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 PetscErrorCode ierr; 50 DM da; 51 PetscReal ftime,dt; 52 AppCtx user; /* user-defined work context */ 53 JacobianType jacType; 54 55 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 56 57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 58 Create distributed array (DMDA) to manage parallel grid and vectors 59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 60 ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,11,1,1,NULL,&da);CHKERRQ(ierr); 61 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 62 ierr = DMSetUp(da);CHKERRQ(ierr); 63 64 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 65 Extract global vectors from DMDA; 66 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 67 ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr); 68 69 /* Initialize user application context */ 70 user.c = -30.0; 71 user.boundary = 0; /* 0: Dirichlet BC; 1: Neumann BC */ 72 user.viewJacobian = PETSC_FALSE; 73 74 ierr = PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL);CHKERRQ(ierr); 75 ierr = PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian);CHKERRQ(ierr); 76 77 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 78 Create timestepping solver context 79 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 80 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 81 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 82 ierr = TSSetType(ts,TSTHETA);CHKERRQ(ierr); 83 ierr = TSThetaSetTheta(ts,1.0);CHKERRQ(ierr); /* Make the Theta method behave like backward Euler */ 84 ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);CHKERRQ(ierr); 85 86 ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr); 87 ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr); 88 jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */ 89 90 ierr = TSSetDM(ts,da);CHKERRQ(ierr); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */ 91 92 ftime = 1.0; 93 ierr = TSSetMaxTime(ts,ftime);CHKERRQ(ierr); 94 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 95 96 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 97 Set initial conditions 98 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 99 ierr = FormInitialSolution(ts,u,&user);CHKERRQ(ierr); 100 ierr = TSSetSolution(ts,u);CHKERRQ(ierr); 101 dt = .01; 102 ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr); 103 104 /* Use slow fd Jacobian or fast fd Jacobian with colorings. 105 Note: this requirs snes which is not created until TSSetUp()/TSSetFromOptions() is called */ 106 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Options for Jacobian evaluation",NULL);CHKERRQ(ierr); 107 ierr = PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0);CHKERRQ(ierr); 108 ierr = PetscOptionsEnd();CHKERRQ(ierr); 109 if (jacType == JACOBIAN_ANALYTIC) { 110 ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);CHKERRQ(ierr); 111 } else if (jacType == JACOBIAN_FD_COLORING) { 112 SNES snes; 113 ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr); 114 ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0);CHKERRQ(ierr); 115 } else if (jacType == JACOBIAN_FD_FULL) { 116 SNES snes; 117 ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr); 118 ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user);CHKERRQ(ierr); 119 } 120 121 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 122 Set runtime options 123 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 124 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 125 126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 127 Integrate ODE system 128 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 129 ierr = TSSolve(ts,u);CHKERRQ(ierr); 130 131 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 Compute diagnostics of the solution 133 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 134 ierr = VecNorm(u,NORM_1,&norm);CHKERRQ(ierr); 135 ierr = VecMax(u,NULL,&vmax);CHKERRQ(ierr); 136 ierr = VecMin(u,NULL,&vmin);CHKERRQ(ierr); 137 ierr = TSGetStepNumber(ts,&nsteps);CHKERRQ(ierr); 138 ierr = TSGetTime(ts,&ftime);CHKERRQ(ierr); 139 ierr = PetscPrintf(PETSC_COMM_WORLD,"timestep %D: time %g, solution norm %g, max %g, min %g\n",nsteps,(double)ftime,(double)norm,(double)vmax,(double)vmin);CHKERRQ(ierr); 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Free work space. 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 ierr = MatDestroy(&J);CHKERRQ(ierr); 145 ierr = VecDestroy(&u);CHKERRQ(ierr); 146 ierr = TSDestroy(&ts);CHKERRQ(ierr); 147 ierr = DMDestroy(&da);CHKERRQ(ierr); 148 ierr = PetscFinalize(); 149 return ierr; 150 } 151 /* ------------------------------------------------------------------- */ 152 static PetscErrorCode FormIFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr) 153 { 154 AppCtx *user=(AppCtx*)ptr; 155 DM da; 156 PetscErrorCode ierr; 157 PetscInt i,Mx,xs,xm; 158 PetscReal hx,sx; 159 PetscScalar *u,*udot,*f; 160 Vec localU; 161 162 PetscFunctionBeginUser; 163 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 164 ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr); 165 ierr = 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);CHKERRQ(ierr); 166 167 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 168 169 /* 170 Scatter ghost points to local vector,using the 2-step process 171 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 172 By placing code between these two statements, computations can be 173 done while messages are in transition. 