Actual source code: ex20.c

  1: static char help[] = "Solves the van der Pol equation.\n\
  2: Input parameters include:\n";

  4: /* ------------------------------------------------------------------------

  6:    This program solves the van der Pol DAE ODE equivalent
  7:        y' = z                 (1)
  8:        z' = \mu ((1-y^2)z-y)
  9:    on the domain 0 <= x <= 1, with the boundary conditions
 10:        y(0) = 2, y'(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
 11:    and
 12:        \mu = 10^6 ( y'(0) ~ -0.6666665432100101).
 13:    This is a nonlinear equation. The well prepared initial condition gives errors that are not dominated by the first few steps of the method when \mu is large.

 15:    Notes:
 16:    This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form.

 18:   ------------------------------------------------------------------------- */

 20: #include <petscts.h>

 22: typedef struct _n_User *User;
 23: struct _n_User {
 24:   PetscReal mu;
 25:   PetscReal next_output;
 26: };

 28: /*
 29:    User-defined routines
 30: */
 31: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
 32: {
 33:   User               user = (User)ctx;
 34:   PetscScalar       *f;
 35:   const PetscScalar *x;

 37:   PetscFunctionBeginUser;
 38:   PetscCall(VecGetArrayRead(X, &x));
 39:   PetscCall(VecGetArray(F, &f));
 40:   f[0] = x[1];
 41:   f[1] = user->mu * (1. - x[0] * x[0]) * x[1] - x[0];
 42:   PetscCall(VecRestoreArrayRead(X, &x));
 43:   PetscCall(VecRestoreArray(F, &f));
 44:   PetscFunctionReturn(PETSC_SUCCESS);
 45: }

 47: static PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
 48: {
 49:   User               user = (User)ctx;
 50:   const PetscScalar *x, *xdot;
 51:   PetscScalar       *f;

 53:   PetscFunctionBeginUser;
 54:   PetscCall(VecGetArrayRead(X, &x));
 55:   PetscCall(VecGetArrayRead(Xdot, &xdot));
 56:   PetscCall(VecGetArray(F, &f));
 57:   f[0] = xdot[0] - x[1];
 58:   f[1] = xdot[1] - user->mu * ((1.0 - x[0] * x[0]) * x[1] - x[0]);
 59:   PetscCall(VecRestoreArrayRead(X, &x));
 60:   PetscCall(VecRestoreArrayRead(Xdot, &xdot));
 61:   PetscCall(VecRestoreArray(F, &f));
 62:   PetscFunctionReturn(PETSC_SUCCESS);
 63: }

 65: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, void *ctx)
 66: {
 67:   User               user     = (User)ctx;
 68:   PetscInt           rowcol[] = {0, 1};
 69:   const PetscScalar *x;
 70:   PetscScalar        J[2][2];

 72:   PetscFunctionBeginUser;
 73:   PetscCall(VecGetArrayRead(X, &x));
 74:   J[0][0] = a;
 75:   J[0][1] = -1.0;
 76:   J[1][0] = user->mu * (2.0 * x[0] * x[1] + 1.0);
 77:   J[1][1] = a - user->mu * (1.0 - x[0] * x[0]);
 78:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
 79:   PetscCall(VecRestoreArrayRead(X, &x));

 81:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 82:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
 83:   if (A != B) {
 84:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
 85:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
 86:   }
 87:   PetscFunctionReturn(PETSC_SUCCESS);
 88: }

 90: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
 91: static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec X, void *ctx)
 92: {
 93:   const PetscScalar *x;
 94:   PetscReal          tfinal, dt;
 95:   User               user = (User)ctx;
 96:   Vec                interpolatedX;

 98:   PetscFunctionBeginUser;
 99:   PetscCall(TSGetTimeStep(ts, &dt));
100:   PetscCall(TSGetMaxTime(ts, &tfinal));

