Actual source code: ex1.c
1: static char help[] = "Nonlinear Reaction Problem from Chemistry.\n";
3: /*F
5: This directory contains examples based on the PDES/ODES given in the book
6: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by
7: W. Hundsdorf and J.G. Verwer
9: Page 3, Section 1.1 Nonlinear Reaction Problems from Chemistry
11: \begin{eqnarray}
12: {U_1}_t - k U_1 U_2 & = & 0 \\
13: {U_2}_t - k U_1 U_2 & = & 0 \\
14: {U_3}_t - k U_1 U_2 & = & 0
15: \end{eqnarray}
17: Helpful runtime monitoring options:
18: -ts_view - prints information about the solver being used
19: -ts_monitor - prints the progress of the solver
20: -ts_adapt_monitor - prints the progress of the time-step adaptor
21: -ts_monitor_lg_timestep - plots the size of each timestep (at each time-step)
22: -ts_monitor_lg_solution - plots each component of the solution as a function of time (at each timestep)
23: -ts_monitor_lg_error - plots each component of the error in the solution as a function of time (at each timestep)
24: -draw_pause -2 - hold the plots a the end of the solution process, enter a mouse press in each window to end the process
26: -ts_monitor_lg_timestep -1 - plots the size of each timestep (at the end of the solution process)
27: -ts_monitor_lg_solution -1 - plots each component of the solution as a function of time (at the end of the solution process)
28: -ts_monitor_lg_error -1 - plots each component of the error in the solution as a function of time (at the end of the solution process)
29: -lg_use_markers false - do NOT show the data points on the plots
30: -draw_save - save the timestep and solution plot as a .Gif image file
32: F*/
34: /*
35: Project: Generate a nicely formatted HTML page using
36: 1) the HTML version of the source code and text in this file, use make html to generate the file ex1.c.html
37: 2) the images (Draw_XXX_0_0.Gif Draw_YYY_0_0.Gif Draw_$_1_0.Gif) and
38: 3) the text output (output.txt) generated by running the following commands.
39: 4) <iframe src="generated_topics.html" scrolling="no" frameborder="0" width=600 height=300></iframe>
41: rm -rf *.Gif
42: ./ex1 -ts_monitor_lg_error -1 -ts_monitor_lg_solution -1 -draw_pause -2 -ts_max_steps 100 -ts_monitor_lg_timestep -1 -draw_save -draw_virtual -ts_monitor -ts_adapt_monitor -ts_view > output.txt
44: For example something like
45: <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
46: <html>
47: <head>
48: <meta http-equiv="content-type" content="text/html;charset=utf-8">
49: <title>PETSc Example -- Nonlinear Reaction Problem from Chemistry</title>
50: </head>
51: <body>
52: <iframe src="ex1.c.html" scrolling="yes" frameborder="1" width=2000 height=400></iframe>
53: <img alt="" src="Draw_0x84000000_0_0.Gif"/><img alt="" src="Draw_0x84000001_0_0.Gif"/><img alt="" src="Draw_0x84000001_1_0.Gif"/>
54: <iframe src="output.txt" scrolling="yes" frameborder="1" width=2000 height=1000></iframe>
55: </body>
56: </html>
58: */
60: /*
61: Include "petscts.h" so that we can use the TS ODE integrators. Note that this
62: file automatically includes:
63: petscsys.h - base PETSc routines
64: petscis.h - index sets
65: petscvec.h - vectors
66: petscmat.h - matrices
67: petscpc.h - preconditioners
68: petscksp.h - linear solvers
69: */
71: #include <petscts.h>
73: typedef struct {
74: PetscScalar k;
75: Vec initialsolution;
76: } AppCtx;
78: PetscErrorCode IFunctionView(AppCtx *ctx, PetscViewer v)
79: {
80: PetscFunctionBegin;
81: PetscCall(PetscViewerBinaryWrite(v, &ctx->k, 1, PETSC_SCALAR));
82: PetscFunctionReturn(PETSC_SUCCESS);
83: }
85: PetscErrorCode IFunctionLoad(AppCtx **ctx, PetscViewer v)
