Actual source code: ex1.c

petsc-3.8.4 2018-03-24
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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_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;

 77: PetscErrorCode IFunctionView(AppCtx *ctx,PetscViewer v)
 78: {

 82:   PetscViewerBinaryWrite(v,&ctx->k,1,PETSC_SCALAR,PETSC_FALSE);
 83:   return(0);
 84: }

 86: PetscErrorCode IFunctionLoad(AppCtx **ctx,PetscViewer v)
 87: {

 91:   PetscNew(ctx);
 92:   PetscViewerBinaryRead(v,&(*ctx)->k,1,NULL,PETSC_SCALAR);
 93:   return(0);
 94: }

 96: /*
 97:      Defines the ODE passed to the ODE solver
 98: */
 99: PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
100: {
101:   PetscErrorCode    ierr;
102:   PetscScalar       *f;
103:   const PetscScalar *u,*udot;

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

119: /*
120:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
121: */
122: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
123: {
124:   PetscErrorCode    ierr;
125:   PetscInt          rowcol[] = {0,1,2};
126:   PetscScalar       J[3][3];
127:   const PetscScalar *u,*udot;

130:   VecGetArrayRead(U,&u);
131:   VecGetArrayRead(Udot,&udot);
132:   J[0][0] = a + ctx->k*u[1];   J[0][1] = ctx->k*u[0];       J[0][2] = 0.0;
133:   J[1][0] = ctx->k*u[1];       J[1][1] = a + ctx->k*u[0];   J[1][2] = 0.0;
134:   J[2][0] = -ctx->k*u[1];      J[2][1] = -ctx->k*u[0];      J[2][2] = a;
135:   MatSetValues(B,3,rowcol,3,rowcol,&J[0][0],INSERT_VALUES);
136:   VecRestoreArrayRead(U,&u);
137:   VecRestoreArrayRead(Udot,&udot);

139:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
140:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
141:   if (A != B) {
142:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
143:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
144:   }
145:   return(0);
146: }

148: /*
149:      Defines the exact (analytic) solution to the ODE
150: */
151: static PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *ctx)
152: {
153:   PetscErrorCode    ierr;
154:   const PetscScalar *uinit;
155:   PetscScalar       *u,d0,q;

158:   VecGetArrayRead(ctx->initialsolution,&uinit);
159:   VecGetArray(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:   VecRestoreArray(U,&u);
167:   VecRestoreArrayRead(ctx->initialsolution,&uinit);
168:   return(0);
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 */
177:   PetscMPIInt    size;
178:   PetscInt       n = 3;
179:   AppCtx         ctx;
180:   PetscScalar    *u;
181:   const char     * const names[] = {"U1","U2","U3",NULL};

183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184:      Initialize program
185:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
186:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
187:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
188:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191:     Create necessary matrix and vectors
192:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193:   MatCreate(PETSC_COMM_WORLD,&A);
194:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
195:   MatSetFromOptions(A);
196:   MatSetUp(A);

198:   MatCreateVecs(A,&U,NULL);

200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201:     Set runtime options
202:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
203:   ctx.k = .9;
204:   PetscOptionsGetScalar(NULL,NULL,"-k",&ctx.k,NULL);
205:   VecDuplicate(U,&ctx.initialsolution);
206:   VecGetArray(ctx.initialsolution,&u);
207:   u[0]  = 1;
208:   u[1]  = .7;
209:   u[2]  = 0;
210:   VecRestoreArray(ctx.initialsolution,&u);
211:   PetscOptionsGetVec(NULL,NULL,"-initial",ctx.initialsolution,NULL);

213:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214:      Create timestepping solver context
215:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
216:   TSCreate(PETSC_COMM_WORLD,&ts);
217:   TSSetProblemType(ts,TS_NONLINEAR);
218:   TSSetType(ts,TSROSW);
219:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
220:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
221:   TSSetSolutionFunction(ts,(TSSolutionFunction)Solution,&ctx);

223:   {
224:     DM   dm;
225:     void *ptr;
226:     TSGetDM(ts,&dm);
227:     PetscDLSym(NULL,"IFunctionView",&ptr);
228:     PetscDLSym(NULL,"IFunctionLoad",&ptr);
229:     DMTSSetIFunctionSerialize(dm,(PetscErrorCode (*)(void*,PetscViewer))IFunctionView,(PetscErrorCode (*)(void**,PetscViewer))IFunctionLoad);
230:     DMTSSetIJacobianSerialize(dm,(PetscErrorCode (*)(void*,PetscViewer))IFunctionView,(PetscErrorCode (*)(void**,PetscViewer))IFunctionLoad);
231:   }

233:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234:      Set initial conditions
235:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236:   Solution(ts,0,U,&ctx);
237:   TSSetSolution(ts,U);

239:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240:      Set solver options
241:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
242:   TSSetTimeStep(ts,.001);
243:   TSSetMaxSteps(ts,1000);
244:   TSSetMaxTime(ts,20.0);
245:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
246:   TSSetFromOptions(ts);
247:   TSMonitorLGSetVariableNames(ts,names);

249:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
250:      Solve nonlinear system
251:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
252:   TSSolve(ts,U);

254:   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:   VecDestroy(&ctx.initialsolution);
260:   MatDestroy(&A);
261:   VecDestroy(&U);
262:   TSDestroy(&ts);

264:   PetscFinalize();
265:   return ierr;
266: }