1 static char help[] = "Solves biharmonic equation in 1d.\n"; 2 3 /* 4 Solves the equation biharmonic equation in split form 5 6 w = -kappa \Delta u 7 u_t = \Delta w 8 -1 <= u <= 1 9 Periodic boundary conditions 10 11 Evolve the biharmonic heat equation with bounds: (same as biharmonic) 12 --------------- 13 ./biharmonic2 -ts_monitor -snes_monitor -ts_monitor_draw_solution -pc_type lu -draw_pause .1 -snes_converged_reason -ts_type beuler -da_refine 5 -draw_fields 1 -ts_dt 9.53674e-9 14 15 w = -kappa \Delta u + u^3 - u 16 u_t = \Delta w 17 -1 <= u <= 1 18 Periodic boundary conditions 19 20 Evolve the Cahn-Hillard equations: (this fails after a few timesteps 12/17/2017) 21 --------------- 22 ./biharmonic2 -ts_monitor -snes_monitor -ts_monitor_draw_solution -pc_type lu -draw_pause .1 -snes_converged_reason -ts_type beuler -da_refine 6 -draw_fields 1 -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard 23 24 */ 25 #include <petscdm.h> 26 #include <petscdmda.h> 27 #include <petscts.h> 28 #include <petscdraw.h> 29 30 /* 31 User-defined routines 32 */ 33 extern PetscErrorCode FormFunction(TS, PetscReal, Vec, Vec, Vec, void *), FormInitialSolution(DM, Vec, PetscReal); 34 typedef struct { 35 PetscBool cahnhillard; 36 PetscReal kappa; 37 PetscInt energy; 38 PetscReal tol; 39 PetscReal theta; 40 PetscReal theta_c; 41 } UserCtx; 42 43 int main(int argc, char **argv) 44 { 45 TS ts; /* nonlinear solver */ 46 Vec x, r; /* solution, residual vectors */ 47 Mat J; /* Jacobian matrix */ 48 PetscInt steps, Mx; 49 DM da; 50 MatFDColoring matfdcoloring; 51 ISColoring iscoloring; 52 PetscReal dt; 53 PetscReal vbounds[] = {-100000, 100000, -1.1, 1.1}; 54 SNES snes; 55 UserCtx ctx; 56 57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 58 Initialize program 59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 60 PetscFunctionBeginUser; 61 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 62 ctx.kappa = 1.0; 63 PetscCall(PetscOptionsGetReal(NULL, NULL, "-kappa", &ctx.kappa, NULL)); 64 ctx.cahnhillard = PETSC_FALSE; 65 66 PetscCall(PetscOptionsGetBool(NULL, NULL, "-cahn-hillard", &ctx.cahnhillard, NULL)); 67 PetscCall(PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD), 2, vbounds)); 68 PetscCall(PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD), 600, 600)); 69 ctx.energy = 1; 70 /*PetscCall(PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL));*/ 71 PetscCall(PetscOptionsGetInt(NULL, NULL, "-energy", &ctx.energy, NULL)); 72 ctx.tol = 1.0e-8; 73 PetscCall(PetscOptionsGetReal(NULL, NULL, "-tol", &ctx.tol, NULL)); 74 ctx.theta = .001; 75 ctx.theta_c = 1.0; 76 PetscCall(PetscOptionsGetReal(NULL, NULL, "-theta", &ctx.theta, NULL)); 77 PetscCall(PetscOptionsGetReal(NULL, NULL, "-theta_c", &ctx.theta_c, NULL)); 78 79 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 80 Create distributed array (DMDA) to manage parallel grid and vectors 81 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 82 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 10, 2, 2, NULL, &da)); 83 PetscCall(DMSetFromOptions(da)); 84 PetscCall(DMSetUp(da)); 85 PetscCall(DMDASetFieldName(da, 0, "Biharmonic heat equation: w = -kappa*u_xx")); 86 PetscCall(DMDASetFieldName(da, 1, "Biharmonic heat equation: u")); 87 PetscCall(DMDAGetInfo(da, 0, &Mx, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 88 dt = 1.0 / (10. * ctx.kappa * Mx * Mx * Mx * Mx); 89 90 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 91 Extract global vectors from DMDA; then duplicate for remaining 92 vectors that are the same types 93 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 94 PetscCall(DMCreateGlobalVector(da, &x)); 95 PetscCall(VecDuplicate(x, &r)); 96 97 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 98 Create timestepping solver context 99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 100 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 