Actual source code: ex5adj.c
1: static char help[] = "Demonstrates adjoint sensitivity analysis for Reaction-Diffusion Equations.\n";
3: /*
4: See ex5.c for details on the equation.
5: This code demonestrates the TSAdjoint interface to a system of time-dependent partial differential equations.
6: It computes the sensitivity of a component in the final solution, which locates in the center of the 2D domain, w.r.t. the initial conditions.
7: The user does not need to provide any additional functions. The required functions in the original simulation are reused in the adjoint run.
9: Runtime options:
10: -forwardonly - run the forward simulation without adjoint
11: -implicitform - provide IFunction and IJacobian to TS, if not set, RHSFunction and RHSJacobian will be used
12: -aijpc - set the preconditioner matrix to be aij (the Jacobian matrix can be of a different type such as ELL)
13: */
14: #include "reaction_diffusion.h"
15: #include <petscdm.h>
16: #include <petscdmda.h>
18: PetscErrorCode InitialConditions(DM, Vec);
20: PetscErrorCode InitializeLambda(DM da, Vec lambda, PetscReal x, PetscReal y)
21: {
22: PetscInt i, j, Mx, My, xs, ys, xm, ym;
23: Field **l;
25: PetscFunctionBegin;
26: 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));
27: /* locate the global i index for x and j index for y */
28: i = (PetscInt)(x * (Mx - 1));
29: j = (PetscInt)(y * (My - 1));
30: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
32: if (xs <= i && i < xs + xm && ys <= j && j < ys + ym) {
33: /* the i,j vertex is on this process */
34: PetscCall(DMDAVecGetArray(da, lambda, &l));
35: l[j][i].u = 1.0;
36: l[j][i].v = 1.0;
37: PetscCall(DMDAVecRestoreArray(da, lambda, &l));
38: }
39: PetscFunctionReturn(PETSC_SUCCESS);
40: }
42: int main(int argc, char **argv)
43: {
44: TS ts; /* ODE integrator */
45: Vec x; /* solution */
46: DM da;
47: AppCtx appctx;
48: Vec lambda[1];
49: PetscBool forwardonly = PETSC_FALSE, implicitform = PETSC_TRUE;
51: PetscFunctionBeginUser;
52: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
53: PetscCall(PetscOptionsGetBool(NULL, NULL, "-forwardonly", &forwardonly, NULL));
54: PetscCall(PetscOptionsGetBool(NULL, NULL, "-implicitform", &implicitform, NULL));
55: appctx.aijpc = PETSC_FALSE;
56: PetscCall(PetscOptionsGetBool(NULL, NULL, "-aijpc", &appctx.aijpc, NULL));
58: appctx.D1 = 8.0e-5;
59: appctx.D2 = 4.0e-5;
60: appctx.gamma = .024;
61: appctx.kappa = .06;
63: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
64: Create distributed array (DMDA) to manage parallel grid and vectors
65: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
66: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC, DMDA_STENCIL_STAR, 64, 64, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, NULL, &da));
67: PetscCall(DMSetFromOptions(da));
68: PetscCall(DMSetUp(da));
69: PetscCall(DMDASetFieldName(da, 0, "u"));
70: PetscCall(DMDASetFieldName(da, 1, "v"));
72: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
73: Extract global vectors from DMDA; then duplicate for remaining
74: vectors that are the same types
75: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
76: PetscCall(DMCreateGlobalVector(da, &x));
78: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
79: Create timestepping solver context
80: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
81: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
82: PetscCall(TSSetDM(ts, da));
83: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
84: PetscCall(TSSetEquationType(ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
85: if (!implicitform) {
86: PetscCall(TSSetType(ts, TSRK));
87: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &appctx));
88: PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSJacobian, &appctx));
