Actual source code: biharmonic2.c
1: static char help[] = "Solves biharmonic equation in 1d.\n";
3: /*
4: Solves the equation biharmonic equation in split form
6: w = -kappa \Delta u
7: u_t = \Delta w
8: -1 <= u <= 1
9: Periodic boundary conditions
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
15: w = -kappa \Delta u + u^3 - u
16: u_t = \Delta w
17: -1 <= u <= 1
18: Periodic boundary conditions
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
24: */
25: #include <petscdm.h>
26: #include <petscdmda.h>
27: #include <petscts.h>
28: #include <petscdraw.h>
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;
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;
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Initialize program
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: PetscFunctionBeginUser;
61: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
62: ctx.kappa = 1.0;
63: PetscCall(PetscOptionsGetReal(NULL, NULL, "-kappa", &ctx.kappa, NULL));
64: ctx.cahnhillard = PETSC_FALSE;
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));
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);
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));
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));
107: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
108: Create matrix data structure; set Jacobian evaluation routine
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
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));
130: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131: Customize nonlinear solver
132: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: PetscCall(TSSetType(ts, TSBEULER));
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Set initial conditions
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: PetscCall(FormInitialSolution(da, x, ctx.kappa));
139: PetscCall(TSSetTimeStep(ts, dt));
140: PetscCall(TSSetSolution(ts, x));
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Set runtime options
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: PetscCall(TSSetFromOptions(ts));
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Solve nonlinear system
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: PetscCall(TSSolve(ts, x));
151: PetscCall(TSGetStepNumber(ts, &steps));
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));
164: PetscCall(PetscFinalize());
165: return 0;
166: }
168: typedef struct {
169: PetscScalar w, u;
170: } Field;
171: /* ------------------------------------------------------------------- */
172: /*
173: FormFunction - Evaluates nonlinear function, F(x).
175: Input Parameters:
176: . ts - the TS context
177: . X - input vector
178: . ptr - optional user-defined context, as set by SNESSetFunction()
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;
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));
198: hx = 1.0 / (PetscReal)Mx;
199: sx = 1.0 / (hx * hx);
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));
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));
219: /*
220: Get local grid boundaries
221: */
222: PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL));
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: }
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: }
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;
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));
269: hx = 1.0 / (PetscReal)Mx;
270: sx = 1.0 / (hx * hx);
272: /*
273: Get pointers to vector data
274: */
275: PetscCall(DMCreateLocalVector(da, &Xg));
276: PetscCall(DMDAVecGetArray(da, Xg, &x));
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));
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;
297: /*
298: Restore vectors
299: */
300: PetscCall(DMDAVecRestoreArray(da, Xg, &x));
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: }
310: /*TEST
312: build:
313: requires: !complex !single
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
319: TEST*/