1 static const char help[] = "Time-dependent PDE in 1d. Simplified from ex15.c for illustrating how to solve DAEs. \n"; 2 /* 3 u_t = uxx 4 0 < x < 1; 5 At t=0: u(x) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5)) < .125 6 u(x) = 0.0 if r >= .125 7 8 Boundary conditions: 9 Dirichlet BC: 10 At x=0, x=1, u = 0.0 11 12 Neumann BC: 13 At x=0, x=1: du(x,t)/dx = 0 14 15 mpiexec -n 2 ./ex17 -da_grid_x 40 -ts_max_steps 2 -snes_monitor -ksp_monitor 16 ./ex17 -da_grid_x 40 -monitor_solution 17 ./ex17 -da_grid_x 100 -ts_type theta -ts_theta_theta 0.5 # Midpoint is not L-stable 18 ./ex17 -jac_type fd_coloring -da_grid_x 500 -boundary 1 19 ./ex17 -da_grid_x 100 -ts_type gl -ts_adapt_type none -ts_max_steps 2 20 */ 21 22 #include <petscdm.h> 23 #include <petscdmda.h> 24 #include <petscts.h> 25 26 typedef enum {JACOBIAN_ANALYTIC,JACOBIAN_FD_COLORING,JACOBIAN_FD_FULL} JacobianType; 27 static const char *const JacobianTypes[] = {"analytic","fd_coloring","fd_full","JacobianType","fd_",0}; 28 29 /* 30 User-defined data structures and routines 31 */ 32 typedef struct { 33 PetscReal c; 34 PetscInt boundary; /* Type of boundary condition */ 35 PetscBool viewJacobian; 36 } AppCtx; 37 38 static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*); 39 static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*); 40 static PetscErrorCode FormInitialSolution(TS,Vec,void*); 41 42 int main(int argc,char **argv) 43 { 44 TS ts; /* nonlinear solver */ 45 Vec u; /* solution, residual vectors */ 46 Mat J; /* Jacobian matrix */ 47 PetscInt nsteps; 48 PetscReal vmin,vmax,norm; 49 DM da; 50 PetscReal ftime,dt; 51 AppCtx user; /* user-defined work context */ 52 JacobianType jacType; 53 54 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 55 56 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57 Create distributed array (DMDA) to manage parallel grid and vectors 58 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 59 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,11,1,1,NULL,&da)); 60 PetscCall(DMSetFromOptions(da)); 61 PetscCall(DMSetUp(da)); 62 63 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 64 Extract global vectors from DMDA; 65 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 66 PetscCall(DMCreateGlobalVector(da,&u)); 67 68 /* Initialize user application context */ 69 user.c = -30.0; 70 user.boundary = 0; /* 0: Dirichlet BC; 1: Neumann BC */ 71 user.viewJacobian = PETSC_FALSE; 72 73 PetscCall(PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL)); 74 PetscCall(PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian)); 75 76 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 77 Create timestepping solver context 78 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 79 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 80 PetscCall(TSSetProblemType(ts,TS_NONLINEAR)); 81 PetscCall(TSSetType(ts,TSTHETA)); 82 PetscCall(TSThetaSetTheta(ts,1.0)); /* Make the Theta method behave like backward Euler */ 83 PetscCall(TSSetIFunction(ts,NULL,FormIFunction,&user)); 84 85 PetscCall(DMSetMatType(da,MATAIJ)); 86 PetscCall(DMCreateMatrix(da,&J)); 87 jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */ 88 89 PetscCall(TSSetDM(ts,da)); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */ 90 91 ftime = 1.0; 92 PetscCall(TSSetMaxTime(ts,ftime)); 93 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 94 95 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 96 Set initial conditions 97 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 98 PetscCall(FormInitialSolution(ts,u,&user)); 99 PetscCall(TSSetSolution(ts,u)); 100 dt = .01; 101 PetscCall(TSSetTimeStep(ts,dt)); 102 103 /* Use slow fd Jacobian or fast fd Jacobian with colorings. 104 Note: this requirs snes which is not created until TSSetUp()/TSSetFromOptions() is called */ 105 PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Options for Jacobian evaluation",NULL); 106 PetscCall(PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0)); 107 PetscOptionsEnd(); 108 if (jacType == JACOBIAN_ANALYTIC) { 109 PetscCall(TSSetIJacobian(ts,J,J,FormIJacobian,&user)); 110 } else if (jacType == JACOBIAN_FD_COLORING) { 111 SNES snes; 112 PetscCall(TSGetSNES(ts,&snes)); 113 PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0)); 114 } else if (jacType == JACOBIAN_FD_FULL) { 115 SNES snes; 116 PetscCall(TSGetSNES(ts,&snes)); 117 PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user)); 118 } 119 120 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 121 Set runtime options 122 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 123 PetscCall(TSSetFromOptions(ts)); 124 125 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 126 Integrate ODE system 127 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 128 PetscCall(TSSolve(ts,u)); 129 130 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 131 Compute diagnostics of the solution 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 133 PetscCall(VecNorm(u,NORM_1,&norm)); 134 PetscCall(VecMax(u,NULL,&vmax)); 135 PetscCall(VecMin(u,NULL,&vmin)); 136 PetscCall(TSGetStepNumber(ts,&nsteps)); 137 PetscCall(TSGetTime(ts,&ftime)); 138 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"timestep %" PetscInt_FMT ": time %g, solution norm %g, max %g, min %g\n",nsteps,(double)ftime,(double)norm,(double)vmax,(double)vmin)); 139 140 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 141 Free work space. 