/* nag_pde_dim1_parab_dae_keller (d03pkc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL pdedef(Integer, double, double, const double[],
const double[], const double[], Integer,
const double[], const double[], double[], Integer *,
Nag_Comm *);
static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc,
const double u[], const double ut[], Integer ncode,
const double v[], const double vdot[], double res[],
Integer *ires, Nag_Comm *);
static void NAG_CALL odedef(Integer, double, Integer, const double[],
const double[], Integer, const double[],
const double[], const double[], const double[],
double[], Integer *, Nag_Comm *);
static void NAG_CALL uvinit(Integer npde, Integer npts, double *x, double *u,
Integer ncode, Integer neqn, double ts);
static void NAG_CALL exact(double, Integer, Integer, double *, double *);
#ifdef __cplusplus
}
#endif
#define UCP(I, J) ucp[npde * ((J)-1) + (I)-1]
int main(void) {
const Integer npde = 2, npts = 21, ncode = 1, nxi = 1, nleft = 1;
const Integer neqn = npde * npts + ncode, lisave = 24;
const Integer nwkres =
npde * (npts + 6 * nxi + 3 * npde + 15) + ncode + nxi + 7 * npts + 2;
const Integer lenode = 11 * neqn + 50,
lrsave = neqn * neqn + neqn + nwkres + lenode;
static double ruser[3] = {-1.0, -1.0, -1.0};
double tout, ts;
Integer exit_status = 0, i, ind, it, itask, itol, itrace;
Nag_Boolean theta;
double *algopt = 0, *atol = 0, *exy = 0, *rsave = 0, *rtol = 0;
double *u = 0, *x = 0, *xi = 0;
Integer *isave = 0;
NagError fail;
Nag_Comm comm;
Nag_D03_Save saved;
INIT_FAIL(fail);
printf("nag_pde_dim1_parab_dae_keller (d03pkc) Example Program Results\n\n");
/* For communication with user-supplied functions: */
comm.user = ruser;
/* Allocate memory */
if (!(algopt = NAG_ALLOC(30, double)) || !(atol = NAG_ALLOC(1, double)) ||
!(exy = NAG_ALLOC(neqn, double)) ||
!(rsave = NAG_ALLOC(lrsave, double)) || !(rtol = NAG_ALLOC(1, double)) ||
!(u = NAG_ALLOC(neqn, double)) || !(x = NAG_ALLOC(npts, double)) ||
!(xi = NAG_ALLOC(nxi, double)) || !(isave = NAG_ALLOC(lisave, Integer))) {
printf("Allocation failure\n");
exit_status = 1;
goto END;
}
itrace = 0;
itol = 1;
atol[0] = 1e-4;
rtol[0] = atol[0];
printf(" Accuracy requirement =%12.3e", atol[0]);
printf(" Number of points = %3" NAG_IFMT "\n\n", npts);
/* Set spatial-mesh points */
for (i = 0; i < npts; ++i)
x[i] = i / (npts - 1.0);
xi[0] = 1.0;
ind = 0;
itask = 1;
/* Set THETA to TRUE if the Theta integrator is required */
theta = Nag_FALSE;
for (i = 0; i < 30; ++i)
algopt[i] = 0.0;
if (theta) {
algopt[0] = 2.0;
} else {
algopt[0] = 0.0;
}
algopt[0] = 1.0;
algopt[12] = 0.005;
/* Loop over output value of t */
ts = 1e-4;
printf(" x %9.3f%9.3f%9.3f%9.3f%9.3f\n\n", x[0], x[4], x[8], x[12],
x[20]);
uvinit(npde, npts, x, u, ncode, neqn, ts);
for (it = 0; it < 5; ++it) {
tout = 0.1 * pow(2.0, (it + 1.0));
/* nag_pde_dim1_parab_dae_keller (d03pkc).
