1 2 static char help[] = "Time-dependent PDE in 2d. Modified from ex13.c for illustrating how to solve DAEs. \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 Boundary conditions: 10 Drichlet BC: 11 At x=0, x=1, y=0, y=1: u = 0.0 12 13 Neumann BC: 14 At x=0, x=1: du(x,y,t)/dx = 0 15 At y=0, y=1: du(x,y,t)/dy = 0 16 17 mpiexec -n 2 ./ex15 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor 18 ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -ts_monitor_draw_solution 19 ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -Jtype 2 -nstencilpts 9 20 21 */ 22 23 #include <petscdm.h> 24 #include <petscdmda.h> 25 #include <petscts.h> 26 27 /* 28 User-defined data structures and routines 29 */ 30 31 /* AppCtx: used by FormIFunction() and FormIJacobian() */ 32 typedef struct { 33 DM da; 34 PetscInt nstencilpts; /* number of stencil points: 5 or 9 */ 35 PetscReal c; 36 PetscInt boundary; /* Type of boundary condition */ 37 PetscBool viewJacobian; 38 } AppCtx; 39 40 extern PetscErrorCode FormIFunction(TS, PetscReal, Vec, Vec, Vec, void *); 41 extern PetscErrorCode FormIJacobian(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *); 42 extern PetscErrorCode FormInitialSolution(Vec, void *); 43 44 int main(int argc, char **argv) 45 { 46 TS ts; /* nonlinear solver */ 47 Vec u, r; /* solution, residual vectors */ 48 Mat J, Jmf = NULL; /* Jacobian matrices */ 49 DM da; 50 PetscReal dt; 51 AppCtx user; /* user-defined work context */ 52 SNES snes; 53 PetscInt Jtype; /* Jacobian type 54 0: user provide Jacobian; 55 1: slow finite difference; 56 2: fd with coloring; */ 57 58 PetscFunctionBeginUser; 59 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 60 /* Initialize user application context */ 61 user.da = NULL; 62 user.nstencilpts = 5; 63 user.c = -30.0; 64 user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */ 65 user.viewJacobian = PETSC_FALSE; 66 67 PetscCall(PetscOptionsGetInt(NULL, NULL, "-nstencilpts", &user.nstencilpts, NULL)); 68 PetscCall(PetscOptionsGetInt(NULL, NULL, "-boundary", &user.boundary, NULL)); 69 PetscCall(PetscOptionsHasName(NULL, NULL, "-viewJacobian", &user.viewJacobian)); 70 71 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 72 Create distributed array (DMDA) to manage parallel grid and vectors 73 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 74 if (user.nstencilpts == 5) { 75 PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 11, 11, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &da)); 76 } else if (user.nstencilpts == 9) { 77 PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX, 11, 11, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &da)); 78 } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "nstencilpts %" PetscInt_FMT " is not supported", user.nstencilpts); 79 PetscCall(DMSetFromOptions(da)); 80 PetscCall(DMSetUp(da)); 81 user.da = da; 82 83 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 84 Extract global vectors from DMDA; 85 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 86 PetscCall(DMCreateGlobalVector(da, &u)); 87 PetscCall(VecDuplicate(u, &r)); 88 89 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 90 Create timestepping solver context 91 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 92 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 93 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 94 PetscCall(TSSetType(ts, TSBEULER)); 95 PetscCall(TSSetDM(ts, da)); 96 PetscCall(TSSetIFunction(ts, r, FormIFunction, &user)); 