Actual source code: ex29.c

petsc-master 2019-07-20
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  1: /*T
  2:    Concepts: KSP^solving a system of linear equations
  3:    Concepts: KSP^Laplacian, 2d
  4:    Processors: n
  5: T*/



  9: /*
 10: Added at the request of Marc Garbey.

 12: Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation

 14:    -div \rho grad u = f,  0 < x,y < 1,

 16: with forcing function

 18:    f = e^{-x^2/\nu} e^{-y^2/\nu}

 20: with Dirichlet boundary conditions

 22:    u = f(x,y) for x = 0, x = 1, y = 0, y = 1

 24: or pure Neumman boundary conditions

 26: This uses multigrid to solve the linear system
 27: */

 29: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";

 31:  #include <petscdm.h>
 32:  #include <petscdmda.h>
 33:  #include <petscksp.h>

 35: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
 36: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

 38: typedef enum {DIRICHLET, NEUMANN} BCType;

 40: typedef struct {
 41:   PetscReal rho;
 42:   PetscReal nu;
 43:   BCType    bcType;
 44: } UserContext;

 46: int main(int argc,char **argv)
 47: {
 48:   KSP            ksp;
 49:   DM             da;
 50:   UserContext    user;
 51:   const char     *bcTypes[2] = {"dirichlet","neumann"};
 53:   PetscInt       bc;
 54:   Vec            b,x;
 55:   PetscBool      testsolver = PETSC_FALSE;

 57:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 58:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 59:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
 60:   DMSetFromOptions(da);
 61:   DMSetUp(da);
 62:   DMDASetUniformCoordinates(da,0,1,0,1,0,0);
 63:   DMDASetFieldName(da,0,"Pressure");

 65:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");
 66:   user.rho    = 1.0;
 67:   PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);
 68:   user.nu     = 0.1;
 69:   PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);
 70:   bc          = (PetscInt)DIRICHLET;
 71:   PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
 72:   user.bcType = (BCType)bc;
 73:   PetscOptionsBool("-testsolver", "Run solver multiple times, useful for performance studies of solver", "ex29.c", testsolver, &testsolver, NULL);
 74:   PetscOptionsEnd();

 76:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
 77:   KSPSetComputeOperators(ksp,ComputeMatrix,&user);
 78:   KSPSetDM(ksp,da);
 79:   KSPSetFromOptions(ksp);
 80:   KSPSetUp(ksp);
 81:   KSPSolve(ksp,NULL,NULL);

 83:   if (testsolver) {
 84:     KSPGetSolution(ksp,&x);
 85:     KSPGetRhs(ksp,&b);
 86:     KSPSetDMActive(ksp,PETSC_FALSE);
 87:     KSPSolve(ksp,b,x);
 88:     {
 89:       PetscLogStage stage;
 90:       PetscInt      i,n = 20;
 91:       PetscLogStageRegister("Solve only",&stage);
 92:       PetscLogStagePush(stage);
 93:       for (i=0; i<n; i++) {
 94:         KSPSolve(ksp,b,x);
 95:       }
 96:       PetscLogStagePop();
 97:     }
 98:   }

100:   DMDestroy(&da);
101:   KSPDestroy(&ksp);
102:   PetscFinalize();
103:   return ierr;
104: }

106: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
107: {
108:   UserContext    *user = (UserContext*)ctx;
110:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
111:   PetscScalar    Hx,Hy;
112:   PetscScalar    **array;
113:   DM             da;

116:   KSPGetDM(ksp,&da);
117:   DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
118:   Hx   = 1.0 / (PetscReal)(mx-1);
119:   Hy   = 1.0 / (PetscReal)(my-1);
120:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
121:   DMDAVecGetArray(da, b, &array);
122:   for (j=ys; j<ys+ym; j++) {
123:     for (i=xs; i<xs+xm; i++) {
124:       array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
125:     }
126:   }
127:   DMDAVecRestoreArray(da, b, &array);
128:   VecAssemblyBegin(b);
129:   VecAssemblyEnd(b);

131:   /* force right hand side to be consistent for singular matrix */
132:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
133:   if (user->bcType == NEUMANN) {
134:     MatNullSpace nullspace;

136:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
137:     MatNullSpaceRemove(nullspace,b);
138:     MatNullSpaceDestroy(&nullspace);
139:   }
140:   return(0);
141: }


144: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
145: {
147:   if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
148:     *rho = centerRho;
149:   } else {
150:     *rho = 1.0;
151:   }
152:   return(0);
153: }

