Actual source code: ex1.c
petsc-3.7.5 2017-01-01
2: static char help[] = "Nonlinear Reaction Problem from Chemistry.\n" ;
This directory contains examples based on the PDES/ODES given in the book
Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by
W. Hundsdorf and J.G. Verwer
Page 3, Section 1.1 Nonlinear Reaction Problems from Chemistry
\begin{eqnarray}
{U_1}_t - k U_1 U_2 & = & 0 \\
{U_2}_t - k U_1 U_2 & = & 0 \\
{U_3}_t - k U_1 U_2 & = & 0
\end{eqnarray}
Helpful runtime monitoring options:
-ts_view - prints information about the solver being used
-ts_monitor - prints the progess of the solver
-ts_adapt_monitor - prints the progress of the time-step adaptor
-ts_monitor_lg_timestep - plots the size of each timestep (at each time-step)
-ts_monitor_lg_solution - plots each component of the solution as a function of time (at each timestep)
-ts_monitor_lg_error - plots each component of the error in the solution as a function of time (at each timestep)
-draw_pause -2 - hold the plots a the end of the solution process, enter a mouse press in each window to end the process
-ts_monitor_lg_timestep -1 - plots the size of each timestep (at the end of the solution process)
-ts_monitor_lg_solution -1 - plots each component of the solution as a function of time (at the end of the solution process)
-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)
-lg_use_markers false - do NOT show the data points on the plots
-draw_save - save the timestep and solution plot as a .Gif image file
35: /*
36: Project: Generate a nicely formated 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_ZZZ_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: */
70: #include <petscts.h>
72: typedef struct {
73: PetscScalar k;
74: Vec initialsolution;
75: } AppCtx;
79: PetscErrorCode IFunctionView(AppCtx *ctx,PetscViewer v)
80: {
84: PetscViewerBinaryWrite (v,&ctx->k,1,PETSC_SCALAR,PETSC_FALSE );
85: return (0);
86: }
90: PetscErrorCode IFunctionLoad(AppCtx **ctx,PetscViewer v)
91: {
95: PetscMalloc (sizeof (AppCtx),ctx);
96: PetscViewerBinaryRead (v,&(*ctx)->k,1,NULL,PETSC_SCALAR);
97: return (0);
98: }
102: /*
103: Defines the ODE passed to the ODE solver
104: */
105: PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
106: {
107: PetscErrorCode ierr;
108: PetscScalar *f;
109: const PetscScalar *u,*udot;
112: /* The next three lines allow us to access the entries of the vectors directly */
113: VecGetArrayRead (U,&u);
114: VecGetArrayRead (Udot,&udot);
115: VecGetArray (F,&f);
116: f[0] = udot[0] + ctx->k*u[0]*u[1];
117: f[1] = udot[1] + ctx->k*u[0]*u[1];
118: f[2] = udot[2] - ctx->k*u[0]*u[1];
119: VecRestoreArrayRead (U,&u);
120: VecRestoreArrayRead (Udot,&udot);
121: VecRestoreArray (F,&f);
122: return (0);
123: }
127: /*
128: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
129: */
130: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
131: {
132: PetscErrorCode ierr;
133: PetscInt rowcol[] = {0,1,2};
134: PetscScalar J[3][3];
135: const PetscScalar *u,*udot;
138: VecGetArrayRead (U,&u);
139: VecGetArrayRead (Udot,&udot);
140: J[0][0] = a + ctx->k*u[1]; J[0][1] = ctx->k*u[0]; J[0][2] = 0.0;
141: J[1][0] = ctx->k*u[1]; J[1][1] = a + ctx->k*u[0]; J[1][2] = 0.0;
142: J[2][0] = -ctx->k*u[1]; J[2][1] = -ctx->k*u[0]; J[2][2] = a;
143: MatSetValues (B,3,rowcol,3,rowcol,&J[0][0],INSERT_VALUES );
144: VecRestoreArrayRead (U,&u);
145: VecRestoreArrayRead (Udot,&udot);
147: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY);
148: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY);
149: if (A != B) {
150: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
151: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
152: }
153: return (0);
154: }
158: /*
159: Defines the exact (analytic) solution to the ODE
160: */
161: static PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *ctx)
162: {
163: PetscErrorCode ierr;
