Actual source code: ex2.c


  2: static char help[] = "Reaction Equation from Chemistry\n";

  4: /*

  6:      Page 6, An example from Atomospheric Chemistry

  8:                  u_1_t =
  9:                  u_2_t =
 10:                  u_3_t =
 11:                  u_4_t =

 13:   -ts_monitor_lg_error -ts_monitor_lg_solution  -ts_view -ts_max_time 2.e4

 15: */

 17: /*
 18:    Include "petscts.h" so that we can use TS solvers.  Note that this
 19:    file automatically includes:
 20:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 21:      petscmat.h - matrices
 22:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 23:      petscviewer.h - viewers               petscpc.h  - preconditioners
 24:      petscksp.h   - linear solvers
 25: */

 27: #include <petscts.h>

 29: typedef struct {
 30:   PetscScalar k1, k2, k3;
 31:   PetscScalar sigma2;
 32:   Vec         initialsolution;
 33: } AppCtx;

 35: PetscScalar k1(AppCtx *ctx, PetscReal t)
 36: {
 37:   PetscReal th    = t / 3600.0;
 38:   PetscReal barth = th - 24.0 * PetscFloorReal(th / 24.0);
 39:   if (((((PetscInt)th) % 24) < 4) || ((((PetscInt)th) % 24) >= 20)) return (1.0e-40);
 40:   else return (ctx->k1 * PetscExpReal(7.0 * PetscPowReal(PetscSinReal(.0625 * PETSC_PI * (barth - 4.0)), .2)));
 41: }

 43: static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx)
 44: {
 45:   PetscScalar       *f;
 46:   const PetscScalar *u, *udot;

 48:   VecGetArrayRead(U, &u);
 49:   VecGetArrayRead(Udot, &udot);
 50:   VecGetArrayWrite(F, &f);
 51:   f[0] = udot[0] - k1(ctx, t) * u[2] + ctx->k2 * u[0];
 52:   f[1] = udot[1] - k1(ctx, t) * u[2] + ctx->k3 * u[1] * u[3] - ctx->sigma2;
 53:   f[2] = udot[2] - ctx->k3 * u[1] * u[3] + k1(ctx, t) * u[2];
 54:   f[3] = udot[3] - ctx->k2 * u[0] + ctx->k3 * u[1] * u[3];
 55:   VecRestoreArrayRead(U, &u);
 56:   VecRestoreArrayRead(Udot, &udot);
 57:   VecRestoreArrayWrite(F, &f);
 58:   return 0;
 59: }

 61: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx)
 62: {
 63:   PetscInt           rowcol[] = {0, 1, 2, 3};
 64:   PetscScalar        J[4][4];
 65:   const PetscScalar *u, *udot;

 67:   VecGetArrayRead(U, &u);
 68:   VecGetArrayRead(Udot, &udot);
 69:   J[0][0] = a + ctx->k2;
 70:   J[0][1] = 0.0;
 71:   J[0][2] = -k1(ctx, t);
 72:   J[0][3] = 0.0;
 73:   J[1][0] = 0.0;
 74:   J[1][1] = a + ctx->k3 * u[3];
 75:   J[1][2] = -k1(ctx, t);
 76:   J[1][3] = ctx->k3 * u[1];
 77:   J[2][0] = 0.0;
 78:   J[2][1] = -ctx->k3 * u[3];
 79:   J[2][2] = a + k1(ctx, t);
 80:   J[2][3] = -ctx->k3 * u[1];
 81:   J[3][0] = -ctx->k2;
 82:   J[3][1] = ctx->k3 * u[3];
 83:   J[3][2] = 0.0;
 84:   J[3][3] = a + ctx->k3 * u[1];
 85:   MatSetValues(B, 4, rowcol, 4, rowcol, &J[0][0], INSERT_VALUES);
 86:   VecRestoreArrayRead(U, &u);
 87:   VecRestoreArrayRead(Udot, &udot);

 89:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
 90:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
 91:   if (A != B) {
 92:     MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
 93:     MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
 94:   }
 95:   return 0;
 96: }

 98: static PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *ctx)
 99: {
100:   VecCopy(ctx->initialsolution, U);
102:   return 0;
103: }

105: int main(int argc, char **argv)
106: {
107:   TS           ts; /* ODE integrator */
108:   Vec          U;  /* solution */
109:   Mat          A;  /* Jacobian matrix */
110:   PetscMPIInt  size;
111:   PetscInt     n = 4;
112:   AppCtx       ctx;
113:   PetscScalar *u;

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:      Initialize program
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119:   PetscInitialize(&argc, &argv, (char *)0, help);
120:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124:     Create necessary matrix and vectors
125:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126:   MatCreate(PETSC_COMM_WORLD, &A);
127:   MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
128:   MatSetFromOptions(A);
129:   MatSetUp(A);

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

133:   ctx.k1     = 1.0e-5;
134:   ctx.k2     = 1.0e5;
135:   ctx.k3     = 1.0e-16;
136:   ctx.sigma2 = 1.0e6;

138:   VecDuplicate(U, &ctx.initialsolution);
139:   VecGetArrayWrite(ctx.initialsolution, &u);
140:   u[0] = 0.0;
141:   u[1] = 1.3e8;
142:   u[2] = 5.0e11;
143:   u[3] = 8.0e11;
144:   VecRestoreArrayWrite(ctx.initialsolution, &u);

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:      Create timestepping solver context
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149:   TSCreate(PETSC_COMM_WORLD, &ts);
150:   TSSetProblemType(ts, TS_NONLINEAR);
151:   TSSetType(ts, TSROSW);
152:   TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx);
153:   TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx);

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:      Set initial conditions
157:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158:   Solution(ts, 0, U, &ctx);
159:   TSSetTime(ts, 4.0 * 3600);
160:   TSSetTimeStep(ts, 1.0);
161:   TSSetSolution(ts, U);

163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164:      Set solver options
165:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166:   TSSetMaxTime(ts, 518400.0);
167:   TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
168:   TSSetMaxStepRejections(ts, 100);
169:   TSSetMaxSNESFailures(ts, -1); /* unlimited */
170:   TSSetFromOptions(ts);

172:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173:      Solve nonlinear system
174:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
175:   TSSolve(ts, U);

177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178:      Free work space.  All PETSc objects should be destroyed when they
179:      are no longer needed.
180:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181:   VecDestroy(&ctx.initialsolution);
182:   MatDestroy(&A);
183:   VecDestroy(&U);
184:   TSDestroy(&ts);

186:   PetscFinalize();
187:   return 0;
188: }

190: /*TEST

192:    test:
193:      args: -ts_view -ts_max_time 2.e4
194:      timeoutfactor: 15
195:      requires: !single

197: TEST*/