101:   if (Brand) {
102:     MatSetRandom(B,NULL);
103:   } else {
104:     PetscScalar *b;

106:     MatDenseGetArrayWrite(B,&b);
107:     for (i=0;i<nlocal*nrhs;i++) b[i] = 1.0;
108:     MatDenseRestoreArrayWrite(B,&b);
109:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
110:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
111:   }
112:   KSPMatSolve(ksp,B,X);
113:   MatViewFromOptions(X,NULL,"-debug");

115:   PetscObjectTypeCompare((PetscObject)ksp,KSPPREONLY,&flg);
116:   if ((flg || nrhs == 1) && !Brand) {
117:     PetscInt          n;
118:     const PetscScalar *xx,*XX;

120:     VecGetArrayRead(fine_ctx.x,&xx);
121:     MatDenseGetArrayRead(X,&XX);
122:     for (n=0;n<nrhs;n++) {
123:       for (i=0;i<nlocal;i++) {
124:         if (PetscAbsScalar(xx[i] - XX[nlocal*n + i]) > PETSC_SMALL) {
125:           PetscPrintf(PETSC_COMM_SELF,"[%d] Error local solve %D, entry %D -> %g + i %g != %g + i %g\n",PetscGlobalRank,n,i,(double)PetscRealPart(xx[i]),(double)PetscImaginaryPart(xx[i]),(double)PetscRealPart(XX[i]),(double)PetscImaginaryPart(XX[i]));
126:         }
127:       }
128:     }
129:     MatDenseRestoreArrayRead(X,&XX);
130:     VecRestoreArrayRead(fine_ctx.x,&xx);
131:   }

133:   /* free data structures */
134:   VecDestroy(&fine_ctx.x);
135:   VecDestroy(&fine_ctx.b);
136:   DMDestroy(&fine_ctx.da);
137:   VecDestroy(&fine_ctx.localX);
138:   VecDestroy(&fine_ctx.localF);
139:   MatDestroy(&A);
140:   MatDestroy(&B);
141:   MatDestroy(&X);
142:   KSPDestroy(&ksp);

144:   PetscFinalize();
145:   return ierr;
146: }

148: PetscErrorCode FormJacobian_Grid(GridCtx *grid,Mat jac)
149: {
150:   PetscErrorCode         ierr;
151:   PetscInt               i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym,col[5];
152:   PetscInt               grow;
153:   const PetscInt         *ltog;
154:   PetscScalar            two = 2.0,one = 1.0,v[5],hx,hy,hxdhy,hydhx,value;
155:   ISLocalToGlobalMapping ltogm;

158:   mx    = grid->mx;            my = grid->my;
159:   hx    = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
160:   hxdhy = hx/hy;            hydhx = hy/hx;

162:   /* Get ghost points */
163:   DMDAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
164:   DMDAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
165:   DMGetLocalToGlobalMapping(grid->da,&ltogm);
166:   ISLocalToGlobalMappingGetIndices(ltogm,&ltog);

168:   /* Evaluate Jacobian of function */
169:   for (j=ys; j<ys+ym; j++) {
170:     row = (j - Ys)*Xm + xs - Xs - 1;
171:     for (i=xs; i<xs+xm; i++) {
172:       row++;
173:       grow = ltog[row];
174:       if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
175:         v[0] = -hxdhy; col[0] = ltog[row - Xm];
176:         v[1] = -hydhx; col[1] = ltog[row - 1];
177:         v[2] = two*(hydhx + hxdhy); col[2] = grow;
178:         v[3] = -hydhx; col[3] = ltog[row + 1];
179:         v[4] = -hxdhy; col[4] = ltog[row + Xm];
180:         MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
181:       } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)) {
182:         value = .5*two*(hydhx + hxdhy);
183:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
184:       } else {
185:         value = .25*two*(hydhx + hxdhy);
186:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
187:       }
188:     }
189:   }
190:   ISLocalToGlobalMappingRestoreIndices(ltogm,&ltog);
191:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
192:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
193:   return(0);
194: }

196: /*TEST

198:     test:
199:       args: -ksp_monitor_short

201:     test:
202:       suffix: 2
203:       args:  -ksp_monitor_short
204:       nsize: 3

206:     test:
207:       suffix: ml_1
208:       args:  -ksp_monitor_short -pc_type ml -mat_no_inode
209:       nsize: 3
210:       requires: ml

212:     test:
213:       suffix: ml_2
214:       args:  -ksp_monitor_short -pc_type ml -mat_no_inode -ksp_max_it 3
215:       nsize: 3
216:       requires: ml

218:     test:
219:       suffix: ml_3
220:       args:  -ksp_monitor_short -pc_type ml -mat_no_inode -pc_mg_type ADDITIVE -ksp_max_it 7
221:       nsize: 1
222:       requires: ml

224:     test:
225:       suffix: cycles
226:       nsize: {{1 2}}
227:       args: -ksp_view_final_residual -pc_type mg -mx 5 -my 5 -pc_mg_levels 3 -pc_mg_galerkin -ksp_monitor -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -pc_mg_type {{additive multiplicative full kaskade}separate output} -nrhs 1

229:     test:
230:       suffix: matcycles
231:       nsize: {{1 2}}
232:       args: -ksp_view_final_residual -ksp_type preonly -pc_type mg -mx 5 -my 5 -pc_mg_levels 3 -pc_mg_galerkin -ksp_monitor -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -pc_mg_type {{additive multiplicative full kaskade}separate output} -nrhs 7 -ksp_matsolve_batch_size {{4 7}separate output}

234:     test:
235:       requires: ml
236:       suffix: matcycles_ml
237:       nsize: {{1 2}}
238:       args: -ksp_view_final_residual -ksp_type preonly -pc_type ml -mx 5 -my 5 -ksp_monitor -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -pc_mg_type {{additive multiplicative full kaskade}separate output} -nrhs 7 -ksp_matsolve_batch_size {{4 7}separate output}

240:     test:
241:       requires: hpddm
242:       suffix: matcycles_hpddm_mg
243:       nsize: {{1 2}}
244:       args: -ksp_view_final_residual -ksp_type hpddm -pc_type mg -pc_mg_levels 3 -pc_mg_galerkin -mx 5 -my 5 -ksp_monitor -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -pc_mg_type {{additive multiplicative full kaskade}separate output} -nrhs 7 -ksp_matsolve_batch_size {{4 7}separate output}

246:     test:
247:       requires: hpddm
248:       nsize: {{1 2}}
249:       suffix: matcycles_hpddm_ilu
250:       args: -ksp_view_final_residual -ksp_type hpddm -pc_type redundant -redundant_pc_type ilu -mx 5 -my 5 -ksp_monitor -nrhs 7 -ksp_matsolve_batch_size {{4 7}separate output}

252: TEST*/