164: const PetscScalar *uinit;
165: PetscScalar *u,d0,q;
168: VecGetArrayRead (ctx->initialsolution,&uinit);
169: VecGetArray (U,&u);
170: d0 = uinit[0] - uinit[1];
171: if (d0 == 0.0) q = ctx->k*t;
172: else q = (1.0 - PetscExpScalar(-ctx->k*t*d0))/d0;
173: u[0] = uinit[0]/(1.0 + uinit[1]*q);
174: u[1] = u[0] - d0;
175: u[2] = uinit[1] + uinit[2] - u[1];
176: VecRestoreArray (U,&u);
177: VecRestoreArrayRead (ctx->initialsolution,&uinit);
178: return (0);
179: }
183: int main(int argc,char **argv)
184: {
185: TS ts; /* ODE integrator */
186: Vec U; /* solution will be stored here */
187: Mat A; /* Jacobian matrix */
189: PetscMPIInt size;
190: PetscInt n = 3;
191: AppCtx ctx;
192: PetscScalar *u;
193: const char * const names[] = {"U1" ,"U2" ,"U3" ,NULL};
195: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: Initialize program
197: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198: PetscInitialize (&argc,&argv,(char*)0,help);
199: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
200: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
202: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: Create necessary matrix and vectors
204: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205: MatCreate (PETSC_COMM_WORLD ,&A);
206: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
207: MatSetFromOptions (A);
208: MatSetUp (A);
210: MatCreateVecs (A,&U,NULL);
212: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: Set runtime options
214: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
215: ctx.k = .9;
216: PetscOptionsGetScalar (NULL,NULL,"-k" ,&ctx.k,NULL);
217: VecDuplicate (U,&ctx.initialsolution);
218: VecGetArray (ctx.initialsolution,&u);
219: u[0] = 1;
220: u[1] = .7;
221: u[2] = 0;
222: VecRestoreArray (ctx.initialsolution,&u);
223: PetscOptionsGetVec(NULL,NULL,"-initial" ,ctx.initialsolution,NULL);
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Create timestepping solver context
227: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
228: TSCreate (PETSC_COMM_WORLD ,&ts);
229: TSSetProblemType (ts,TS_NONLINEAR);
230: TSSetType (ts,TSROSW );
231: TSSetIFunction (ts,NULL,(TSIFunction) IFunction,&ctx);
232: TSSetIJacobian (ts,A,A,(TSIJacobian)IJacobian,&ctx);
233: TSSetSolutionFunction (ts,(TSSolutionFunction)Solution,&ctx);
235: {
236: DM dm;
237: void *ptr;
238: TSGetDM (ts,&dm);
239: PetscDLSym (NULL,"IFunctionView" ,&ptr);
240: PetscDLSym (NULL,"IFunctionLoad" ,&ptr);
241: DMTSSetIFunctionSerialize (dm,(PetscErrorCode (*)(void*,PetscViewer ))IFunctionView,(PetscErrorCode (*)(void**,PetscViewer ))IFunctionLoad);
242: DMTSSetIJacobianSerialize (dm,(PetscErrorCode (*)(void*,PetscViewer ))IFunctionView,(PetscErrorCode (*)(void**,PetscViewer ))IFunctionLoad);
243: }
245: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
246: Set initial conditions
247: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
248: Solution(ts,0,U,&ctx);
249: TSSetSolution (ts,U);
251: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
252: Set solver options
253: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
254: TSSetDuration (ts,1000,20.0);
255: TSSetInitialTimeStep (ts,0.0,.001);
256: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_STEPOVER);
257: TSSetFromOptions (ts);
258: TSMonitorLGSetVariableNames (ts,names);
260: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: Solve nonlinear system
262: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
263: TSSolve (ts,U);
265: TSView (ts,PETSC_VIEWER_BINARY_WORLD );
267: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
268: Free work space. All PETSc objects should be destroyed when they are no longer needed.
269: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
270: VecDestroy (&ctx.initialsolution);
271: MatDestroy (&A);
272: VecDestroy (&U);
273: TSDestroy (&ts);
275: PetscFinalize ();
276: return (0);
277: }