/* nag_pde_parab_1d_coll_ode (d03pjc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include #include #ifdef __cplusplus extern "C" { #endif static void NAG_CALL pdedef(Integer, double, const double[], Integer, 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, const double[], double[], Integer, double[], Nag_Comm *); static void NAG_CALL exact(double, Integer, double *, double *); #ifdef __cplusplus } #endif #define U(I, J) u[npde*((J) -1)+(I) -1] #define UX(I, J) ux[npde*((J) -1)+(I) -1] #define UCP(I, J) ucp[npde*((J) -1)+(I) -1] #define UCPX(I, J) ucpx[npde*((J) -1)+(I) -1] #define P(I, J, K) p[npde*(npde*((K) -1)+(J) -1)+(I) -1] #define Q(I, J) q[npde*((J) -1)+(I) -1] #define R(I, J) r[npde*((J) -1)+(I) -1] int main(int argc, char *argv[]) { FILE *fpout; const Integer npde = 1, ncode = 1, npoly = 2, m = 0, nbkpts = 11; const Integer nel = nbkpts-1, npts = nel*npoly+1, neqn = npde*npts+ncode; const Integer nxi = 1, lisave = 24, npl1 = npoly+1; const Integer nwkres = 3*npl1*npl1+npl1*(npde*npde+6*npde+nbkpts+1)+8*npde +nxi*(5*npde+1)+ncode+3; const Integer lenode = 11*neqn+50, lrsave = neqn*neqn+neqn+nwkres+lenode; 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, *xbkpts = 0, *xi = 0; Integer *isave = 0; NagError fail; Nag_Comm comm; Nag_D03_Save saved; INIT_FAIL(fail); /* Check for command-line IO options */ fpout = nag_example_file_io(argc, argv, "-results", NULL); fprintf(fpout, " nag_pde_parab_1d_coll_ode (d03pjc) Example Program Results\n"); /* Allocate memory */ if (!(algopt = NAG_ALLOC(30, double)) || !(atol = NAG_ALLOC(1, double)) || !(exy = NAG_ALLOC(nbkpts, double)) || !(rsave = NAG_ALLOC(lrsave, double)) || !(rtol = NAG_ALLOC(1, double)) || !(u = NAG_ALLOC(neqn, double)) || !(x = NAG_ALLOC(npts, double)) || !(xbkpts = NAG_ALLOC(nbkpts, double)) || !(xi = NAG_ALLOC(nxi, double)) || !(isave = NAG_ALLOC(lisave, Integer))) { fprintf(fpout, "Allocation failure\n"); exit_status = 1; goto END; } itrace = 0; itol = 1; atol[0] = 1e-4; rtol[0] = atol[0]; fprintf(fpout, " Degree of Polynomial =%4ld", npoly); fprintf(fpout, " No. of elements =%4ld\n\n\n", nbkpts-1); fprintf(fpout, " Simple coupled PDE using BDF\n "); fprintf(fpout, " Accuracy requirement =%12.3e", atol[0]); fprintf(fpout, " Number of points = %4ld\n\n", npts); /* Set break-points */ for (i = 0; i < nbkpts; ++i) xbkpts[i] = i/(nbkpts-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; } else { algopt[0] = 0.0; } /* Loop over output value of t */ ts = 1.e-4; comm.p = (Pointer)&ts; tout = 0.0; fprintf(fpout, " x %9.3f%9.3f%9.3f%9.3f%9.3f\n\n", xbkpts[0], xbkpts[2], xbkpts[4], xbkpts[6], xbkpts[10]); for (it = 0; it < 5; ++it) { tout = 0.1*pow((double) npoly, (it+1.0)); /* nag_pde_parab_1d_coll_ode (d03pjc). * General system of parabolic PDEs, coupled DAEs, method of * lines, Chebyshev C^0 collocation, one space variable */ nag_pde_parab_1d_coll_ode(npde, m, &ts, tout, pdedef, bndary, u, nbkpts, xbkpts, npoly, npts, x, ncode, odedef, nxi, xi, neqn, uvinit, rtol, atol, itol, Nag_TwoNorm, Nag_LinAlgFull, algopt, rsave, lrsave, isave, lisave, itask, itrace, 0, &ind, &comm, &saved, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_pde_parab_1d_coll_ode (d03pjc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Check against the exact solution */ exact(tout, nbkpts, xbkpts, exy); fprintf(fpout, " t = %6.3f\n", ts); fprintf(fpout, " App. sol. %7.3f%9.3f%9.3f%9.3f%9.3f", u[0], u[4], u[8], u[12], u[20]); fprintf(fpout, " ODE sol. =%8.3f\n", u[21]); fprintf(fpout, " Exact sol. %7.3f%9.3f%9.3f%9.3f%9.3f", exy[0], exy[2], exy[4], exy[6], exy[10]); fprintf(fpout, " ODE sol. =%8.3f\n\n", ts); } fprintf(fpout, " Number of integration steps in time = %6ld\n", isave[0]); fprintf(fpout, " Number of function evaluations = %6ld\n", isave[1]); fprintf(fpout, " Number of Jacobian evaluations =%6ld\n", isave[2]); fprintf(fpout, " Number of iterations = %6ld\n\n", isave[4]); END: if (fpout != stdout) fclose(fpout); if (algopt) NAG_FREE(algopt); if (atol) NAG_FREE(atol); if (exy) NAG_FREE(exy); if (rsave) NAG_FREE(rsave); if (rtol) NAG_FREE(rtol); if (u) NAG_FREE(u); if (x) NAG_FREE(x); if (xbkpts) NAG_FREE(xbkpts); if (xi) NAG_FREE(xi); if (isave) NAG_FREE(isave); return exit_status; } static void NAG_CALL uvinit(Integer npde, Integer npts, const double x[], double u[], Integer ncode, double v[], Nag_Comm *comm) { /* Routine for PDE initial values (start time is 0.1e-6) */ double *ts = (double *) comm->p; Integer i; v[0] = *ts; for (i = 1; i <= npts; ++i) U(1, i) = exp(*ts*(1.0- x[i-1])) - 1.0; 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 (*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 pdedef(Integer npde, double t, const double x[], Integer nptl, 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) { Integer i; for (i = 1; i <= nptl; ++i) { P(1, 1, i) = v[0]*v[0]; R(1, i) = UX(1, i); Q(1, i) = -x[i-1]*UX(1, i)*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) { 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 exact(double time, Integer npts, double *x, double *u) { /* Exact solution (for comparison purposes) */ Integer i; for (i = 0; i < npts; ++i) u[i] = exp(time*(1.0 - x[i])) - 1.0; return; }