1 2 static char help[] = "Time-dependent PDE in 2d. Simplified from ex7.c for illustrating how to use TS on a structured domain. \n"; 3 /* 4 u_t = uxx + uyy 5 0 < x < 1, 0 < y < 1; 6 At t=0: u(x,y) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)) < .125 7 u(x,y) = 0.0 if r >= .125 8 9 mpiexec -n 2 ./ex13 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor 10 mpiexec -n 1 ./ex13 -snes_fd_color -ts_monitor_draw_solution 11 mpiexec -n 2 ./ex13 -ts_type sundials -ts_monitor 12 */ 13 14 #include <petscdm.h> 15 #include <petscdmda.h> 16 #include <petscts.h> 17 18 /* 19 User-defined data structures and routines 20 */ 21 typedef struct { 22 PetscReal c; 23 } AppCtx; 24 25 extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*); 26 extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*); 27 extern PetscErrorCode FormInitialSolution(DM,Vec,void*); 28 29 int main(int argc,char **argv) 30 { 31 TS ts; /* nonlinear solver */ 32 Vec u,r; /* solution, residual vector */ 33 Mat J; /* Jacobian matrix */ 34 PetscInt steps; /* iterations for convergence */ 35 PetscErrorCode ierr; 36 DM da; 37 PetscReal ftime,dt; 38 AppCtx user; /* user-defined work context */ 39 40 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 41 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 42 Create distributed array (DMDA) to manage parallel grid and vectors 43 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 44 ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr); 45 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 46 ierr = DMSetUp(da);CHKERRQ(ierr); 47 48 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 49 Extract global vectors from DMDA; 50 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 51 ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr); 52 ierr = VecDuplicate(u,&r);CHKERRQ(ierr); 53 54 /* Initialize user application context */ 55 user.c = -30.0; 56 57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 58 Create timestepping solver context 59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 60 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 61 ierr = TSSetDM(ts,da);CHKERRQ(ierr); 62 ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr); 63 ierr = TSSetRHSFunction(ts,r,RHSFunction,&user);CHKERRQ(ierr); 64 65 /* Set Jacobian */ 66 ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr); 67 ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr); 68 ierr = TSSetRHSJacobian(ts,J,J,RHSJacobian,NULL);CHKERRQ(ierr); 69 70 ftime = 1.0; 71 ierr = TSSetMaxTime(ts,ftime);CHKERRQ(ierr); 72 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 73 74 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 75 Set initial conditions 76 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 77 ierr = FormInitialSolution(da,u,&user);CHKERRQ(ierr); 78 dt = .01; 79 ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr); 80 81 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 82 Set runtime options 83 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 84 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 85 86 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 87 Solve nonlinear system 88 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 89 ierr = TSSolve(ts,u);CHKERRQ(ierr); 90 ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr); 91 ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr); 92 93 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 94 Free work space. 95 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 96 ierr = MatDestroy(&J);CHKERRQ(ierr); 97 ierr = VecDestroy(&u);CHKERRQ(ierr); 98 ierr = VecDestroy(&r);CHKERRQ(ierr); 99 ierr = TSDestroy(&ts);CHKERRQ(ierr); 100 ierr = DMDestroy(&da);CHKERRQ(ierr); 101 102 ierr = PetscFinalize(); 103 return ierr; 104 } 105 /* ------------------------------------------------------------------- */ 106 /* 107 RHSFunction - Evaluates nonlinear function, F(u). 108 109 Input Parameters: 110 . ts - the TS context 111 . U - input vector 112 . ptr - optional user-defined context, as set by TSSetFunction() 113 114 Output Parameter: 115 . F - function vector 116 */ 117 PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr) 118 { 119 /* PETSC_UNUSED AppCtx *user=(AppCtx*)ptr; */ 120 DM da; 121 PetscErrorCode ierr; 122 PetscInt i,j,Mx,My,xs,ys,xm,ym; 123 PetscReal two = 2.0,hx,hy,sx,sy; 124 PetscScalar u,uxx,uyy,**uarray,**f; 125 Vec localU; 126 127 PetscFunctionBeginUser; 128 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 129 ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr); 130 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr); 131 132 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 133 hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy); 134 135 /* 136 Scatter ghost points to local vector,using the 2-step process 137 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 138 By placing code between these two statements, computations can be 139 done while messages are in transition. 