Actual source code: ex1.c

petsc-3.5.4 2015-05-23
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  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_indicate_data_points 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,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: {
108:   PetscScalar    *u,*udot,*f;

111:   /*  The next three lines allow us to access the entries of the vectors directly */
112:   VecGetArray(U,&u);
113:   VecGetArray(Udot,&udot);
114:   VecGetArray(F,&f);
115:   f[0] = udot[0] + ctx->k*u[0]*u[1];
116:   f[1] = udot[1] + ctx->k*u[0]*u[1];
117:   f[2] = udot[2] - ctx->k*u[0]*u[1];
118:   VecRestoreArray(U,&u);
119:   VecRestoreArray(Udot,&udot);
120:   VecRestoreArray(F,&f);
121:   return(0);
122: }

126: /*
127:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
128: */
129: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
130: {
132:   PetscInt       rowcol[] = {0,1,2};
133:   PetscScalar    *u,*udot,J[3][3];

136:   VecGetArray(U,&u);
137:   VecGetArray(Udot,&udot);
138:   J[0][0] = a + ctx->k*u[1];   J[0][1] = ctx->k*u[0];       J[0][2] = 0.0;
139:   J[1][0] = ctx->k*u[1];       J[1][1] = a + ctx->k*u[0];   J[1][2] = 0.0;
140:   J[2][0] = -ctx->k*u[1];      J[2][1] = -ctx->k*u[0];      J[2][2] = a;
141:   MatSetValues(B,3,rowcol,3,rowcol,&J[0][0],INSERT_VALUES);
142:   VecRestoreArray(U,&u);
143:   VecRestoreArray(Udot,&udot);

145:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
146:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
147:   if (A != B) {
148:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
149:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
150:   }
151:   return(0);
152: }

156: /*
157:      Defines the exact (analytic) solution to the ODE
158: */
159: static PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *ctx)
160: {
161:   PetscErrorCode    ierr;
162:   const PetscScalar *uinit;
163:   PetscScalar       *u,d0,q;

166:   VecGetArrayRead(ctx->initialsolution,&uinit);
167:   VecGetArray(U,&u);
168:   d0   = uinit[0] - uinit[1];
169:   if (d0 == 0.0) q = ctx->k*t;
170:   else q = (1.0 - PetscExpScalar(-ctx->k*t*d0))/d0;
171:   u[0] = uinit[0]/(1.0 + uinit[1]*q);
172:   u[1] = u[0] - d0;
173:   u[2] = uinit[1] + uinit[2] - u[1];
174:   VecRestoreArray(U,&u);
175:   VecRestoreArrayRead(ctx->initialsolution,&uinit);
176:   return(0);
177: }

181: int main(int argc,char **argv)
182: {
183:   TS             ts;            /* ODE integrator */
184:   Vec            U;             /* solution will be stored here */
185:   Mat            A;             /* Jacobian matrix */
187:   PetscMPIInt    size;
188:   PetscInt       n = 3;
189:   AppCtx         ctx;
190:   PetscScalar    *u;

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193:      Initialize program
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195:   PetscInitialize(&argc,&argv,(char*)0,help);
196:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
197:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

199:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200:     Create necessary matrix and vectors
201:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202:   MatCreate(PETSC_COMM_WORLD,&A);
203:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
204:   MatSetFromOptions(A);
205:   MatSetUp(A);

207:   MatGetVecs(A,&U,NULL);

209:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
210:     Set runtime options
211:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
212:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options","");
213:   {
214:     ctx.k = .9;
215:     PetscOptionsScalar("-k","Reaction coefficient","",ctx.k,&ctx.k,NULL);
216:     VecDuplicate(U,&ctx.initialsolution);
217:     VecGetArray(ctx.initialsolution,&u);
218:     u[0]  = 1;
219:     u[1]  = .7;
220:     u[2]  = 0;
221:     VecRestoreArray(ctx.initialsolution,&u);
222:     PetscOptionsVec("-initial","Initial values","",ctx.initialsolution,NULL);
223:   }
224:   PetscOptionsEnd();

226:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
227:      Create timestepping solver context
228:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
229:   TSCreate(PETSC_COMM_WORLD,&ts);
230:   TSSetProblemType(ts,TS_NONLINEAR);
231:   TSSetType(ts,TSROSW);
232:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
233:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
234:   TSSetSolutionFunction(ts,(TSSolutionFunction)Solution,&ctx);

236:   {
237:     DM   dm;
238:     void *ptr;
239:     TSGetDM(ts,&dm);
240:     PetscDLSym(NULL,"IFunctionView",&ptr);
241:     PetscDLSym(NULL,"IFunctionLoad",&ptr);
242:     DMTSSetIFunctionSerialize(dm,(PetscErrorCode (*)(void*,PetscViewer))IFunctionView,(PetscErrorCode (*)(void**,PetscViewer))IFunctionLoad);
243:     DMTSSetIJacobianSerialize(dm,(PetscErrorCode (*)(void*,PetscViewer))IFunctionView,(PetscErrorCode (*)(void**,PetscViewer))IFunctionLoad);
244:   }

246:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
247:      Set initial conditions
248:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
249:   Solution(ts,0,U,&ctx);
250:   TSSetSolution(ts,U);

252:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
253:      Set solver options
254:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
255:   TSSetDuration(ts,1000,20.0);
256:   TSSetInitialTimeStep(ts,0.0,.001);
257:   TSSetFromOptions(ts);

259:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
260:      Solve nonlinear system
261:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
262:   TSSolve(ts,U);

264:   TSView(ts,PETSC_VIEWER_BINARY_WORLD);

266:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
267:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
268:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
269:   VecDestroy(&ctx.initialsolution);
270:   MatDestroy(&A);
271:   VecDestroy(&U);
272:   TSDestroy(&ts);

274:   PetscFinalize();
275:   return(0);
276: }