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