140 */ 141 ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr); 142 ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr); 143 144 /* Get pointers to vector data */ 145 ierr = DMDAVecGetArrayRead(da,localU,&uarray);CHKERRQ(ierr); 146 ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr); 147 148 /* Get local grid boundaries */ 149 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 150 151 /* Compute function over the locally owned part of the grid */ 152 for (j=ys; j<ys+ym; j++) { 153 for (i=xs; i<xs+xm; i++) { 154 if (i == 0 || j == 0 || i == Mx-1 || j == My-1) { 155 f[j][i] = uarray[j][i]; 156 continue; 157 } 158 u = uarray[j][i]; 159 uxx = (-two*u + uarray[j][i-1] + uarray[j][i+1])*sx; 160 uyy = (-two*u + uarray[j-1][i] + uarray[j+1][i])*sy; 161 f[j][i] = uxx + uyy; 162 } 163 } 164 165 /* Restore vectors */ 166 ierr = DMDAVecRestoreArrayRead(da,localU,&uarray);CHKERRQ(ierr); 167 ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr); 168 ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr); 169 ierr = PetscLogFlops(11.0*ym*xm);CHKERRQ(ierr); 170 PetscFunctionReturn(0); 171 } 172 173 /* --------------------------------------------------------------------- */ 174 /* 175 RHSJacobian - User-provided routine to compute the Jacobian of 176 the nonlinear right-hand-side function of the ODE. 177 178 Input Parameters: 179 ts - the TS context 180 t - current time 181 U - global input vector 182 dummy - optional user-defined context, as set by TSetRHSJacobian() 183 184 Output Parameters: 185 J - Jacobian matrix 186 Jpre - optionally different preconditioning matrix 187 str - flag indicating matrix structure 188 */ 189 PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat J,Mat Jpre,void *ctx) 190 { 191 PetscErrorCode ierr; 192 DM da; 193 DMDALocalInfo info; 194 PetscInt i,j; 195 PetscReal hx,hy,sx,sy; 196 197 PetscFunctionBeginUser; 198 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 199 ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr); 200 hx = 1.0/(PetscReal)(info.mx-1); sx = 1.0/(hx*hx); 201 hy = 1.0/(PetscReal)(info.my-1); sy = 1.0/(hy*hy); 202 for (j=info.ys; j<info.ys+info.ym; j++) { 203 for (i=info.xs; i<info.xs+info.xm; i++) { 204 PetscInt nc = 0; 205 MatStencil row,col[5]; 206 PetscScalar val[5]; 207 row.i = i; row.j = j; 208 if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) { 209 col[nc].i = i; col[nc].j = j; val[nc++] = 1.0; 210 } else { 211 col[nc].i = i-1; col[nc].j = j; val[nc++] = sx; 212 col[nc].i = i+1; col[nc].j = j; val[nc++] = sx; 213 col[nc].i = i; col[nc].j = j-1; val[nc++] = sy; 214 col[nc].i = i; col[nc].j = j+1; val[nc++] = sy; 215 col[nc].i = i; col[nc].j = j; val[nc++] = -2*sx - 2*sy; 216 } 217 ierr = MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);CHKERRQ(ierr); 218 } 219 } 220 ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 221 ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 222 if (J != Jpre) { 223 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 224 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 225 } 226 PetscFunctionReturn(0); 227 } 228 229 /* ------------------------------------------------------------------- */ 230 PetscErrorCode FormInitialSolution(DM da,Vec U,void* ptr) 231 { 232 AppCtx *user=(AppCtx*)ptr; 233 PetscReal c=user->c; 234 PetscErrorCode ierr; 235 PetscInt i,j,xs,ys,xm,ym,Mx,My; 236 PetscScalar **u; 237 PetscReal hx,hy,x,y,r; 238 239 PetscFunctionBeginUser; 240 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr); 241 242 hx = 1.0/(PetscReal)(Mx-1); 243 hy = 1.0/(PetscReal)(My-1); 244 245 /* Get pointers to vector data */ 246 ierr = DMDAVecGetArray(da,U,&u);CHKERRQ(ierr); 247 248 /* Get local grid boundaries */ 249 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 250 251 /* Compute function over the locally owned part of the grid */ 252 for (j=ys; j<ys+ym; j++) { 253 y = j*hy; 254 for (i=xs; i<xs+xm; i++) { 255 x = i*hx; 256 r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)); 257 if (r < .125) u[j][i] = PetscExpReal(c*r*r*r); 258 else u[j][i] = 0.0; 259 } 260 } 261 262 /* Restore vectors */ 263 ierr = DMDAVecRestoreArray(da,U,&u);CHKERRQ(ierr); 264 PetscFunctionReturn(0); 265 } 266 267 /*TEST 268 269 test: 270 args: -ts_max_steps 5 -ts_monitor 271 272 test: 273 suffix: 2 274 args: -ts_max_steps 5 -ts_monitor 275 276 test: 277 suffix: 3 278 args: -ts_max_steps 5 -snes_fd_color -ts_monitor 279 280 TEST*/ 281