1 2 static char help[] = "Solves biharmonic equation in 1d.\n"; 3 4 /* 5 Solves the equation biharmonic equation in split form 6 7 w = -kappa \Delta u 8 u_t = \Delta w 9 -1 <= u <= 1 10 Periodic boundary conditions 11 12 Evolve the biharmonic heat equation with bounds: (same as biharmonic) 13 --------------- 14 ./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 15 16 w = -kappa \Delta u + u^3 - u 17 u_t = \Delta w 18 -1 <= u <= 1 19 Periodic boundary conditions 20 21 Evolve the Cahn-Hillard equations: (this fails after a few timesteps 12/17/2017) 22 --------------- 23 ./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 24 25 */ 26 #include <petscdm.h> 27 #include <petscdmda.h> 28 #include <petscts.h> 29 #include <petscdraw.h> 30 31 /* 32 User-defined routines 33 */ 34 extern PetscErrorCode FormFunction(TS, PetscReal, Vec, Vec, Vec, void *), FormInitialSolution(DM, Vec, PetscReal); 35 typedef struct { 36 PetscBool cahnhillard; 37 PetscReal kappa; 38 PetscInt energy; 39 PetscReal tol; 40 PetscReal theta; 41 PetscReal theta_c; 42 } UserCtx; 43 44 int main(int argc, char **argv) 45 { 46 TS ts; /* nonlinear solver */ 47 Vec x, r; /* solution, residual vectors */ 48 Mat J; /* Jacobian matrix */ 49 PetscInt steps, Mx; 50 DM da; 51 MatFDColoring matfdcoloring; 52 ISColoring iscoloring; 53 PetscReal dt; 54 PetscReal vbounds[] = {-100000, 100000, -1.1, 1.1}; 55 SNES snes; 56 UserCtx ctx; 57 58 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 59 Initialize program 60 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 61 PetscFunctionBeginUser; 62 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 63 ctx.kappa = 1.0; 64 PetscCall(PetscOptionsGetReal(NULL, NULL, "-kappa", &ctx.kappa, NULL)); 65 ctx.cahnhillard = PETSC_FALSE; 66 67 PetscCall(PetscOptionsGetBool(NULL, NULL, "-cahn-hillard", &ctx.cahnhillard, NULL)); 68 PetscCall(PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD), 2, vbounds)); 69 PetscCall(PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD), 600, 600)); 70 ctx.energy = 1; 71 /*PetscCall(PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL));*/ 72 PetscCall(PetscOptionsGetInt(NULL, NULL, "-energy", &ctx.energy, NULL)); 73 ctx.tol = 1.0e-8; 74 PetscCall(PetscOptionsGetReal(NULL, NULL, "-tol", &ctx.tol, NULL)); 75 ctx.theta = .001; 76 ctx.theta_c = 1.0; 77 PetscCall(PetscOptionsGetReal(NULL, NULL, "-theta", &ctx.theta, NULL)); 78 PetscCall(PetscOptionsGetReal(NULL, NULL, "-theta_c", &ctx.theta_c, NULL)); 79 80 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 81 Create distributed array (DMDA) to manage parallel grid and vectors 82 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 83 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 10, 2, 2, NULL, &da)); 84 PetscCall(DMSetFromOptions(da)); 85 PetscCall(DMSetUp(da)); 86 PetscCall(DMDASetFieldName(da, 0, "Biharmonic heat equation: w = -kappa*u_xx")); 87 PetscCall(DMDASetFieldName(da, 1, "Biharmonic heat equation: u")); 88 PetscCall(DMDAGetInfo(da, 0, &Mx, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 89 dt = 1.0 / (10. * ctx.kappa * Mx * Mx * Mx * Mx); 90 91 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 92 Extract global vectors from DMDA; then duplicate for remaining 93 vectors that are the same types 94 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 95 PetscCall(DMCreateGlobalVector(da, &x)); 96 PetscCall(VecDuplicate(x, &r)); 97 98 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 99 Create timestepping solver context 100 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 101 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 102 PetscCall(TSSetDM(ts, da)); 