142 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 143 PetscCall(MatDestroy(&J)); 144 PetscCall(VecDestroy(&u)); 145 PetscCall(TSDestroy(&ts)); 146 PetscCall(DMDestroy(&da)); 147 PetscCall(PetscFinalize()); 148 return 0; 149 } 150 /* ------------------------------------------------------------------- */ 151 static PetscErrorCode FormIFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr) 152 { 153 AppCtx *user=(AppCtx*)ptr; 154 DM da; 155 PetscInt i,Mx,xs,xm; 156 PetscReal hx,sx; 157 PetscScalar *u,*udot,*f; 158 Vec localU; 159 160 PetscFunctionBeginUser; 161 PetscCall(TSGetDM(ts,&da)); 162 PetscCall(DMGetLocalVector(da,&localU)); 163 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE)); 164 165 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 166 167 /* 168 Scatter ghost points to local vector,using the 2-step process 169 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 170 By placing code between these two statements, computations can be 171 done while messages are in transition. 172 */ 173 PetscCall(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU)); 174 PetscCall(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU)); 175 176 /* Get pointers to vector data */ 177 PetscCall(DMDAVecGetArrayRead(da,localU,&u)); 178 PetscCall(DMDAVecGetArrayRead(da,Udot,&udot)); 179 PetscCall(DMDAVecGetArray(da,F,&f)); 180 181 /* Get local grid boundaries */ 182 PetscCall(DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL)); 183 184 /* Compute function over the locally owned part of the grid */ 185 for (i=xs; i<xs+xm; i++) { 186 if (user->boundary == 0) { /* Dirichlet BC */ 187 if (i == 0 || i == Mx-1) f[i] = u[i]; /* F = U */ 188 else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx; 189 } else { /* Neumann BC */ 190 if (i == 0) f[i] = u[0] - u[1]; 191 else if (i == Mx-1) f[i] = u[i] - u[i-1]; 192 else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx; 193 } 194 } 195 196 /* Restore vectors */ 197 PetscCall(DMDAVecRestoreArrayRead(da,localU,&u)); 198 PetscCall(DMDAVecRestoreArrayRead(da,Udot,&udot)); 199 PetscCall(DMDAVecRestoreArray(da,F,&f)); 200 PetscCall(DMRestoreLocalVector(da,&localU)); 201 PetscFunctionReturn(0); 202 } 203 204 /* --------------------------------------------------------------------- */ 205 /* 206 IJacobian - Compute IJacobian = dF/dU + a dF/dUdot 207 */ 208 PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx) 209 { 210 PetscInt i,rstart,rend,Mx; 211 PetscReal hx,sx; 212 AppCtx *user = (AppCtx*)ctx; 213 DM da; 214 MatStencil col[3],row; 215 PetscInt nc; 216 PetscScalar vals[3]; 217 218 PetscFunctionBeginUser; 219 PetscCall(TSGetDM(ts,&da)); 220 PetscCall(MatGetOwnershipRange(Jpre,&rstart,&rend)); 221 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE)); 222 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 223 for (i=rstart; i<rend; i++) { 224 nc = 0; 225 row.i = i; 226 if (user->boundary == 0 && (i == 0 || i == Mx-1)) { 227 col[nc].i = i; vals[nc++] = 1.0; 228 } else if (user->boundary > 0 && i == 0) { /* Left Neumann */ 229 col[nc].i = i; vals[nc++] = 1.0; 230 col[nc].i = i+1; vals[nc++] = -1.0; 231 } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */ 232 col[nc].i = i-1; vals[nc++] = -1.0; 233 col[nc].i = i; vals[nc++] = 1.0; 234 } else { /* Interior */ 235 col[nc].i = i-1; vals[nc++] = -1.0*sx; 236 col[nc].i = i; vals[nc++] = 2.0*sx + a; 237 col[nc].i = i+1; vals[nc++] = -1.0*sx; 238 } 239 PetscCall(MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES)); 240 } 241 242 PetscCall(MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY)); 243 PetscCall(MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY)); 244 if (J != Jpre) { 245 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 246 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 247 } 248 if (user->viewJacobian) { 249 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Jpre:\n")); 250 PetscCall(MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD)); 251 } 252 PetscFunctionReturn(0); 253 } 254 255 /* ------------------------------------------------------------------- */ 256 PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ptr) 257 { 258 AppCtx *user=(AppCtx*)ptr; 259 PetscReal c =user->c; 260 DM da; 261 PetscInt i,xs,xm,Mx; 262 PetscScalar *u; 263 PetscReal hx,x,r; 264 265 PetscFunctionBeginUser; 266 PetscCall(TSGetDM(ts,&da)); 267 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE)); 268 269 hx = 1.0/(PetscReal)(Mx-1); 270 271 /* Get pointers to vector data */ 272 PetscCall(DMDAVecGetArray(da,U,&u)); 273 274 /* Get local grid boundaries */ 275 PetscCall(DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL)); 276 277 /* Compute function over the locally owned part of the grid */ 278 for (i=xs; i<xs+xm; i++) { 279 x = i*hx; 280 r = PetscSqrtReal((x-.5)*(x-.5)); 281 if (r < .125) u[i] = PetscExpReal(c*r*r*r); 282 else u[i] = 0.0; 283 } 284 285 /* Restore vectors */ 286 PetscCall(DMDAVecRestoreArray(da,U,&u)); 287 PetscFunctionReturn(0); 288 } 289 290 /*TEST 291 292 test: 293 requires: !single 294 args: -da_grid_x 40 -ts_max_steps 2 -snes_monitor_short -ksp_monitor_short -ts_monitor 295 296 test: 297 suffix: 2 298 requires: !single 299 args: -da_grid_x 100 -ts_type theta -ts_theta_theta 0.5 300 301 TEST*/ 302