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 TS solvers.  Note that this
     62:    file automatically includes:
     63:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     64:      petscmat.h - matrices
     65:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     66:      petscviewer.h - viewers               petscpc.h  - preconditioners
     67:      petscksp.h   - linear solvers
     68: */

     70: #include <petscts.h>

     72: typedef struct {
     73:   PetscScalar k;
     74:   Vec         initialsolution;
     75: } AppCtx;

     77: PetscErrorCode IFunctionView(AppCtx *ctx, PetscViewer v)
     78: {
     79:   PetscFunctionBegin;
     80:   PetscCall(PetscViewerBinaryWrite(v, &ctx->k, 1, PETSC_SCALAR));
     81:   PetscFunctionReturn(PETSC_SUCCESS);
     82: }

     84: PetscErrorCode IFunctionLoad(AppCtx **ctx, PetscViewer v)
     85: {
     86:   PetscFunctionBegin;
     87:   PetscCall(PetscNew(ctx));
     88:   PetscCall(PetscViewerBinaryRead(v, &(*ctx)->k, 1, NULL, PETSC_SCALAR));
     89:   PetscFunctionReturn(PETSC_SUCCESS);
     90: }

     92: /*
     93:      Defines the ODE passed to the ODE solver
     94: */
     95: PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx)
     96: {
     97:   PetscScalar       *f;
     98:   const PetscScalar *u, *udot;

    100:   PetscFunctionBegin;
    101:   /*  The next three lines allow us to access the entries of the vectors directly */
    102:   PetscCall(VecGetArrayRead(U, &u));
    103:   PetscCall(VecGetArrayRead(Udot, &udot));
    104:   PetscCall(VecGetArrayWrite(F, &f));
    105:   f[0] = udot[0] + ctx->k * u[0] * u[1];
    106:   f[1] = udot[1] + ctx->k * u[0] * u[1];
    107:   f[2] = udot[2] - ctx->k * u[0] * u[1];
    108:   PetscCall(VecRestoreArrayRead(U, &u));
    109:   PetscCall(VecRestoreArrayRead(Udot, &udot));
    110:   PetscCall(VecRestoreArrayWrite(F, &f));
    111:   PetscFunctionReturn(PETSC_SUCCESS);
    112: }

    114: /*
    115:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
    116: */
    117: PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx)
    118: {
    119:   PetscInt           rowcol[] = {0, 1, 2};
    120:   PetscScalar        J[3][3];
    121:   const PetscScalar *u, *udot;

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

    139:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    140:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
    141:   if (A != B) {
    142:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    143:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    144:   }
    145:   PetscFunctionReturn(PETSC_SUCCESS);
    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:   const PetscScalar *uinit;
    154:   PetscScalar       *u, d0, q;

    156:   PetscFunctionBegin;
    157:   PetscCall(VecGetArrayRead(ctx->initialsolution, &uinit));
    158:   PetscCall(VecGetArrayWrite(U, &u));
    159:   d0 = uinit[0] - uinit[1];
    160:   if (d0 == 0.0) q = ctx->k * t;
    161:   else q = (1.0 - PetscExpScalar(-ctx->k * t * d0)) / d0;
    162:   u[0] = uinit[0] / (1.0 + uinit[1] * q);
    163:   u[1] = u[0] - d0;
    164:   u[2] = uinit[1] + uinit[2] - u[1];
    165:   PetscCall(VecRestoreArrayWrite(U, &u));
    166:   PetscCall(VecRestoreArrayRead(ctx->initialsolution, &uinit));
    167:   PetscFunctionReturn(PETSC_SUCCESS);
    168: }

    170: int main(int argc, char **argv)
    171: {
    172:   TS                ts; /* ODE integrator */
    173:   Vec               U;  /* solution will be stored here */
    174:   Mat               A;  /* Jacobian matrix */
    175:   PetscMPIInt       size;
    176:   PetscInt          n = 3;
    177:   AppCtx            ctx;
    178:   PetscScalar      *u;
    179:   const char *const names[] = {"U1", "U2", "U3", NULL};
    180:   PetscBool         mf      = PETSC_FALSE;

    182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    183:      Initialize program
    184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    185:   PetscFunctionBeginUser;
    186:   PetscCall(PetscInitialize(&argc, &argv, NULL, 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:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-snes_mf_operator", &mf, NULL));

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

    200:   PetscCall(MatCreateVecs(A, &U, NULL));

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

    215:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    216:      Create timestepping solver context
    217:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    218:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
    219:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
    220:   PetscCall(TSSetType(ts, TSROSW));
    221:   PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &ctx));
    222:   if (!mf) PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &ctx));
    223:   else PetscCall(TSSetIJacobian(ts, NULL, NULL, (TSIJacobianFn *)IJacobian, &ctx));
    224:   PetscCall(TSSetSolutionFunction(ts, (TSSolutionFn *)Solution, &ctx));

    226:   {
    227:     DM    dm;
    228:     void *ptr;
    229:     PetscCall(TSGetDM(ts, &dm));
    230:     PetscCall(PetscDLSym(NULL, "IFunctionView", &ptr));
    231:     PetscCall(PetscDLSym(NULL, "IFunctionLoad", &ptr));
    232:     PetscCall(DMTSSetIFunctionSerialize(dm, (PetscErrorCode (*)(void *, PetscViewer))IFunctionView, (PetscErrorCode (*)(void **, PetscViewer))IFunctionLoad));
    233:     PetscCall(DMTSSetIJacobianSerialize(dm, (PetscErrorCode (*)(void *, PetscViewer))IFunctionView, (PetscErrorCode (*)(void **, PetscViewer))IFunctionLoad));
    234:   }

    236:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    237:      Set initial conditions
    238:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    239:   PetscCall(Solution(ts, 0, U, &ctx));
    240:   PetscCall(TSSetSolution(ts, U));

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

    252:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    253:      Solve nonlinear system
    254:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    255:   PetscCall(TSSolve(ts, U));

    257:   PetscCall(TSView(ts, PETSC_VIEWER_BINARY_WORLD));

    259:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    260:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    261:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    262:   PetscCall(VecDestroy(&ctx.initialsolution));
    263:   PetscCall(MatDestroy(&A));
    264:   PetscCall(VecDestroy(&U));
    265:   PetscCall(TSDestroy(&ts));

    267:   PetscCall(PetscFinalize());
    268:   return 0;
    269: }

    271: /*TEST

    273:    test:
    274:      args: -ts_view
    275:      requires: dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)

    277:    test:
    278:      suffix: 2
    279:      args: -ts_monitor_lg_error -ts_monitor_lg_solution -ts_view
    280:      requires: x dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)
    281:      output_file: output/ex1_1.out

    283:    test:
    284:      requires: !single
    285:      suffix: 3
    286:      args: -ts_view -snes_mf_operator
    287:      requires: dlsym defined(PETSC_HAVE_DYNAMIC_LIBRARIES)

    289: TEST*/