1 static char help[] ="Solves a time-dependent nonlinear PDE.\n"; 2 3 /* ------------------------------------------------------------------------ 4 5 This program solves the two-dimensional time-dependent Bratu problem 6 u_t = u_xx + u_yy + \lambda*exp(u), 7 on the domain 0 <= x,y <= 1, 8 with the boundary conditions 9 u(t,0,y) = 0, u_x(t,1,y) = 0, 10 u(t,x,0) = 0, u_x(t,x,1) = 0, 11 and the initial condition 12 u(0,x,y) = 0. 13 We discretize the right-hand side using finite differences with 14 uniform grid spacings hx,hy: 15 u_xx = (u_{i+1} - 2u_{i} + u_{i-1})/(hx^2) 16 u_yy = (u_{j+1} - 2u_{j} + u_{j-1})/(hy^2) 17 18 ------------------------------------------------------------------------- */ 19 20 #include <petscdmda.h> 21 #include <petscts.h> 22 23 /* 24 User-defined application context - contains data needed by the 25 application-provided call-back routines. 26 */ 27 typedef struct { 28 PetscReal lambda; 29 } AppCtx; 30 31 /* 32 FormIFunctionLocal - Evaluates nonlinear implicit function on local process patch 33 */ 34 static PetscErrorCode FormIFunctionLocal(DMDALocalInfo *info,PetscReal t,PetscScalar **x,PetscScalar **xdot,PetscScalar **f,AppCtx *app) 35 { 36 PetscInt i,j; 37 PetscReal lambda,hx,hy; 38 PetscScalar ut,u,ue,uw,un,us,uxx,uyy; 39 40 PetscFunctionBeginUser; 41 lambda = app->lambda; 42 hx = 1.0/(PetscReal)(info->mx-1); 43 hy = 1.0/(PetscReal)(info->my-1); 44 45 /* 46 Compute RHS function over the locally owned part of the grid 47 */ 48 for (j=info->ys; j<info->ys+info->ym; j++) { 49 for (i=info->xs; i<info->xs+info->xm; i++) { 50 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { 51 /* boundary points */ 52 f[j][i] = x[j][i] - (PetscReal)0; 53 } else { 54 /* interior points */ 55 ut = xdot[j][i]; 56 u = x[j][i]; 57 uw = x[j][i-1]; 58 ue = x[j][i+1]; 59 un = x[j+1][i]; 60 us = x[j-1][i]; 61 62 uxx = (uw - 2.0*u + ue)/(hx*hx); 63 uyy = (un - 2.0*u + us)/(hy*hy); 64 f[j][i] = ut - uxx - uyy - lambda*PetscExpScalar(u); 65 } 66 } 67 } 68 PetscFunctionReturn(0); 69 } 70 71 /* 72 FormIJacobianLocal - Evaluates implicit Jacobian matrix on local process patch 73 */ 74 static PetscErrorCode FormIJacobianLocal(DMDALocalInfo *info,PetscReal t,PetscScalar **x,PetscScalar **xdot,PetscScalar shift,Mat jac,Mat jacpre,AppCtx *app) 75 { 76 PetscInt i,j,k; 77 MatStencil col[5],row; 78 PetscScalar v[5],lambda,hx,hy; 79 80 PetscFunctionBeginUser; 81 lambda = app->lambda; 82 hx = 1.0/(PetscReal)(info->mx-1); 83 hy = 1.0/(PetscReal)(info->my-1); 84 85 /* 86 Compute Jacobian entries for the locally owned part of the grid 87 */ 88 for (j=info->ys; j<info->ys+info->ym; j++) { 89 for (i=info->xs; i<info->xs+info->xm; i++) { 90 row.j = j; row.i = i; k = 0; 91 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { 92 /* boundary points */ 93 v[0] = 1.0; 94 PetscCall(MatSetValuesStencil(jacpre,1,&row,1,&row,v,INSERT_VALUES)); 95 } else { 96 /* interior points */ 97 v[k] = -1.0/(hy*hy); col[k].j = j-1; col[k].i = i; k++; 98 v[k] = -1.0/(hx*hx); col[k].j = j; col[k].i = i-1; k++; 99 100 v[k] = shift + 2.0/(hx*hx) + 2.0/(hy*hy) - lambda*PetscExpScalar(x[j][i]); 101 col[k].j = j; col[k].i = i; k++; 102 103 v[k] = -1.0/(hx*hx); col[k].j = j; col[k].i = i+1; k++; 104 v[k] = -1.0/(hy*hy); col[k].j = j+1; col[k].i = i; k++; 105 106 PetscCall(MatSetValuesStencil(jacpre,1,&row,k,col,v,INSERT_VALUES)); 107 } 108 } 109 } 110 111 /* 112 Assemble matrix 113 */ 114 PetscCall(MatAssemblyBegin(jacpre,MAT_FINAL_ASSEMBLY)); 115 PetscCall(MatAssemblyEnd(jacpre,MAT_FINAL_ASSEMBLY)); 116 PetscFunctionReturn(0); 117 } 118 119 int main(int argc,char **argv) 120 { 121 