101 PetscCall(TSSetDM(ts, da)); 102 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 103 PetscCall(TSSetIFunction(ts, NULL, FormFunction, &ctx)); 104 PetscCall(TSSetMaxTime(ts, .02)); 105 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_INTERPOLATE)); 106 107 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 108 Create matrix data structure; set Jacobian evaluation routine 109 110 < Set Jacobian matrix data structure and default Jacobian evaluation 111 routine. User can override with: 112 -snes_mf : matrix-free Newton-Krylov method with no preconditioning 113 (unless user explicitly sets preconditioner) 114 -snes_mf_operator : form preconditioning matrix as set by the user, 115 but use matrix-free approx for Jacobian-vector 116 products within Newton-Krylov method 117 118 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 119 PetscCall(TSGetSNES(ts, &snes)); 120 PetscCall(DMCreateColoring(da, IS_COLORING_GLOBAL, &iscoloring)); 121 PetscCall(DMSetMatType(da, MATAIJ)); 122 PetscCall(DMCreateMatrix(da, &J)); 123 PetscCall(MatFDColoringCreate(J, iscoloring, &matfdcoloring)); 124 PetscCall(MatFDColoringSetFunction(matfdcoloring, (PetscErrorCode(*)(void))SNESTSFormFunction, ts)); 125 PetscCall(MatFDColoringSetFromOptions(matfdcoloring)); 126 PetscCall(MatFDColoringSetUp(J, iscoloring, matfdcoloring)); 127 PetscCall(ISColoringDestroy(&iscoloring)); 128 PetscCall(SNESSetJacobian(snes, J, J, SNESComputeJacobianDefaultColor, matfdcoloring)); 129 130 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 131 Customize nonlinear solver 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 133 PetscCall(TSSetType(ts, TSBEULER)); 134 135 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 136 Set initial conditions 137 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 138 PetscCall(FormInitialSolution(da, x, ctx.kappa)); 139 PetscCall(TSSetTimeStep(ts, dt)); 140 PetscCall(TSSetSolution(ts, x)); 141 142 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 143 Set runtime options 144 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 145 PetscCall(TSSetFromOptions(ts)); 146 147 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 148 Solve nonlinear system 149 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 150 PetscCall(TSSolve(ts, x)); 151 PetscCall(TSGetStepNumber(ts, &steps)); 152 153 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 154 Free work space. All PETSc objects should be destroyed when they 155 are no longer needed. 156 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 157 PetscCall(MatDestroy(&J)); 158 PetscCall(MatFDColoringDestroy(&matfdcoloring)); 159 PetscCall(VecDestroy(&x)); 160 PetscCall(VecDestroy(&r)); 161 PetscCall(TSDestroy(&ts)); 162 PetscCall(DMDestroy(&da)); 163 164 PetscCall(PetscFinalize()); 165 return 0; 166 } 167 168 typedef struct { 169 PetscScalar w, u; 170 } Field; 171 /* ------------------------------------------------------------------- */ 172 /* 173 FormFunction - Evaluates nonlinear function, F(x). 174 175 Input Parameters: 176 . ts - the TS context 177 . X - input vector 178 . ptr - optional user-defined context, as set by SNESSetFunction() 179 180 Output Parameter: 181 . F - function vector 182 */ 183 PetscErrorCode FormFunction(TS ts, PetscReal ftime, Vec X, Vec Xdot, Vec F, void *ptr) 184 { 185 DM da; 186 PetscInt i, Mx, xs, xm; 187 PetscReal hx, sx; 188 Field *x, *xdot, *f; 189 Vec localX, localXdot; 190 UserCtx *ctx = (UserCtx *)ptr; 191 192 PetscFunctionBegin; 193 PetscCall(TSGetDM(ts, &da)); 194 PetscCall(DMGetLocalVector(da, &localX)); 195 PetscCall(DMGetLocalVector(da, &localXdot)); 196 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)); 197 198 hx = 1.0 / (PetscReal)Mx; 199 sx = 1.0 / (hx * hx); 200 201 /* 202 Scatter ghost points to local vector,using the 2-step process 203 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 204 By placing code between these two statements, computations can be 205 done while messages are in transition. 