89: } else {
90: PetscCall(TSSetType(ts, TSCN));
91: PetscCall(TSSetIFunction(ts, NULL, IFunction, &appctx));
92: if (appctx.aijpc) {
93: Mat A, B;
95: PetscCall(DMSetMatType(da, MATSELL));
96: PetscCall(DMCreateMatrix(da, &A));
97: PetscCall(MatConvert(A, MATAIJ, MAT_INITIAL_MATRIX, &B));
98: /* FIXME do we need to change viewer to display matrix in natural ordering as DMCreateMatrix_DA does? */
99: PetscCall(TSSetIJacobian(ts, A, B, IJacobian, &appctx));
100: PetscCall(MatDestroy(&A));
101: PetscCall(MatDestroy(&B));
102: } else {
103: PetscCall(TSSetIJacobian(ts, NULL, NULL, IJacobian, &appctx));
104: }
105: }
107: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
108: Set initial conditions
109: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
110: PetscCall(InitialConditions(da, x));
111: PetscCall(TSSetSolution(ts, x));
113: /*
114: Have the TS save its trajectory so that TSAdjointSolve() may be used
115: */
116: if (!forwardonly) PetscCall(TSSetSaveTrajectory(ts));
118: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: Set solver options
120: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: PetscCall(TSSetMaxTime(ts, 200.0));
122: PetscCall(TSSetTimeStep(ts, 0.5));
123: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
124: PetscCall(TSSetFromOptions(ts));
126: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127: Solve ODE system
128: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129: PetscCall(TSSolve(ts, x));
130: if (!forwardonly) {
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Start the Adjoint model
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: PetscCall(VecDuplicate(x, &lambda[0]));
135: /* Reset initial conditions for the adjoint integration */
136: PetscCall(InitializeLambda(da, lambda[0], 0.5, 0.5));
137: PetscCall(TSSetCostGradients(ts, 1, lambda, NULL));
138: PetscCall(TSAdjointSolve(ts));
139: PetscCall(VecDestroy(&lambda[0]));
140: }
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Free work space. All PETSc objects should be destroyed when they
143: are no longer needed.
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: PetscCall(VecDestroy(&x));
146: PetscCall(TSDestroy(&ts));
147: PetscCall(DMDestroy(&da));
148: PetscCall(PetscFinalize());
149: return 0;
150: }
152: /* ------------------------------------------------------------------- */
153: PetscErrorCode InitialConditions(DM da, Vec U)
154: {
155: PetscInt i, j, xs, ys, xm, ym, Mx, My;
156: Field **u;
157: PetscReal hx, hy, x, y;
159: PetscFunctionBegin;
160: 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));
162: hx = 2.5 / (PetscReal)Mx;
163: hy = 2.5 / (PetscReal)My;
165: /*
166: Get pointers to vector data
167: */
168: PetscCall(DMDAVecGetArray(da, U, &u));
170: /*
171: Get local grid boundaries
172: */
173: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
175: /*
176: Compute function over the locally owned part of the grid
177: */
178: for (j = ys; j < ys + ym; j++) {
179: y = j * hy;
180: for (i = xs; i < xs + xm; i++) {
181: x = i * hx;
182: if (PetscApproximateGTE(x, 1.0) && PetscApproximateLTE(x, 1.5) && PetscApproximateGTE(y, 1.0) && PetscApproximateLTE(y, 1.5))
183: u[j][i].v = PetscPowReal(PetscSinReal(4.0 * PETSC_PI * x), 2.0) * PetscPowReal(PetscSinReal(4.0 * PETSC_PI * y), 2.0) / 4.0;
184: else u[j][i].v = 0.0;
186: u[j][i].u = 1.0 - 2.0 * u[j][i].v;
187: }
188: }
190: /*
191: Restore vectors
192: */
193: PetscCall(DMDAVecRestoreArray(da, U, &u));
194: PetscFunctionReturn(PETSC_SUCCESS);
195: }
197: /*TEST
199: build:
200: depends: reaction_diffusion.c
201: requires: !complex !single
203: test:
204: args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -da_grid_x 20 -da_grid_y 20
205: output_file: output/ex5adj_1.out