102:   while (user->next_output <= t && user->next_output <= tfinal) {
103:     PetscCall(VecDuplicate(X, &interpolatedX));
104:     PetscCall(TSInterpolate(ts, user->next_output, interpolatedX));
105:     PetscCall(VecGetArrayRead(interpolatedX, &x));
106:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%.1f] %" PetscInt_FMT " TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", (double)user->next_output, step, (double)t, (double)dt, (double)PetscRealPart(x[0]), (double)PetscRealPart(x[1])));
107:     PetscCall(VecRestoreArrayRead(interpolatedX, &x));
108:     PetscCall(VecDestroy(&interpolatedX));
109:     user->next_output += 0.1;
110:   }
111:   PetscFunctionReturn(PETSC_SUCCESS);
112: }

114: int main(int argc, char **argv)
115: {
116:   TS             ts; /* nonlinear solver */
117:   Vec            x;  /* solution, residual vectors */
118:   Mat            A;  /* Jacobian matrix */
119:   PetscInt       steps;
120:   PetscReal      ftime   = 0.5;
121:   PetscBool      monitor = PETSC_FALSE, implicitform = PETSC_TRUE;
122:   PetscScalar   *x_ptr;
123:   PetscMPIInt    size;
124:   struct _n_User user;

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:      Initialize program
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129:   PetscFunctionBeginUser;
130:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
131:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
132:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:     Set runtime options
136:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137:   user.next_output = 0.0;
138:   user.mu          = 1.0e3;
139:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL));
140:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-implicitform", &implicitform, NULL));
141:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Physical parameters", NULL);
142:   PetscCall(PetscOptionsReal("-mu", "Stiffness parameter", "<1.0e6>", user.mu, &user.mu, NULL));
143:   PetscOptionsEnd();

145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146:     Create necessary matrix and vectors, solve same ODE on every process
147:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
149:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
150:   PetscCall(MatSetFromOptions(A));
151:   PetscCall(MatSetUp(A));

153:   PetscCall(MatCreateVecs(A, &x, NULL));

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:      Create timestepping solver context
157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
159:   if (implicitform) {
160:     PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
161:     PetscCall(TSSetIJacobian(ts, A, A, IJacobian, &user));
162:     PetscCall(TSSetType(ts, TSBEULER));
163:   } else {
164:     PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
165:     PetscCall(TSSetType(ts, TSRK));
166:   }
167:   PetscCall(TSSetMaxTime(ts, ftime));
168:   PetscCall(TSSetTimeStep(ts, 0.001));
169:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
170:   if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));

172:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173:      Set initial conditions
174:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
175:   PetscCall(VecGetArray(x, &x_ptr));
176:   x_ptr[0] = 2.0;
177:   x_ptr[1] = -2.0 / 3.0 + 10.0 / (81.0 * user.mu) - 292.0 / (2187.0 * user.mu * user.mu);
178:   PetscCall(VecRestoreArray(x, &x_ptr));

180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181:      Set runtime options
182:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183:   PetscCall(TSSetFromOptions(ts));

185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186:      Solve nonlinear system
187:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188:   PetscCall(TSSolve(ts, x));
189:   PetscCall(TSGetSolveTime(ts, &ftime));
190:   PetscCall(TSGetStepNumber(ts, &steps));
191:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "steps %" PetscInt_FMT ", ftime %g\n", steps, (double)ftime));
192:   PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));

194:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195:      Free work space.  All PETSc objects should be destroyed when they
196:      are no longer needed.
197:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198:   PetscCall(MatDestroy(&A));
199:   PetscCall(VecDestroy(&x));
200:   PetscCall(TSDestroy(&ts));

202:   PetscCall(PetscFinalize());
203:   return (0);
204: }

206: /*TEST

208:     test:
209:       requires: !single
210:       args: -mu 1e6

212:     test:
213:       requires: !single
214:       suffix: 2
215:       args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp

217:     test:
218:       requires: !single
219:       suffix: 3
220:       args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312

222: TEST*/