206 */ 207 PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX)); 208 PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX)); 209 PetscCall(DMGlobalToLocalBegin(da, Xdot, INSERT_VALUES, localXdot)); 210 PetscCall(DMGlobalToLocalEnd(da, Xdot, INSERT_VALUES, localXdot)); 211 212 /* 213 Get pointers to vector data 214 */ 215 PetscCall(DMDAVecGetArrayRead(da, localX, &x)); 216 PetscCall(DMDAVecGetArrayRead(da, localXdot, &xdot)); 217 PetscCall(DMDAVecGetArray(da, F, &f)); 218 219 /* 220 Get local grid boundaries 221 */ 222 PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL)); 223 224 /* 225 Compute function over the locally owned part of the grid 226 */ 227 for (i = xs; i < xs + xm; i++) { 228 f[i].w = x[i].w + ctx->kappa * (x[i - 1].u + x[i + 1].u - 2.0 * x[i].u) * sx; 229 if (ctx->cahnhillard) { 230 switch (ctx->energy) { 231 case 1: /* double well */ 232 f[i].w += -x[i].u * x[i].u * x[i].u + x[i].u; 233 break; 234 case 2: /* double obstacle */ 235 f[i].w += x[i].u; 236 break; 237 case 3: /* logarithmic */ 238 if (PetscRealPart(x[i].u) < -1.0 + 2.0 * ctx->tol) f[i].w += .5 * ctx->theta * (-PetscLogReal(ctx->tol) + PetscLogScalar((1.0 - x[i].u) / 2.0)) + ctx->theta_c * x[i].u; 239 else if (PetscRealPart(x[i].u) > 1.0 - 2.0 * ctx->tol) f[i].w += .5 * ctx->theta * (-PetscLogScalar((1.0 + x[i].u) / 2.0) + PetscLogReal(ctx->tol)) + ctx->theta_c * x[i].u; 240 else f[i].w += .5 * ctx->theta * (-PetscLogScalar((1.0 + x[i].u) / 2.0) + PetscLogScalar((1.0 - x[i].u) / 2.0)) + ctx->theta_c * x[i].u; 241 break; 242 } 243 } 244 f[i].u = xdot[i].u - (x[i - 1].w + x[i + 1].w - 2.0 * x[i].w) * sx; 245 } 246 247 /* 248 Restore vectors 249 */ 250 PetscCall(DMDAVecRestoreArrayRead(da, localXdot, &xdot)); 251 PetscCall(DMDAVecRestoreArrayRead(da, localX, &x)); 252 PetscCall(DMDAVecRestoreArray(da, F, &f)); 253 PetscCall(DMRestoreLocalVector(da, &localX)); 254 PetscCall(DMRestoreLocalVector(da, &localXdot)); 255 PetscFunctionReturn(PETSC_SUCCESS); 256 } 257 258 /* ------------------------------------------------------------------- */ 259 PetscErrorCode FormInitialSolution(DM da, Vec X, PetscReal kappa) 260 { 261 PetscInt i, xs, xm, Mx, xgs, xgm; 262 Field *x; 263 PetscReal hx, xx, r, sx; 264 Vec Xg; 265 266 PetscFunctionBegin; 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; 270 sx = 1.0 / (hx * hx); 271 272 /* 273 Get pointers to vector data 274 */ 275 PetscCall(DMCreateLocalVector(da, &Xg)); 276 PetscCall(DMDAVecGetArray(da, Xg, &x)); 277 278 /* 279 Get local grid boundaries 280 */ 281 PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL)); 282 PetscCall(DMDAGetGhostCorners(da, &xgs, NULL, NULL, &xgm, NULL, NULL)); 283 284 /* 285 Compute u function over the locally owned part of the grid including ghost points 286 */ 287 for (i = xgs; i < xgs + xgm; i++) { 288 xx = i * hx; 289 r = PetscSqrtReal((xx - .5) * (xx - .5)); 290 if (r < .125) x[i].u = 1.0; 291 else x[i].u = -.50; 292 /* fill in x[i].w so that valgrind doesn't detect use of uninitialized memory */ 293 x[i].w = 0; 294 } 295 for (i = xs; i < xs + xm; i++) x[i].w = -kappa * (x[i - 1].u + x[i + 1].u - 2.0 * x[i].u) * sx; 296 297 /* 298 Restore vectors 299 */ 300 PetscCall(DMDAVecRestoreArray(da, Xg, &x)); 301 302 /* Grab only the global part of the vector */ 303 PetscCall(VecSet(X, 0)); 304 PetscCall(DMLocalToGlobalBegin(da, Xg, ADD_VALUES, X)); 305 PetscCall(DMLocalToGlobalEnd(da, Xg, ADD_VALUES, X)); 306 PetscCall(VecDestroy(&Xg)); 307 PetscFunctionReturn(PETSC_SUCCESS); 308 } 309 310 /*TEST 311 312 build: 313 requires: !complex !single 314 315 test: 316 args: -ts_monitor -snes_monitor -pc_type lu -snes_converged_reason -ts_type beuler -da_refine 5 -ts_dt 9.53674e-9 -ts_max_steps 50 317 requires: x 318 319 TEST*/ 320