86: {
87: PetscFunctionBegin;
88: PetscCall(PetscNew(ctx));
89: PetscCall(PetscViewerBinaryRead(v, &(*ctx)->k, 1, NULL, PETSC_SCALAR));
90: PetscFunctionReturn(PETSC_SUCCESS);
91: }
93: /*
94: Defines the ODE passed to the ODE solver
95: */
96: PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx)
97: {
98: PetscScalar *f;
99: const PetscScalar *u, *udot;
101: PetscFunctionBegin;
102: /* The next three lines allow us to access the entries of the vectors directly */
103: PetscCall(VecGetArrayRead(U, &u));
104: PetscCall(VecGetArrayRead(Udot, &udot));
105: PetscCall(VecGetArrayWrite(F, &f));
106: f[0] = udot[0] + ctx->k * u[0] * u[1];
107: f[1] = udot[1] + ctx->k * u[0] * u[1];
108: f[2] = udot[2] - ctx->k * u[0] * u[1];
109: PetscCall(VecRestoreArrayRead(U, &u));
110: PetscCall(VecRestoreArrayRead(Udot, &udot));
111: PetscCall(VecRestoreArrayWrite(F, &f));
112: PetscFunctionReturn(PETSC_SUCCESS);
113: }
115: /*
116: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
117: */
118: PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx)
119: {
120: PetscInt rowcol[] = {0, 1, 2};
121: PetscScalar J[3][3];
122: const PetscScalar *u, *udot;
124: PetscFunctionBegin;
125: PetscCall(VecGetArrayRead(U, &u));
126: PetscCall(VecGetArrayRead(Udot, &udot));
127: J[0][0] = a + ctx->k * u[1];
128: J[0][1] = ctx->k * u[0];
129: J[0][2] = 0.0;
130: J[1][0] = ctx->k * u[1];
131: J[1][1] = a + ctx->k * u[0];
132: J[1][2] = 0.0;
133: J[2][0] = -ctx->k * u[1];
134: J[2][1] = -ctx->k * u[0];
135: J[2][2] = a;
136: PetscCall(MatSetValues(B, 3, rowcol, 3, rowcol, &J[0][0], INSERT_VALUES));
137: PetscCall(VecRestoreArrayRead(U, &u));
138: PetscCall(VecRestoreArrayRead(Udot, &udot));
140: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
141: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
142: if (A != B) {
143: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
144: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
145: }
146: PetscFunctionReturn(PETSC_SUCCESS);
147: }
149: /*
150: Defines the exact (analytic) solution to the ODE
151: */
152: static PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *ctx)
153: {
154: const PetscScalar *uinit;
155: PetscScalar *u, d0, q;
157: PetscFunctionBegin;
158: PetscCall(VecGetArrayRead(ctx->initialsolution, &uinit));
159: PetscCall(VecGetArrayWrite(U, &u));
160: d0 = uinit[0] - uinit[1];
161: if (d0 == 0.0) q = ctx->k * t;
162: else q = (1.0 - PetscExpScalar(-ctx->k * t * d0)) / d0;
163: u[0] = uinit[0] / (1.0 + uinit[1] * q);
164: u[1] = u[0] - d0;
165: u[2] = uinit[1] + uinit[2] - u[1];
166: PetscCall(VecRestoreArrayWrite(U, &u));
167: PetscCall(VecRestoreArrayRead(ctx->initialsolution, &uinit));
168: PetscFunctionReturn(PETSC_SUCCESS);
169: }
171: int main(int argc, char **argv)
172: {
173: TS ts; /* ODE integrator */
174: Vec U; /* solution will be stored here */
175: Mat A; /* Jacobian matrix */
176: PetscMPIInt size;
177: PetscInt n = 3;
178: AppCtx ctx;
179: PetscScalar *u;
180: const char *const names[] = {"U1", "U2", "U3", NULL};
181: PetscBool mf = PETSC_FALSE;
183: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184: Initialize program
185: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
186: PetscFunctionBeginUser;
187: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
188: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
189: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
191: PetscCall(PetscOptionsGetBool(NULL, NULL, "-snes_mf_operator", &mf, NULL));
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Create necessary matrix and vectors
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