103 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 104 PetscCall(TSSetIFunction(ts, NULL, FormFunction, &ctx)); 105 PetscCall(TSSetMaxTime(ts, .02)); 106 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_INTERPOLATE)); 107 108 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 109 Create matrix data structure; set Jacobian evaluation routine 110 111 < Set Jacobian matrix data structure and default Jacobian evaluation 112 routine. User can override with: 113 -snes_mf : matrix-free Newton-Krylov method with no preconditioning 114 (unless user explicitly sets preconditioner) 115 -snes_mf_operator : form preconditioning matrix as set by the user, 116 but use matrix-free approx for Jacobian-vector 117 products within Newton-Krylov method 118 119 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 120 PetscCall(TSGetSNES(ts, &snes)); 121 PetscCall(DMCreateColoring(da, IS_COLORING_GLOBAL, &iscoloring)); 122 PetscCall(DMSetMatType(da, MATAIJ)); 123 PetscCall(DMCreateMatrix(da, &J)); 124 PetscCall(MatFDColoringCreate(J, iscoloring, &matfdcoloring)); 125 PetscCall(MatFDColoringSetFunction(matfdcoloring, (PetscErrorCode(*)(void))SNESTSFormFunction, ts)); 126 PetscCall(MatFDColoringSetFromOptions(matfdcoloring)); 127 PetscCall(MatFDColoringSetUp(J, iscoloring, matfdcoloring)); 128 PetscCall(ISColoringDestroy(&iscoloring)); 129 PetscCall(SNESSetJacobian(snes, J, J, SNESComputeJacobianDefaultColor, matfdcoloring)); 130 131 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 Customize nonlinear solver 133 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 134 PetscCall(TSSetType(ts, TSBEULER)); 135 136 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 137 Set initial conditions 138 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 139 PetscCall(FormInitialSolution(da, x, ctx.kappa)); 140 PetscCall(TSSetTimeStep(ts, dt)); 141 PetscCall(TSSetSolution(ts, x)); 142 143 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 144 Set runtime options 145 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 146 PetscCall(TSSetFromOptions(ts)); 147 148 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 149 Solve nonlinear system 150 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 151 PetscCall(TSSolve(ts, x)); 152 PetscCall(TSGetStepNumber(ts, &steps)); 153 154 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 155 Free work space. All PETSc objects should be destroyed when they 156 are no longer needed. 157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 158 PetscCall(MatDestroy(&J)); 159 PetscCall(MatFDColoringDestroy(&matfdcoloring)); 160 PetscCall(VecDestroy(&x)); 161 PetscCall(VecDestroy(&r)); 162 PetscCall(TSDestroy(&ts)); 163 PetscCall(DMDestroy(&da)); 164 165 PetscCall(PetscFinalize()); 166 return 0; 167 } 168 169 typedef struct { 170 PetscScalar w, u; 171 } Field; 172 /* ------------------------------------------------------------------- */ 173 /* 174 FormFunction - Evaluates nonlinear function, F(x). 175 176 Input Parameters: 177 . ts - the TS context 178 . X - input vector 179 . ptr - optional user-defined context, as set by SNESSetFunction() 180 181 Output Parameter: 182 . F - function vector 183 */ 184 PetscErrorCode FormFunction(TS ts, PetscReal ftime, Vec X, Vec Xdot, Vec F, void *ptr) 185 { 186 DM da; 187 PetscInt i, Mx, xs, xm; 188 PetscReal hx, sx; 189 Field *x, *xdot, *f; 190 Vec localX, localXdot; 191 UserCtx *ctx = (UserCtx *)ptr; 192 193 PetscFunctionBegin; 194 PetscCall(TSGetDM(ts, &da)); 195 PetscCall(DMGetLocalVector(da, &localX)); 196 PetscCall(DMGetLocalVector(da, &localXdot)); 197 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)); 198 199 hx = 1.0 / (PetscReal)Mx; 200 sx = 1.0 / (hx * hx); 201 202 /* 203 Scatter ghost points to local vector,using the 2-step process 204 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 205 By placing code between these two statements, computations can be 206 done while messages are in transition. 