Actual source code: ex1.c
2: static char help[] = "Nonlinear Reaction Problem from Chemistry.\n";
4: /*F
6: This directory contains examples based on the PDES/ODES given in the book
7: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by
8: W. Hundsdorf and J.G. Verwer
10: Page 3, Section 1.1 Nonlinear Reaction Problems from Chemistry
12: \begin{eqnarray}
13: {U_1}_t - k U_1 U_2 & = & 0 \\
14: {U_2}_t - k U_1 U_2 & = & 0 \\
15: {U_3}_t - k U_1 U_2 & = & 0
16: \end{eqnarray}
18: Helpful runtime monitoring options:
19: -ts_view - prints information about the solver being used
20: -ts_monitor - prints the progress of the solver
21: -ts_adapt_monitor - prints the progress of the time-step adaptor
22: -ts_monitor_lg_timestep - plots the size of each timestep (at each time-step)
23: -ts_monitor_lg_solution - plots each component of the solution as a function of time (at each timestep)
24: -ts_monitor_lg_error - plots each component of the error in the solution as a function of time (at each timestep)
25: -draw_pause -2 - hold the plots a the end of the solution process, enter a mouse press in each window to end the process
27: -ts_monitor_lg_timestep -1 - plots the size of each timestep (at the end of the solution process)
28: -ts_monitor_lg_solution -1 - plots each component of the solution as a function of time (at the end of the solution process)
29: -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)
30: -lg_use_markers false - do NOT show the data points on the plots
31: -draw_save - save the timestep and solution plot as a .Gif image file
33: F*/
35: /*
36: Project: Generate a nicely formatted HTML page using
37: 1) the HTML version of the source code and text in this file, use make html to generate the file ex1.c.html
38: 2) the images (Draw_XXX_0_0.Gif Draw_YYY_0_0.Gif Draw_$_1_0.Gif) and
39: 3) the text output (output.txt) generated by running the following commands.
40: 4) <iframe src="generated_topics.html" scrolling="no" frameborder="0" width=600 height=300></iframe>
42: rm -rf *.Gif
43: ./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
45: For example something like
46: <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
47: <html>
48: <head>
49: <meta http-equiv="content-type" content="text/html;charset=utf-8">
50: <title>PETSc Example -- Nonlinear Reaction Problem from Chemistry</title>
51: </head>
52: <body>
53: <iframe src="ex1.c.html" scrolling="yes" frameborder="1" width=2000 height=400></iframe>
54: <img alt="" src="Draw_0x84000000_0_0.Gif"/><img alt="" src="Draw_0x84000001_0_0.Gif"/><img alt="" src="Draw_0x84000001_1_0.Gif"/>
55: <iframe src="output.txt" scrolling="yes" frameborder="1" width=2000 height=1000></iframe>
56: </body>
57: </html>
59: */
61: /*
62: Include "petscts.h" so that we can use TS solvers. Note that this
63: file automatically includes:
64: petscsys.h - base PETSc routines petscvec.h - vectors
65: petscmat.h - matrices
66: petscis.h - index sets petscksp.h - Krylov subspace methods
67: petscviewer.h - viewers 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};
182: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183: Initialize program
184: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
185: PetscFunctionBeginUser;
186: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
187: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
188: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Create necessary matrix and vectors
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
194: PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
195: PetscCall(MatSetFromOptions(A));
196: PetscCall(MatSetUp(A));
198: PetscCall(MatCreateVecs(A, &U, NULL));
200: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201: Set runtime options
202: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
203: ctx.k = .9;
204: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-k", &ctx.k, NULL));
205: PetscCall(VecDuplicate(U, &ctx.initialsolution));
206: PetscCall(VecGetArrayWrite(ctx.initialsolution, &u));
207: u[0] = 1;
208: u[1] = .7;
209: u[2] = 0;
210: PetscCall(VecRestoreArrayWrite(ctx.initialsolution, &u));
211: PetscCall(PetscOptionsGetVec(NULL, NULL, "-initial", ctx.initialsolution, NULL));
213: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: Create timestepping solver context
215: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
216: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
217: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
218: PetscCall(TSSetType(ts, TSROSW));
219: PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx));
220: PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx));
221: PetscCall(TSSetSolutionFunction(ts, (TSSolutionFunction)Solution, &ctx));
223: {
224: DM dm;
225: void *ptr;
226: PetscCall(TSGetDM(ts, &dm));
227: PetscCall(PetscDLSym(NULL, "IFunctionView", &ptr));
228: PetscCall(PetscDLSym(NULL, "IFunctionLoad", &ptr));
229: PetscCall(DMTSSetIFunctionSerialize(dm, (PetscErrorCode(*)(void *, PetscViewer))IFunctionView, (PetscErrorCode(*)(void **, PetscViewer))IFunctionLoad));
230: PetscCall(DMTSSetIJacobianSerialize(dm, (PetscErrorCode(*)(void *, PetscViewer))IFunctionView, (PetscErrorCode(*)(void **, PetscViewer))IFunctionLoad));
231: }
233: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234: Set initial conditions
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: PetscCall(Solution(ts, 0, U, &ctx));
237: PetscCall(TSSetSolution(ts, U));
239: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240: Set solver options
241: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
242: PetscCall(TSSetTimeStep(ts, .001));
243: PetscCall(TSSetMaxSteps(ts, 1000));
244: PetscCall(TSSetMaxTime(ts, 20.0));
245: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
246: PetscCall(TSSetFromOptions(ts));
247: PetscCall(TSMonitorLGSetVariableNames(ts, names));
249: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
250: Solve nonlinear system
251: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
252: PetscCall(TSSolve(ts, U));
254: PetscCall(TSView(ts, PETSC_VIEWER_BINARY_WORLD));
256: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
257: Free work space. All PETSc objects should be destroyed when they are no longer needed.
258: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
259: PetscCall(VecDestroy(&ctx.initialsolution));
260: PetscCall(MatDestroy(&A));
261: PetscCall(VecDestroy(&U));
262: PetscCall(TSDestroy(&ts));
264: PetscCall(PetscFinalize());
265: return 0;
266: }
268: /*TEST
270: test:
271: args: -ts_view
272: requires: dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)
274: test:
275: suffix: 2
276: args: -ts_monitor_lg_error -ts_monitor_lg_solution -ts_view
277: requires: x dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)
278: output_file: output/ex1_1.out
280: TEST*/