197: PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
198: PetscCall(MatSetFromOptions(A));
199: PetscCall(MatSetUp(A));
201: PetscCall(MatCreateVecs(A, &U, NULL));
203: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: Set runtime options
205: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206: ctx.k = .9;
207: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-k", &ctx.k, NULL));
208: PetscCall(VecDuplicate(U, &ctx.initialsolution));
209: PetscCall(VecGetArrayWrite(ctx.initialsolution, &u));
210: u[0] = 1;
211: u[1] = .7;
212: u[2] = 0;
213: PetscCall(VecRestoreArrayWrite(ctx.initialsolution, &u));
214: PetscCall(PetscOptionsGetVec(NULL, NULL, "-initial", ctx.initialsolution, NULL));
216: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: Create timestepping solver context
218: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
219: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
220: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
221: PetscCall(TSSetType(ts, TSROSW));
222: PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &ctx));
223: if (!mf) PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &ctx));
224: else PetscCall(TSSetIJacobian(ts, NULL, NULL, (TSIJacobianFn *)IJacobian, &ctx));
225: PetscCall(TSSetSolutionFunction(ts, (TSSolutionFn *)Solution, &ctx));
227: {
228: DM dm;
229: void *ptr;
230: PetscCall(TSGetDM(ts, &dm));
231: PetscCall(PetscDLSym(NULL, "IFunctionView", &ptr));
232: PetscCall(PetscDLSym(NULL, "IFunctionLoad", &ptr));
233: PetscCall(DMTSSetIFunctionSerialize(dm, (PetscErrorCode (*)(void *, PetscViewer))IFunctionView, (PetscErrorCode (*)(void **, PetscViewer))IFunctionLoad));
234: PetscCall(DMTSSetIJacobianSerialize(dm, (PetscErrorCode (*)(void *, PetscViewer))IFunctionView, (PetscErrorCode (*)(void **, PetscViewer))IFunctionLoad));
235: }
237: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
238: Set initial conditions
239: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
240: PetscCall(Solution(ts, 0, U, &ctx));
241: PetscCall(TSSetSolution(ts, U));
243: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
244: Set solver options
245: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
246: PetscCall(TSSetTimeStep(ts, .001));
247: PetscCall(TSSetMaxSteps(ts, 1000));
248: PetscCall(TSSetMaxTime(ts, 20.0));
249: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
250: PetscCall(TSSetFromOptions(ts));
251: PetscCall(TSMonitorLGSetVariableNames(ts, names));
253: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
254: Solve nonlinear system
255: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
256: PetscCall(TSSolve(ts, U));
258: PetscCall(TSView(ts, PETSC_VIEWER_BINARY_WORLD));
260: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: Free work space. All PETSc objects should be destroyed when they are no longer needed.
262: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
263: PetscCall(VecDestroy(&ctx.initialsolution));
264: PetscCall(MatDestroy(&A));
265: PetscCall(VecDestroy(&U));
266: PetscCall(TSDestroy(&ts));
268: PetscCall(PetscFinalize());
269: return 0;
270: }
272: /*TEST
274: test:
275: args: -ts_view
276: requires: dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)
278: test:
279: suffix: 2
280: args: -ts_monitor_lg_error -ts_monitor_lg_solution -ts_view
281: requires: x dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)
282: output_file: output/ex1_1.out
284: test:
285: requires: !single
286: suffix: 3
287: args: -ts_view -snes_mf_operator
288: requires: dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)
290: TEST*/