97 PetscCall(TSSetMaxTime(ts, 1.0)); 98 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 99 100 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 101 Set initial conditions 102 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 103 PetscCall(FormInitialSolution(u, &user)); 104 PetscCall(TSSetSolution(ts, u)); 105 dt = .01; 106 PetscCall(TSSetTimeStep(ts, dt)); 107 108 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 109 Set Jacobian evaluation routine 110 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 111 PetscCall(DMSetMatType(da, MATAIJ)); 112 PetscCall(DMCreateMatrix(da, &J)); 113 Jtype = 0; 114 PetscCall(PetscOptionsGetInt(NULL, NULL, "-Jtype", &Jtype, NULL)); 115 if (Jtype == 0) { /* use user provided Jacobian evaluation routine */ 116 PetscCheck(user.nstencilpts == 5, PETSC_COMM_WORLD, PETSC_ERR_SUP, "user Jacobian routine FormIJacobian() does not support nstencilpts=%" PetscInt_FMT, user.nstencilpts); 117 PetscCall(TSSetIJacobian(ts, J, J, FormIJacobian, &user)); 118 } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */ 119 PetscCall(TSGetSNES(ts, &snes)); 120 PetscCall(MatCreateSNESMF(snes, &Jmf)); 121 if (Jtype == 1) { /* slow finite difference J; */ 122 PetscCall(SNESSetJacobian(snes, Jmf, J, SNESComputeJacobianDefault, NULL)); 123 } else if (Jtype == 2) { /* Use coloring to compute finite difference J efficiently */ 124 PetscCall(SNESSetJacobian(snes, Jmf, J, SNESComputeJacobianDefaultColor, 0)); 125 } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Jtype is not supported"); 126 } 127 128 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 129 Sets various TS parameters from user options 130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 131 PetscCall(TSSetFromOptions(ts)); 132 133 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 134 Solve nonlinear system 135 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 136 PetscCall(TSSolve(ts, u)); 137 138 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 139 Free work space. 140 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 141 PetscCall(MatDestroy(&J)); 142 PetscCall(MatDestroy(&Jmf)); 143 PetscCall(VecDestroy(&u)); 144 PetscCall(VecDestroy(&r)); 145 PetscCall(TSDestroy(&ts)); 146 PetscCall(DMDestroy(&da)); 147 148 PetscCall(PetscFinalize()); 149 return 0; 150 } 151 152 /* --------------------------------------------------------------------- */ 153 /* 154 FormIFunction = Udot - RHSFunction 155 */ 156 PetscErrorCode FormIFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx) 157 { 158 AppCtx *user = (AppCtx *)ctx; 159 DM da = (DM)user->da; 160 PetscInt i, j, Mx, My, xs, ys, xm, ym; 161 PetscReal hx, hy, sx, sy; 162 PetscScalar u, uxx, uyy, **uarray, **f, **udot; 163 Vec localU; 164 165 PetscFunctionBeginUser; 166 PetscCall(DMGetLocalVector(da, &localU)); 167 PetscCall(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)); 168 169 hx = 1.0 / (PetscReal)(Mx - 1); 170 sx = 1.0 / (hx * hx); 171 hy = 1.0 / (PetscReal)(My - 1); 172 sy = 1.0 / (hy * hy); 173 PetscCheck(user->nstencilpts != 9 || hx == hy, PETSC_COMM_WORLD, PETSC_ERR_SUP, "hx must equal hy when nstencilpts = 9 for this example"); 174 175 /* 176 Scatter ghost points to local vector,using the 2-step process 177 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 178 By placing code between these two statements, computations can be 179 done while messages are in transition. 