* General system of first-order PDEs, coupled DAEs, method
* of lines, Keller box discretization, one space variable
*/
nag_pde_dim1_parab_dae_keller(
npde, &ts, tout, pdedef, bndary, u, npts, x, nleft, ncode, odedef, nxi,
xi, neqn, rtol, atol, itol, Nag_TwoNorm, Nag_LinAlgFull, algopt, rsave,
lrsave, isave, lisave, itask, itrace, 0, &ind, &comm, &saved, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_pde_dim1_parab_dae_keller (d03pkc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Check against the exact solution */
exact(tout, neqn, npts, x, exy);
printf(" t = %6.3f\n", ts);
printf(" App. sol. %7.3f%9.3f%9.3f%9.3f%9.3f", u[0], u[8], u[16], u[24],
u[40]);
printf(" ODE sol. =%8.3f\n", u[42]);
printf(" Exact sol. %7.3f%9.3f%9.3f%9.3f%9.3f", exy[0], exy[8], exy[16],
exy[24], exy[40]);
printf(" ODE sol. =%8.3f\n\n", ts);
}
printf(" Number of integration steps in time = %6" NAG_IFMT "\n", isave[0]);
printf(" Number of function evaluations = %6" NAG_IFMT "\n", isave[1]);
printf(" Number of Jacobian evaluations =%6" NAG_IFMT "\n", isave[2]);
printf(" Number of iterations = %6" NAG_IFMT "\n\n", isave[4]);
END:
NAG_FREE(algopt);
NAG_FREE(atol);
NAG_FREE(exy);
NAG_FREE(rsave);
NAG_FREE(rtol);
NAG_FREE(u);
NAG_FREE(x);
NAG_FREE(xi);
NAG_FREE(isave);
return exit_status;
}
static void NAG_CALL uvinit(Integer npde, Integer npts, double *x, double *u,
Integer ncode, Integer neqn, double ts) {
Integer i, k;
/* Routine for PDE initial values */
k = 0;
for (i = 0; i < npts; ++i) {
u[k] = exp(ts * (1.0 - x[i])) - 1.0;
u[k + 1] = -ts * exp(ts * (1.0 - x[i]));
k += 2;
}
u[neqn - 1] = ts;
return;
}
static void NAG_CALL odedef(Integer npde, double t, Integer ncode,
const double v[], const double vdot[], Integer nxi,
const double xi[], const double ucp[],
const double ucpx[], const double ucpt[],
double f[], Integer *ires, Nag_Comm *comm) {
if (comm->user[0] == -1.0) {
printf("(User-supplied callback odedef, first invocation.)\n");
comm->user[0] = 0.0;
}
if (*ires == -1) {
f[0] = vdot[0];
} else {
f[0] = vdot[0] - v[0] * UCP(1, 1) - UCP(2, 1) - 1.0 - t;
}
return;
}
static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[],
const double ut[], const double ux[], Integer ncode,
const double v[], const double vdot[], double res[],
Integer *ires, Nag_Comm *comm) {
if (comm->user[1] == -1.0) {
printf("(User-supplied callback pdedef, first invocation.)\n");
comm->user[1] = 0.0;
}
if (*ires == -1) {
res[0] = v[0] * v[0] * ut[0] - x * u[1] * v[0] * vdot[0];
res[1] = 0.0;
} else {
res[0] = v[0] * v[0] * ut[0] - x * u[1] * v[0] * vdot[0] - ux[1];
res[1] = u[1] - ux[0];
}
return;
}
static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc,
const double u[], const double ut[], Integer ncode,
const double v[], const double vdot[], double res[],
Integer *ires, Nag_Comm *comm) {
if (comm->user[2] == -1.0) {
printf("(User-supplied callback bndary, first invocation.)\n");
comm->user[2] = 0.0;
}
if (ibnd == 0) {
if (*ires == -1) {
res[0] = 0.0;
} else {
res[0] = u[1] + v[0] * exp(t);
}
} else {
if (*ires == -1) {
res[0] = v[0] * vdot[0];
} else {
res[0] = u[1] + v[0] * vdot[0];
}
}
return;
}
static void NAG_CALL exact(double time, Integer neqn, Integer npts, double *x,
double *u) {
/* Exact solution (for comparison purposes) */
Integer i, k;
k = 0;
for (i = 0; i < npts; ++i) {
u[k] = exp(time * (1.0 - x[i])) - 1.0;
k += 2;
}
return;
}