/*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,MatStructure*,void*); extern PetscErrorCode ComputeRHS(KSP,Vec,void*); typedef enum {DIRICHLET, NEUMANN} BCType; typedef struct { PetscScalar rho; PetscScalar nu; BCType bcType; } UserContext; #undef __FUNCT__ #define __FUNCT__ "main" 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; PetscInitialize(&argc,&argv,(char *)0,help); ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr); ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-3,-3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr); ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq"); user.rho = 1.0; ierr = PetscOptionsScalar("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, PETSC_NULL);CHKERRQ(ierr); user.nu = 0.1; ierr = PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, PETSC_NULL);CHKERRQ(ierr); bc = (PetscInt)DIRICHLET; ierr = PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,PETSC_NULL);CHKERRQ(ierr); user.bcType = (BCType)bc; ierr = PetscOptionsEnd(); 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,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr); ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr); ierr = DMDestroy(&da);CHKERRQ(ierr); ierr = KSPDestroy(&ksp);CHKERRQ(ierr); ierr = PetscFinalize(); return 0; } #undef __FUNCT__ #define __FUNCT__ "ComputeRHS" PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx) { UserContext *user = (UserContext*)ctx; PetscErrorCode ierr; PetscInt i,j,mx,my,xm,ym,xs,ys; PetscScalar Hx,Hy; PetscScalar **array; DM da; PetscFunctionBegin; ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr); 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); ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr); ierr = DMDAVecGetArray(da, b, &array);CHKERRQ(ierr); for (j=ys; jnu)*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,PETSC_NULL);CHKERRQ(ierr); ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr); } PetscFunctionReturn(0); } #undef __FUNCT__ #define __FUNCT__ "ComputeRho" PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscScalar centerRho, PetscScalar *rho) { PetscFunctionBegin; 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); } #undef __FUNCT__ #define __FUNCT__ "ComputeMatrix" PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,MatStructure *str,void *ctx) { UserContext *user = (UserContext*)ctx; PetscScalar centerRho; PetscErrorCode ierr; PetscInt i,j,mx,my,xm,ym,xs,ys,num; PetscScalar v[5],Hx,Hy,HydHx,HxdHy,rho; MatStencil row, col[5]; DM da; PetscFunctionBegin; 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) { num = 0; if (j!=0) { v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1; num++; } if (i!=0) { v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j; num++; } if (i!=mx-1) { v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j; num++; } if (j!=my-1) { v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1; num++; } v[num] = (num/2.0)*rho*(HxdHy + HydHx); 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); if (user->bcType == NEUMANN) { MatNullSpace nullspace; ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr); ierr = MatSetNullSpace(jac,nullspace);CHKERRQ(ierr); ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr); } PetscFunctionReturn(0); }