180 */ 181 PetscCall(DMGlobalToLocalBegin(da, U, INSERT_VALUES, localU)); 182 PetscCall(DMGlobalToLocalEnd(da, U, INSERT_VALUES, localU)); 183 184 /* Get pointers to vector data */ 185 PetscCall(DMDAVecGetArrayRead(da, localU, &uarray)); 186 PetscCall(DMDAVecGetArray(da, F, &f)); 187 PetscCall(DMDAVecGetArray(da, Udot, &udot)); 188 189 /* Get local grid boundaries */ 190 PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL)); 191 192 /* Compute function over the locally owned part of the grid */ 193 for (j = ys; j < ys + ym; j++) { 194 for (i = xs; i < xs + xm; i++) { 195 /* Boundary conditions */ 196 if (i == 0 || j == 0 || i == Mx - 1 || j == My - 1) { 197 if (user->boundary == 0) { /* Drichlet BC */ 198 f[j][i] = uarray[j][i]; /* F = U */ 199 } else { /* Neumann BC */ 200 if (i == 0 && j == 0) { /* SW corner */ 201 f[j][i] = uarray[j][i] - uarray[j + 1][i + 1]; 202 } else if (i == Mx - 1 && j == 0) { /* SE corner */ 203 f[j][i] = uarray[j][i] - uarray[j + 1][i - 1]; 204 } else if (i == 0 && j == My - 1) { /* NW corner */ 205 f[j][i] = uarray[j][i] - uarray[j - 1][i + 1]; 206 } else if (i == Mx - 1 && j == My - 1) { /* NE corner */ 207 f[j][i] = uarray[j][i] - uarray[j - 1][i - 1]; 208 } else if (i == 0) { /* Left */ 209 f[j][i] = uarray[j][i] - uarray[j][i + 1]; 210 } else if (i == Mx - 1) { /* Right */ 211 f[j][i] = uarray[j][i] - uarray[j][i - 1]; 212 } else if (j == 0) { /* Bottom */ 213 f[j][i] = uarray[j][i] - uarray[j + 1][i]; 214 } else if (j == My - 1) { /* Top */ 215 f[j][i] = uarray[j][i] - uarray[j - 1][i]; 216 } 217 } 218 } else { /* Interior */ 219 u = uarray[j][i]; 220 /* 5-point stencil */ 221 uxx = (-2.0 * u + uarray[j][i - 1] + uarray[j][i + 1]); 222 uyy = (-2.0 * u + uarray[j - 1][i] + uarray[j + 1][i]); 223 if (user->nstencilpts == 9) { 224 /* 9-point stencil: assume hx=hy */ 225 uxx = 2.0 * uxx / 3.0 + (0.5 * (uarray[j - 1][i - 1] + uarray[j - 1][i + 1] + uarray[j + 1][i - 1] + uarray[j + 1][i + 1]) - 2.0 * u) / 6.0; 226 uyy = 2.0 * uyy / 3.0 + (0.5 * (uarray[j - 1][i - 1] + uarray[j - 1][i + 1] + uarray[j + 1][i - 1] + uarray[j + 1][i + 1]) - 2.0 * u) / 6.0; 227 } 228 f[j][i] = udot[j][i] - (uxx * sx + uyy * sy); 229 } 230 } 231 } 232 233 /* Restore vectors */ 234 PetscCall(DMDAVecRestoreArrayRead(da, localU, &uarray)); 235 PetscCall(DMDAVecRestoreArray(da, F, &f)); 236 PetscCall(DMDAVecRestoreArray(da, Udot, &udot)); 237 PetscCall(DMRestoreLocalVector(da, &localU)); 238 PetscCall(PetscLogFlops(11.0 * ym * xm)); 239 PetscFunctionReturn(0); 240 } 241 242 /* --------------------------------------------------------------------- */ 243 /* 244 FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot 245 This routine is not used with option '-use_coloring' 246 */ 247 PetscErrorCode FormIJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat J, Mat Jpre, void *ctx) 248 { 249 PetscInt i, j, Mx, My, xs, ys, xm, ym, nc; 250 AppCtx *user = (AppCtx *)ctx; 251 DM da = (DM)user->da; 252 MatStencil col[5], row; 253 PetscScalar vals[5], hx, hy, sx, sy; 254 255 PetscFunctionBeginUser; 256 PetscCall(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)); 257 PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL)); 258 259 hx = 1.0 / (PetscReal)(Mx - 1); 260 sx = 1.0 / (hx * hx); 261 hy = 1.0 / (PetscReal)(My - 1); 262 sy = 1.0 / (hy * hy); 263 264 for (j = ys; j < ys + ym; j++) { 265 for (i = xs; i < xs + xm; i++) { 266 nc = 0; 267 row.j = j; 268 row.i = i; 269 if (user->boundary == 0 && (i == 0 || i == Mx - 1 || j == 0 || j == My - 1)) { 270 col[nc].j = j; 