# petsc / src / ksp / ksp / examples / tutorials / ex32.c

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 /*T Concepts: KSP^solving a system of linear equations Concepts: KSP^Laplacian, 2d Processors: n T*/ /* Laplacian in 2D. Modeled by the partial differential equation div grad u = f, 0 < x,y < 1, with forcing function f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu} with pure Neumann boundary conditions The functions are cell-centered This uses multigrid to solve the linear system Contributed by Andrei Draganescu Note the nice multigrid convergence despite the fact it is only using peicewise constant interpolation/restriction. This is because cell-centered multigrid does not need the same rule: polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE that vertex based multigrid needs. */ 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 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; PetscInitialize(&argc,&argv,(char*)0,help); ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr); ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr); ierr = DMDASetInterpolationType(da, DMDA_Q0);CHKERRQ(ierr); ierr = KSPSetDM(ksp,da);CHKERRQ(ierr); ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM"); user.nu = 0.1; ierr = PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);CHKERRQ(ierr); bc = (PetscInt)NEUMANN; ierr = PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);CHKERRQ(ierr); user.bcType = (BCType)bc; ierr = PetscOptionsEnd(); ierr = KSPSetComputeRHS(ksp,ComputeRHS,&user);CHKERRQ(ierr); ierr = KSPSetComputeOperators(ksp,ComputeMatrix,&user);CHKERRQ(ierr); ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr); ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr); ierr = KSPDestroy(&ksp);CHKERRQ(ierr); ierr = DMDestroy(&da);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; PetscFunctionBeginUser; 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); Hy = 1.0 / (PetscReal)(my); 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+0.5)*Hy)*(((PetscReal)j+0.5)*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); } #undef __FUNCT__ #define __FUNCT__ "ComputeMatrix" PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac,MatStructure *str, void *ctx) { UserContext *user = (UserContext*)ctx; PetscErrorCode ierr; PetscInt i,j,mx,my,xm,ym,xs,ys,num, numi, numj; PetscScalar v[5],Hx,Hy,HydHx,HxdHy; MatStencil row, col[5]; DM da; PetscFunctionBeginUser; 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); Hy = 1.0 / (PetscReal)(my); 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*(HxdHy + HydHx); ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr); SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !\n"); } else if (user->bcType == NEUMANN) { num = 0; numi=0; numj=0; if (j!=0) { v[num] = -HxdHy; col[num].i = i; col[num].j = j-1; num++; numj++; } if (i!=0) { v[num] = -HydHx; col[num].i = i-1; col[num].j = j; num++; numi++; } if (i!=mx-1) { v[num] = -HydHx; col[num].i = i+1; col[num].j = j; num++; numi++; } if (j!=my-1) { v[num] = -HxdHy; col[num].i = i; col[num].j = j+1; num++; numj++; } v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*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] = -HxdHy; col[0].i = i; col[0].j = j-1; v[1] = -HydHx; col[1].i = i-1; col[1].j = j; v[2] = 2.0*(HxdHy + HydHx); col[2].i = i; col[2].j = j; v[3] = -HydHx; col[3].i = i+1; col[3].j = j; v[4] = -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); }