TS ts; /* ODE integrator */ 122 DM da; /* DM context */ 123 Vec U; /* solution vector */ 124 DMBoundaryType bt = DM_BOUNDARY_NONE; 125 DMDAStencilType st = DMDA_STENCIL_STAR; 126 PetscInt sw = 1; 127 PetscInt N = 17; 128 PetscInt n = PETSC_DECIDE; 129 AppCtx app; 130 131 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 Initialize program 133 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 134 PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 135 PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex21 options",""); 136 { 137 app.lambda = 6.8; app.lambda = 6.0; 138 PetscCall(PetscOptionsReal("-lambda","","",app.lambda,&app.lambda,NULL)); 139 } 140 PetscOptionsEnd(); 141 142 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 143 Create DM context 144 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 145 PetscCall(DMDACreate2d(PETSC_COMM_WORLD,bt,bt,st,N,N,n,n,1,sw,NULL,NULL,&da)); 146 PetscCall(DMSetFromOptions(da)); 147 PetscCall(DMSetUp(da)); 148 PetscCall(DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0,1.0)); 149 150 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 151 Create timestepping solver context 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 153 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 154 PetscCall(TSSetProblemType(ts,TS_NONLINEAR)); 155 PetscCall(TSSetDM(ts,da)); 156 PetscCall(DMDestroy(&da)); 157 158 PetscCall(TSGetDM(ts,&da)); 159 PetscCall(DMDATSSetIFunctionLocal(da,INSERT_VALUES,(DMDATSIFunctionLocal)FormIFunctionLocal,&app)); 160 PetscCall(DMDATSSetIJacobianLocal(da,(DMDATSIJacobianLocal)FormIJacobianLocal,&app)); 161 162 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 163 Set solver options 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 165 PetscCall(TSSetType(ts,TSBDF)); 166 PetscCall(TSSetTimeStep(ts,1e-4)); 167 PetscCall(TSSetMaxTime(ts,1.0)); 168 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 169 PetscCall(TSSetFromOptions(ts)); 170 171 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 172 Set initial conditions 173 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 174 PetscCall(TSGetDM(ts,&da)); 175 PetscCall(DMCreateGlobalVector(da,&U)); 176 PetscCall(VecSet(U,0.0)); 177 PetscCall(TSSetSolution(ts,U)); 178 179 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 180 Run timestepping solver 181 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 182 PetscCall(TSSolve(ts,U)); 183 184 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 185 All PETSc objects should be destroyed when they are no longer needed. 186 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 187 PetscCall(VecDestroy(&U)); 188 PetscCall(TSDestroy(&ts)); 189 PetscCall(PetscFinalize()); 190 return 0; 191 } 192 193 /*TEST 194 195 testset: 196 requires: !single !complex 197 args: -da_grid_x 5 -da_grid_y 5 -da_refine 2 -dm_view -ts_type bdf -ts_adapt_type none -ts_dt 1e-3 -ts_monitor -ts_max_steps 5 -ts_view -snes_rtol 1e-6 -snes_type ngmres -npc_snes_type fas 198 filter: grep -v "total number of" 199 test: 200 suffix: 1_bdf_ngmres_fas_ms 201 args: -prefix_push npc_fas_levels_ -snes_type ms -snes_max_it 5 -ksp_type preonly -prefix_pop 202 test: 203 suffix: 2_bdf_ngmres_fas_ms 204 args: -prefix_push npc_fas_levels_ -snes_type ms -snes_max_it 5 -ksp_type preonly -prefix_pop 205 nsize: 2 206 test: 207 suffix: 1_bdf_ngmres_fas_ngs 208 args: -prefix_push npc_fas_levels_ -snes_type ngs -snes_max_it 5 -prefix_pop 209 test: 210 suffix: 2_bdf_ngmres_fas_ngs 211 args: -prefix_push npc_fas_levels_ -snes_type ngs -snes_max_it 5 -prefix_pop 212 nsize: 2 213 214 TEST*/ 215