271 col[nc].i = i; 272 vals[nc++] = 1.0; 273 274 } else if (user->boundary > 0 && i == 0) { /* Left Neumann */ 275 col[nc].j = j; 276 col[nc].i = i; 277 vals[nc++] = 1.0; 278 col[nc].j = j; 279 col[nc].i = i + 1; 280 vals[nc++] = -1.0; 281 } else if (user->boundary > 0 && i == Mx - 1) { /* Right Neumann */ 282 col[nc].j = j; 283 col[nc].i = i; 284 vals[nc++] = 1.0; 285 col[nc].j = j; 286 col[nc].i = i - 1; 287 vals[nc++] = -1.0; 288 } else if (user->boundary > 0 && j == 0) { /* Bottom Neumann */ 289 col[nc].j = j; 290 col[nc].i = i; 291 vals[nc++] = 1.0; 292 col[nc].j = j + 1; 293 col[nc].i = i; 294 vals[nc++] = -1.0; 295 } else if (user->boundary > 0 && j == My - 1) { /* Top Neumann */ 296 col[nc].j = j; 297 col[nc].i = i; 298 vals[nc++] = 1.0; 299 col[nc].j = j - 1; 300 col[nc].i = i; 301 vals[nc++] = -1.0; 302 } else { /* Interior */ 303 col[nc].j = j - 1; 304 col[nc].i = i; 305 vals[nc++] = -sy; 306 col[nc].j = j; 307 col[nc].i = i - 1; 308 vals[nc++] = -sx; 309 col[nc].j = j; 310 col[nc].i = i; 311 vals[nc++] = 2.0 * (sx + sy) + a; 312 col[nc].j = j; 313 col[nc].i = i + 1; 314 vals[nc++] = -sx; 315 col[nc].j = j + 1; 316 col[nc].i = i; 317 vals[nc++] = -sy; 318 } 319 PetscCall(MatSetValuesStencil(Jpre, 1, &row, nc, col, vals, INSERT_VALUES)); 320 } 321 } 322 PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY)); 323 PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY)); 324 if (J != Jpre) { 325 PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); 326 PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); 327 } 328 329 if (user->viewJacobian) { 330 PetscCall(PetscPrintf(PetscObjectComm((PetscObject)Jpre), "Jpre:\n")); 331 PetscCall(MatView(Jpre, PETSC_VIEWER_STDOUT_WORLD)); 332 } 333 PetscFunctionReturn(0); 334 } 335 336 /* ------------------------------------------------------------------- */ 337 PetscErrorCode FormInitialSolution(Vec U, void *ptr) 338 { 339 AppCtx *user = (AppCtx *)ptr; 340 DM da = user->da; 341 PetscReal c = user->c; 342 PetscInt i, j, xs, ys, xm, ym, Mx, My; 343 PetscScalar **u; 344 PetscReal hx, hy, x, y, r; 345 346 PetscFunctionBeginUser; 347 PetscCall(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)); 348 349 hx = 1.0 / (PetscReal)(Mx - 1); 350 hy = 1.0 / (PetscReal)(My - 1); 351 352 /* Get pointers to vector data */ 353 PetscCall(DMDAVecGetArray(da, U, &u)); 354 355 /* Get local grid boundaries */ 356 PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL)); 357 358 /* Compute function over the locally owned part of the grid */ 359 for (j = ys; j < ys + ym; j++) { 360 y = j * hy; 361 for (i = xs; i < xs + xm; i++) { 362 x = i * hx; 363 r = PetscSqrtReal((x - .5) * (x - .5) + (y - .5) * (y - .5)); 364 if (r < .125) u[j][i] = PetscExpReal(c * r * r * r); 365 else u[j][i] = 0.0; 366 } 367 } 368 369 /* Restore vectors */ 370 PetscCall(DMDAVecRestoreArray(da, U, &u)); 371 PetscFunctionReturn(0); 372 } 373 374 /*TEST 375 376 test: 377 args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -ts_monitor 378 379 test: 380 suffix: 2 381 args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 2 -ts_monitor 382 383 test: 384 suffix: 3 385 requires: !single 386 args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor 387 388 test: 389 suffix: 4 390 requires: !single 391 nsize: 2 392 args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor 393 394 test: 395 suffix: 5 396 nsize: 1 397 args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 1 -ts_monitor 398 399 TEST*/ 400