/*T Concepts: KSP^solving a system of linear equations Concepts: KSP^Laplacian, 2d Processors: n T*/ /* Added at the request of Marc Garbey. Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation -div \rho grad u = f, 0 < x,y < 1, with forcing function f = e^{-x^2/\nu} e^{-y^2/\nu} with Dirichlet boundary conditions u = f(x,y) for x = 0, x = 1, y = 0, y = 1 or pure Neumman boundary conditions This uses multigrid to solve the linear system */ static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n"; #include #include #include extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*); extern PetscErrorCode ComputeRHS(KSP,Vec,void*); typedef enum {DIRICHLET, NEUMANN} BCType; typedef struct { PetscReal rho; PetscReal nu; BCType bcType; } UserContext; int main(int argc,char **argv) { KSP ksp; DM da; UserContext user; const char *bcTypes[2] = {"dirichlet","neumann"}; PetscErrorCode ierr; PetscInt bc; Vec b,x; PetscBool testsolver = PETSC_FALSE; ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr); ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr); ierr = DMSetFromOptions(da);CHKERRQ(ierr); ierr = DMSetUp(da);CHKERRQ(ierr); ierr = DMDASetUniformCoordinates(da,0,1,0,1,0,0);CHKERRQ(ierr); ierr = DMDASetFieldName(da,0,"Pressure");CHKERRQ(ierr); ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");CHKERRQ(ierr); user.rho = 1.0; ierr = PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);CHKERRQ(ierr); user.nu = 0.1; ierr = PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);CHKERRQ(ierr); bc = (PetscInt)DIRICHLET; ierr = PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);CHKERRQ(ierr); user.bcType = (BCType)bc; ierr = PetscOptionsBool("-testsolver", "Run solver multiple times, useful for performance studies of solver", "ex29.c", testsolver, &testsolver, NULL);CHKERRQ(ierr); ierr = PetscOptionsEnd();CHKERRQ(ierr); ierr = KSPSetComputeRHS(ksp,ComputeRHS,&user);CHKERRQ(ierr); ierr = KSPSetComputeOperators(ksp,ComputeMatrix,&user);CHKERRQ(ierr); ierr = KSPSetDM(ksp,da);CHKERRQ(ierr); ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr); ierr = KSPSetUp(ksp);CHKERRQ(ierr); ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr); if (testsolver) { ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr); ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr); KSPSetDMActive(ksp,PETSC_FALSE); ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr); { #if defined(PETSC_USE_LOG) PetscLogStage stage; #endif PetscInt i,n = 20; ierr = PetscLogStageRegister("Solve only",&stage);CHKERRQ(ierr); ierr = PetscLogStagePush(stage);CHKERRQ(ierr); for (i=0; inu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy; } } ierr = DMDAVecRestoreArray(da, b, &array);CHKERRQ(ierr); ierr = VecAssemblyBegin(b);CHKERRQ(ierr); ierr = VecAssemblyEnd(b);CHKERRQ(ierr); /* force right hand side to be consistent for singular matrix */ /* note this is really a hack, normally the model would provide you with a consistent right handside */ if (user->bcType == NEUMANN) { MatNullSpace nullspace; ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr); ierr = MatNullSpaceRemove(nullspace,b);CHKERRQ(ierr); ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr); } PetscFunctionReturn(0); } PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho) { PetscFunctionBeginUser; if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) { *rho = centerRho; } else { *rho = 1.0; } PetscFunctionReturn(0); } PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx) { UserContext *user = (UserContext*)ctx; PetscReal centerRho; PetscErrorCode ierr; PetscInt i,j,mx,my,xm,ym,xs,ys; PetscScalar v[5]; PetscReal Hx,Hy,HydHx,HxdHy,rho; MatStencil row, col[5]; DM da; PetscBool check_matis = PETSC_FALSE; PetscFunctionBeginUser; ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr); centerRho = user->rho; ierr = DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr); Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); HxdHy = Hx/Hy; HydHx = Hy/Hx; ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr); for (j=ys; jbcType == DIRICHLET) { v[0] = 2.0*rho*(HxdHy + HydHx); ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr); } else if (user->bcType == NEUMANN) { PetscInt numx = 0, numy = 0, num = 0; if (j!=0) { v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1; numy++; num++; } if (i!=0) { v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j; numx++; num++; } if (i!=mx-1) { v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j; numx++; num++; } if (j!=my-1) { v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1; numy++; num++; } v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i; col[num].j = j; num++; ierr = MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr); } } else { v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1; v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j; v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j; v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j; v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1; ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr); } } } ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatViewFromOptions(jac,NULL,"-view_mat");CHKERRQ(ierr); ierr = PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);CHKERRQ(ierr); if (check_matis) { void (*f)(void); Mat J2; MatType jtype; PetscReal nrm; ierr = MatGetType(jac,&jtype);CHKERRQ(ierr); ierr = MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);CHKERRQ(ierr); ierr = MatViewFromOptions(J2,NULL,"-view_conv");CHKERRQ(ierr); ierr = MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);CHKERRQ(ierr); ierr = MatGetOperation(jac,MATOP_VIEW,&f);CHKERRQ(ierr); ierr = MatSetOperation(J2,MATOP_VIEW,f);CHKERRQ(ierr); ierr = MatSetDM(J2,da);CHKERRQ(ierr); ierr = MatViewFromOptions(J2,NULL,"-view_conv_assembled");CHKERRQ(ierr); ierr = MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr); ierr = MatNorm(J2,NORM_FROBENIUS,&nrm);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);CHKERRQ(ierr); ierr = MatViewFromOptions(J2,NULL,"-view_conv_err");CHKERRQ(ierr); ierr = MatDestroy(&J2);CHKERRQ(ierr); } if (user->bcType == NEUMANN) { MatNullSpace nullspace; ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr); ierr = MatSetNullSpace(J,nullspace);CHKERRQ(ierr); ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr); } PetscFunctionReturn(0); } /*TEST test: args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -ksp_rtol 1.e-3 test: suffix: 2 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 requires: !single test: suffix: telescope nsize: 4 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 test: suffix: 3 args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_pc_type jacobi test: suffix: 4 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 test: suffix: 5 nsize: 2 requires: hypre !complex args: -pc_type mg -da_refine 2 -ksp_monitor -matptap_via hypre -pc_mg_galerkin both TEST*/