174 */ 175 ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr); 176 ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr); 177 178 /* Get pointers to vector data */ 179 ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr); 180 ierr = DMDAVecGetArrayRead(da,Udot,&udot);CHKERRQ(ierr); 181 ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr); 182 183 /* Get local grid boundaries */ 184 ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr); 185 186 /* Compute function over the locally owned part of the grid */ 187 for (i=xs; i<xs+xm; i++) { 188 if (user->boundary == 0) { /* Dirichlet BC */ 189 if (i == 0 || i == Mx-1) f[i] = u[i]; /* F = U */ 190 else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx; 191 } else { /* Neumann BC */ 192 if (i == 0) f[i] = u[0] - u[1]; 193 else if (i == Mx-1) f[i] = u[i] - u[i-1]; 194 else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx; 195 } 196 } 197 198 /* Restore vectors */ 199 ierr = DMDAVecRestoreArrayRead(da,localU,&u);CHKERRQ(ierr); 200 ierr = DMDAVecRestoreArrayRead(da,Udot,&udot);CHKERRQ(ierr); 201 ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr); 202 ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr); 203 PetscFunctionReturn(0); 204 } 205 206 /* --------------------------------------------------------------------- */ 207 /* 208 IJacobian - Compute IJacobian = dF/dU + a dF/dUdot 209 */ 210 PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx) 211 { 212 PetscErrorCode ierr; 213 PetscInt i,rstart,rend,Mx; 214 PetscReal hx,sx; 215 AppCtx *user = (AppCtx*)ctx; 216 DM da; 217 MatStencil col[3],row; 218 PetscInt nc; 219 PetscScalar vals[3]; 220 221 PetscFunctionBeginUser; 222 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 223 ierr = MatGetOwnershipRange(Jpre,&rstart,&rend);CHKERRQ(ierr); 224 ierr = 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);CHKERRQ(ierr); 225 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 226 for (i=rstart; i<rend; i++) { 227 nc = 0; 228 row.i = i; 229 if (user->boundary == 0 && (i == 0 || i == Mx-1)) { 230 col[nc].i = i; vals[nc++] = 1.0; 231 } else if (user->boundary > 0 && i == 0) { /* Left Neumann */ 232 col[nc].i = i; vals[nc++] = 1.0; 233 col[nc].i = i+1; vals[nc++] = -1.0; 234 } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */ 235 col[nc].i = i-1; vals[nc++] = -1.0; 236 col[nc].i = i; vals[nc++] = 1.0; 237 } else { /* Interior */ 238 col[nc].i = i-1; vals[nc++] = -1.0*sx; 239 col[nc].i = i; vals[nc++] = 2.0*sx + a; 240 col[nc].i = i+1; vals[nc++] = -1.0*sx; 241 } 242 ierr = MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES);CHKERRQ(ierr); 243 } 244 245 ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 246 ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 247 if (J != Jpre) { 248 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 249 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 250 } 251 if (user->viewJacobian) { 252 ierr = PetscPrintf(PETSC_COMM_WORLD,"Jpre:\n");CHKERRQ(ierr); 253 ierr = MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 254 } 255 PetscFunctionReturn(0); 256 } 257 258 /* ------------------------------------------------------------------- */ 259 PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ptr) 260 { 261 AppCtx *user=(AppCtx*)ptr; 262 PetscReal c =user->c; 263 DM da; 264 PetscErrorCode ierr; 265 PetscInt i,xs,xm,Mx; 266 PetscScalar *u; 267 PetscReal hx,x,r; 268 269 PetscFunctionBeginUser; 270 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 271 ierr = 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);CHKERRQ(ierr); 272 273 hx = 1.0/(PetscReal)(Mx-1); 274 275 /* Get pointers to vector data */ 276 ierr = DMDAVecGetArray(da,U,&u);CHKERRQ(ierr); 277 278 /* Get local grid boundaries */ 279 ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr); 280 281 /* Compute function over the locally owned part of the grid */ 282 for (i=xs; i<xs+xm; i++) { 283 x = i*hx; 284 r = PetscSqrtReal((x-.5)*(x-.5)); 285 if (r < .125) u[i] = PetscExpReal(c*r*r*r); 286 else u[i] = 0.0; 287 } 288 289 /* Restore vectors */ 290 ierr = DMDAVecRestoreArray(da,U,&u);CHKERRQ(ierr); 291 PetscFunctionReturn(0); 292 } 293 294 /*TEST 295 296 test: 297 requires: !single 298 args: -da_grid_x 40 -ts_max_steps 2 -snes_monitor_short -ksp_monitor_short -ts_monitor 299 300 test: 301 suffix: 2 302 requires: !single 303 args: -da_grid_x 100 -ts_type theta -ts_theta_theta 0.5 304 305 TEST*/ 306 307