155: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
156: {
157:   UserContext    *user = (UserContext*)ctx;
158:   PetscReal      centerRho;
160:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
161:   PetscScalar    v[5];
162:   PetscReal      Hx,Hy,HydHx,HxdHy,rho;
163:   MatStencil     row, col[5];
164:   DM             da;
165:   PetscBool      check_matis = PETSC_FALSE;

168:   KSPGetDM(ksp,&da);
169:   centerRho = user->rho;
170:   DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
171:   Hx        = 1.0 / (PetscReal)(mx-1);
172:   Hy        = 1.0 / (PetscReal)(my-1);
173:   HxdHy     = Hx/Hy;
174:   HydHx     = Hy/Hx;
175:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
176:   for (j=ys; j<ys+ym; j++) {
177:     for (i=xs; i<xs+xm; i++) {
178:       row.i = i; row.j = j;
179:       ComputeRho(i, j, mx, my, centerRho, &rho);
180:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
181:         if (user->bcType == DIRICHLET) {
182:           v[0] = 2.0*rho*(HxdHy + HydHx);
183:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
184:         } else if (user->bcType == NEUMANN) {
185:           PetscInt numx = 0, numy = 0, num = 0;
186:           if (j!=0) {
187:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j-1;
188:             numy++; num++;
189:           }
190:           if (i!=0) {
191:             v[num] = -rho*HydHx;              col[num].i = i-1; col[num].j = j;
192:             numx++; num++;
193:           }
194:           if (i!=mx-1) {
195:             v[num] = -rho*HydHx;              col[num].i = i+1; col[num].j = j;
196:             numx++; num++;
197:           }
198:           if (j!=my-1) {
199:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j+1;
200:             numy++; num++;
201:           }
202:           v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i;   col[num].j = j;
203:           num++;
204:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
205:         }
206:       } else {
207:         v[0] = -rho*HxdHy;              col[0].i = i;   col[0].j = j-1;
208:         v[1] = -rho*HydHx;              col[1].i = i-1; col[1].j = j;
209:         v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
210:         v[3] = -rho*HydHx;              col[3].i = i+1; col[3].j = j;
211:         v[4] = -rho*HxdHy;              col[4].i = i;   col[4].j = j+1;
212:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
213:       }
214:     }
215:   }
216:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
217:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
218:   MatViewFromOptions(jac,NULL,"-view_mat");
219:   PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);
220:   if (check_matis) {
221:     void      (*f)(void);
222:     Mat       J2;
223:     MatType   jtype;
224:     PetscReal nrm;

226:     MatGetType(jac,&jtype);
227:     MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);
228:     MatViewFromOptions(J2,NULL,"-view_conv");
229:     MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);
230:     MatGetOperation(jac,MATOP_VIEW,&f);
231:     MatSetOperation(J2,MATOP_VIEW,f);
232:     MatSetDM(J2,da);
233:     MatViewFromOptions(J2,NULL,"-view_conv_assembled");
234:     MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);
235:     MatNorm(J2,NORM_FROBENIUS,&nrm);
236:     PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);
237:     MatViewFromOptions(J2,NULL,"-view_conv_err");
238:     MatDestroy(&J2);
239:   }
240:   if (user->bcType == NEUMANN) {
241:     MatNullSpace nullspace;

243:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
244:     MatSetNullSpace(J,nullspace);
245:     MatNullSpaceDestroy(&nullspace);
246:   }
247:   return(0);
248: }


251: /*TEST

253:    test:
254:       args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -ksp_rtol 1.e-3

256:    test:
257:       suffix: 2
258:       args: -bc_type neumann -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -mg_coarse_pc_factor_shift_type nonzero
259:       requires: !single

261:    test:
262:       suffix: telescope
263:       nsize: 4
264:       args: -ksp_monitor_short -da_grid_x 257 -da_grid_y 257 -pc_type mg -pc_mg_galerkin pmat -pc_mg_levels 4 -ksp_type richardson -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_ignore_kspcomputeoperators -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_galerkin pmat -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_levels_ksp_type chebyshev -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_coarse_pc_telescope_reduction_factor 4

266:    test:
267:       suffix: 3
268:       args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_pc_type jacobi

270:    test:
271:       suffix: 4
272:       args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_ksp_max_it 3 -mg_levels_ksp_max_it 4

274:    test:
275:       suffix: 5
276:       nsize: 2
277:       requires: hypre !complex
278:       args: -pc_type mg  -da_refine 2 -ksp_monitor  -matptap_via hypre -pc_mg_galerkin both

280: TEST*/