207: test:
208: suffix: 2
209: nsize: 2
210: args: -ts_max_steps 10 -ts_dt 10 -ts_monitor -ts_adjoint_monitor -ksp_monitor_short -da_grid_x 20 -da_grid_y 20 -ts_trajectory_dirname Test-dir -ts_trajectory_file_template test-%06D.cp
212: test:
213: suffix: 3
214: nsize: 2
215: args: -ts_max_steps 10 -ts_dt 10 -ts_adjoint_monitor_draw_sensi
217: test:
218: suffix: 4
219: nsize: 2
220: args: -ts_max_steps 10 -ts_dt 10 -ts_monitor -ts_adjoint_monitor -ksp_monitor_short -da_grid_x 20 -da_grid_y 20 -snes_fd_color
221: output_file: output/ex5adj_2.out
223: test:
224: suffix: 5
225: nsize: 2
226: args: -ts_max_steps 10 -implicitform 0 -ts_type rk -ts_rk_type 4 -ts_monitor -ts_adjoint_monitor -da_grid_x 20 -da_grid_y 20 -snes_fd_color
227: output_file: output/ex5adj_1.out
229: test:
230: suffix: knl
231: args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -ts_trajectory_type memory -ts_trajectory_solution_only 0 -malloc_hbw -ts_trajectory_use_dram 1
232: output_file: output/ex5adj_3.out
233: requires: knl
235: test:
236: suffix: sell
237: nsize: 4
238: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type sell -pc_type none
239: output_file: output/ex5adj_sell_1.out
241: test:
242: suffix: aijsell
243: nsize: 4
244: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type aijsell -pc_type none
245: output_file: output/ex5adj_sell_1.out
247: test:
248: suffix: sell2
249: nsize: 4
250: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type sell -pc_type mg -pc_mg_levels 2 -mg_coarse_pc_type sor
251: output_file: output/ex5adj_sell_2.out
253: test:
254: suffix: aijsell2
255: nsize: 4
256: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type aijsell -pc_type mg -pc_mg_levels 2 -mg_coarse_pc_type sor
257: output_file: output/ex5adj_sell_2.out
259: test:
260: suffix: sell3
261: nsize: 4
262: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type sell -pc_type mg -pc_mg_levels 2 -mg_coarse_pc_type bjacobi -mg_levels_pc_type bjacobi
263: output_file: output/ex5adj_sell_3.out
265: test:
266: suffix: sell4
267: nsize: 4
268: args: -forwardonly -implicitform -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type sell -pc_type mg -pc_mg_levels 2 -mg_coarse_pc_type bjacobi -mg_levels_pc_type bjacobi
269: output_file: output/ex5adj_sell_4.out
271: test:
272: suffix: sell5
273: nsize: 4
274: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type sell -aijpc
275: output_file: output/ex5adj_sell_5.out
277: test:
278: suffix: aijsell5
279: nsize: 4
280: args: -forwardonly -ts_max_steps 10 -ts_monitor -snes_monitor_short -dm_mat_type aijsell
281: output_file: output/ex5adj_sell_5.out
283: test:
284: suffix: sell6
285: args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -ts_trajectory_type memory -ts_trajectory_solution_only 0 -dm_mat_type sell -pc_type jacobi
286: output_file: output/ex5adj_sell_6.out
288: test:
289: suffix: sell7
290: args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -ts_trajectory_type memory -ts_trajectory_solution_only 0 -dm_mat_type sellcuda -dm_vec_type cuda -pc_type jacobi
291: output_file: output/ex5adj_sell_6.out
292: requires: cuda
294: test:
295: suffix: gamg1
296: args: -pc_type gamg -pc_gamg_esteig_ksp_type gmres -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor_short -ts_max_steps 2 -ts_monitor -ts_adjoint_monitor -ts_trajectory_type memory -ksp_rtol 1e-2 -pc_gamg_use_sa_esteig 0
297: output_file: output/ex5adj_gamg.out
299: test:
300: suffix: gamg2
301: args: -pc_type gamg -pc_gamg_esteig_ksp_type gmres -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor_short -ts_max_steps 2 -ts_monitor -ts_adjoint_monitor -ts_trajectory_type memory -ksp_use_explicittranspose -ksp_rtol 1e-2 -pc_gamg_use_sa_esteig 0
302: output_file: output/ex5adj_gamg.out
303: TEST*/