207 */ 208 PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX)); 209 PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX)); 210 PetscCall(DMGlobalToLocalBegin(da, Xdot, INSERT_VALUES, localXdot)); 211 PetscCall(DMGlobalToLocalEnd(da, Xdot, INSERT_VALUES, localXdot)); 212 213 /* 214 Get pointers to vector data 215 */ 216 PetscCall(DMDAVecGetArrayRead(da, localX, &x)); 217 PetscCall(DMDAVecGetArrayRead(da, localXdot, &xdot)); 218 PetscCall(DMDAVecGetArray(da, F, &f)); 219 220 /* 221 Get local grid boundaries 222 */ 223 PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL)); 224 225 /* 226 Compute function over the locally owned part of the grid 227 */ 228 for (i = xs; i < xs + xm; i++) { 229 f[i].w = x[i].w + ctx->kappa * (x[i - 1].u + x[i + 1].u - 2.0 * x[i].u) * sx; 230 if (ctx->cahnhillard) { 231 switch (ctx->energy) { 232 case 1: /* double well */ 233 f[i].w += -x[i].u * x[i].u * x[i].u + x[i].u; 234 break; 235 case 2: /* double obstacle */ 236 f[i].w += x[i].u; 237 break; 238 case 3: /* logarithmic */ 239 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; 240 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; 241 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; 242 break; 243 } 244 } 245 f[i].u = xdot[i].u - (x[i - 1].w + x[i + 1].w - 2.0 * x[i].w) * sx; 246 } 247 248 /* 249 Restore vectors 250 */ 251 PetscCall(DMDAVecRestoreArrayRead(da, localXdot, &xdot)); 252 PetscCall(DMDAVecRestoreArrayRead(da, localX, &x)); 253 PetscCall(DMDAVecRestoreArray(da, F, &f)); 254 PetscCall(DMRestoreLocalVector(da, &localX)); 255 PetscCall(DMRestoreLocalVector(da, &localXdot)); 256 PetscFunctionReturn(0); 257 } 258 259 /* ------------------------------------------------------------------- */ 260 PetscErrorCode FormInitialSolution(DM da, Vec X, PetscReal kappa) 261 { 262 PetscInt i, xs, xm, Mx, xgs, xgm; 263 Field *x; 264 PetscReal hx, xx, r, sx; 265 Vec Xg; 266 267 PetscFunctionBegin; 268 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)); 269 270 hx = 1.0 / (PetscReal)Mx; 271 sx = 1.0 / (hx * hx); 272 273 /* 274 Get pointers to vector data 275 */ 276 PetscCall(DMCreateLocalVector(da, &Xg)); 277 PetscCall(DMDAVecGetArray(da, Xg, &x)); 278 279 /* 280 Get local grid boundaries 281 */ 282 PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL)); 283 PetscCall(DMDAGetGhostCorners(da, &xgs, NULL, NULL, &xgm, NULL, NULL)); 284 285 /* 286 Compute u function over the locally owned part of the grid including ghost points 287 */ 288 for (i = xgs; i < xgs + xgm; i++) { 289 xx = i * hx; 290 r = PetscSqrtReal((xx - .5) * (xx - .5)); 291 if (r < .125) x[i].u = 1.0; 292 else x[i].u = -.50; 293 /* fill in x[i].w so that valgrind doesn't detect use of uninitialized memory */ 294 x[i].w = 0; 295 } 296 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; 297 298 /* 299 Restore vectors 300 */ 301 PetscCall(DMDAVecRestoreArray(da, Xg, &x)); 302 303 /* Grab only the global part of the vector */ 304 PetscCall(VecSet(X, 0)); 305 PetscCall(DMLocalToGlobalBegin(da, Xg, ADD_VALUES, X)); 306 PetscCall(DMLocalToGlobalEnd(da, Xg, ADD_VALUES, X)); 307 PetscCall(VecDestroy(&Xg)); 308 PetscFunctionReturn(0); 309 } 310 311 /*TEST 312 313 build: 314 requires: !complex !single 315 316 test: 317 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 50 318 requires: x 319 320 TEST*/ 321