/* nag_pde_dim1_parab_dae_fd (d03phc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.2, 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[], Integer, const double[],
const double[], double[], double[], double[],
Integer *, Nag_Comm *);
static void NAG_CALL bndary(Integer, double, const double[], const double[],
Integer, const double[], const double[], Integer,
double[], double[], Integer *, Nag_Comm *);
static void NAG_CALL odedef(Integer, double, Integer, const double[],
const double[], Integer, const double[],
const double[], const double[], const double[],
const double[], const double[], double[], Integer *,
Nag_Comm *);
static void NAG_CALL uvinit(Integer, Integer, double *, double *, Integer,
Integer, double);
#ifdef __cplusplus
}
#endif
#define P(I, J) p[npde * ((J)-1) + (I)-1]
#define UCPX(I, J) ucpx[npde * ((J)-1) + (I)-1]
#define UCP(I, J) ucp[npde * ((J)-1) + (I)-1]
int main(void) {
/* Constants */
const Integer print_stat = 0;
const Integer npde = 1, npts = 121, ncode = 1, m = 0, nxi = 1;
const Integer neqn = npde * npts + ncode;
const Integer lisave = 24, lenode = 11 * neqn + 50;
const Integer nwkres =
neqn + npde * (6 * nxi + 3 * npde + 15) + nxi + 7 * npts + 2;
const Integer lrsave = neqn * neqn + neqn + nwkres + lenode;
static double ruser[3] = {-1.0, -1.0, -1.0};
/* Scalars */
double tout, ts;
Integer exit_status = 0, i, ind, it, itask, itol, itrace;
/* Arrays */
double *algopt = 0, *atol = 0, *rsave = 0, *rtol = 0;
double *u = 0, *x = 0, *xi = 0;
Integer *isave = 0;
/* Nag Types */
NagError fail;
Nag_Boolean theta;
Nag_Comm comm;
Nag_D03_Save saved;
INIT_FAIL(fail);
printf("nag_pde_dim1_parab_dae_fd (d03phc) 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)) ||
!(rsave = NAG_ALLOC(lrsave, double)) || !(rtol = NAG_ALLOC(1, double)) ||
!(u = NAG_ALLOC(neqn, double)) || !(x = NAG_ALLOC(npts, double)) ||
!(xi = NAG_ALLOC(1, double)) || !(isave = NAG_ALLOC(lisave, Integer))) {
printf("Allocation failure\n");
exit_status = 1;
goto END;
}
itrace = 0;
itol = 1;
atol[0] = 1e-6;
rtol[0] = atol[0];
/* Set break-points */
for (i = 0; i < npts; ++i) {
x[i] = i / (npts - 1.0);
}
xi[0] = 1.0;
ind = 0;
itask = 1;
/* Set theta = 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;
/* Loop over output value of t */
printf(" Simple coupled PDE using BDF\n");
printf(" Accuracy requirement =%12.3e", atol[0]);
printf(" Number of points = %4" NAG_IFMT "\n\n", npts);
printf("%7s%8s%s\n", "time", "", "solution at x=0");
ts = 1e-4;
uvinit(npde, npts, x, u, npde, neqn, ts);
for (it = 0; it < 5; ++it) {
tout = 0.1 * pow(2.0, (it + 1.0));
/* nag_pde_dim1_parab_dae_fd (d03phc).
* General system of parabolic PDEs, coupled DAEs, method of
* lines, finite differences, one space variable
*/
nag_pde_dim1_parab_dae_fd(
npde, m, &ts, tout, pdedef, bndary, u, npts, x, 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_fd (d03phc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("%7.1f%15s%6.2f\n", ts, "", u[0]);
}
if (print_stat) {
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(rsave);
NAG_FREE(rtol);
NAG_FREE(u);
NAG_FREE(x);
NAG_FREE(xi);
NAG_FREE(isave);
return exit_status;
}
static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[],
const double ux[], Integer ncode, const double v[],
const double vdot[], double p[], double q[],
double r[], Integer *ires, Nag_Comm *comm) {
if (comm->user[0] == -1.0) {
/* printf("(User-supplied callback pdedef, first invocation.)\n"); */
comm->user[0] = 0.0;
}
P(1, 1) = v[0] * v[0];
r[0] = ux[0];
q[0] = -(x)*ux[0] * v[0] * vdot[0];
return;
}
static void NAG_CALL bndary(Integer npde, double t, const double u[],
const double ux[], Integer ncode, const double v[],
const double vdot[], Integer ibnd, double beta[],
double gamma[], Integer *ires, Nag_Comm *comm) {
if (comm->user[1] == -1.0) {
/* printf("(User-supplied callback bndary, first invocation.)\n"); */
comm->user[1] = 0.0;
}
beta[0] = 1.0;
if (ibnd == 0) {
gamma[0] = -v[0] * exp(t);
} else {
gamma[0] = -v[0] * vdot[0];
}
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 rcp[],
const double ucpt[], const double ucptx[],
double f[], Integer *ires, Nag_Comm *comm) {
if (comm->user[2] == -1.0) {
/* printf("(User-supplied callback odedef, first invocation.)\n"); */
comm->user[2] = 0.0;
}
if (*ires == 1) {
f[0] = vdot[0] - v[0] * UCP(1, 1) - UCPX(1, 1) - 1.0 - t;
} else if (*ires == -1) {
f[0] = vdot[0];
}
return;
}
static void NAG_CALL uvinit(Integer npde, Integer npts, double *x, double *u,
Integer ncode, Integer neqn, double ts) {
/* Routine for PDE initial values */
Integer i;
for (i = 0; i < npts; ++i) {
u[i] = exp(ts * (1.0 - x[i])) - 1.0;
}
u[neqn - 1] = ts;
return;
}