/* nag_pde_parab_1d_fd (d03pcc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include #include #include #include #ifdef __cplusplus extern "C" { #endif static void NAG_CALL pdedef(Integer, double, double, const double[], const double[], double[], double[], double[], Integer *, Nag_Comm *); static void NAG_CALL bndary(Integer, double, const double[], const double[], Integer, double[], double[], Integer *, Nag_Comm *); static int NAG_CALL uinit(double *, double *, Integer, Integer, double); #ifdef __cplusplus } #endif #define U(I, J) u[npde*((J) -1)+(I) -1] #define P(I, J) p[npde*((J) -1)+(I) -1] #define UOUT(I, J, K) uout[npde*(intpts*((K) -1)+(J) -1)+(I) -1] int main(int argc, char *argv[]) { FILE *fpout; const Integer npts = 20, npde = 2, neqn = npts*npde, intpts = 6, itype = 1; const Integer nwk = (10+6*npde)*neqn, lisave = neqn+24; const Integer lrsave = nwk+(21+3*npde)*npde+7*npts+54; Integer exit_status = 0, i, ind, it, itask, itrace, m; double acc, alpha, hx, piby2, tout, ts; double xout[6] = { 0., .4, .6, .8, .9, 1. }; double *rsave = 0, *u = 0, *uout = 0, *x = 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_fd (d03pcc) Example Program Results\n\n"); /* Allocate memory */ if (!(rsave = NAG_ALLOC(lrsave, double)) || !(u = NAG_ALLOC(npde*npts, double)) || !(uout = NAG_ALLOC(npde*intpts*itype, double)) || !(x = NAG_ALLOC(npts, double)) || !(isave = NAG_ALLOC(lisave, Integer))) { fprintf(fpout, "Allocation failure\n"); exit_status = 1; goto END; } acc = 0.001; m = 1; itrace = 0; alpha = 1.0; comm.p = (Pointer)α ind = 0; itask = 1; /* Set spatial mesh points */ piby2 = 0.5*nag_pi; hx = piby2/19; x[0] = 0.0; x[19] = 1.0; for (i = 1; i < 19; ++i) { x[i] = sin(hx*i); } /* Set initial conditions */ ts = 0.0; tout = 1e-5; fprintf(fpout, "Accuracy requirement = %12.5f\n", acc); fprintf(fpout, "Parameter alpha = %12.3f\n\n", alpha); fprintf(fpout, " t / x "); for (i = 0; i < 6; ++i) { fprintf(fpout, "%8.4f", xout[i]); fprintf(fpout, (i+1)%6 == 0 || i == 5?"\n":""); } /* Set the initial values */ uinit(u, x, npde, npts, alpha); for (it = 0; it < 5; ++it) { tout *= 10.0; /* Solve for next iteration step */ /* nag_pde_parab_1d_fd (d03pcc). * General system of parabolic PDEs, method of lines, finite * differences, one space variable */ nag_pde_parab_1d_fd(npde, m, &ts, tout, pdedef, bndary, u, npts, x, acc, rsave, lrsave, isave, lisave, itask, itrace, 0, &ind, &comm, &saved, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_pde_parab_1d_fd (d03pcc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Interpolate at required spatial points */ /* nag_pde_interp_1d_fd (d03pzc). * PDEs, spatial interpolation with nag_pde_parab_1d_fd (d03pcc), * nag_pde_parab_1d_keller (d03pec), * nag_pde_parab_1d_cd (d03pfc), * nag_pde_parab_1d_fd_ode (d03phc), * nag_pde_parab_1d_keller_ode (d03pkc), * nag_pde_parab_1d_cd_ode (d03plc), * nag_pde_parab_1d_fd_ode_remesh (d03ppc), * nag_pde_parab_1d_keller_ode_remesh (d03prc) or * nag_pde_parab_1d_cd_ode_remesh (d03psc) */ nag_pde_interp_1d_fd(npde, m, u, npts, x, xout, intpts, 1, uout, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_pde_interp_1d_fd (d03pzc).\n%s\n", fail.message); exit_status = 1; goto END; } fprintf(fpout, "\n %6.4f u(1)", tout); for (i = 1; i <= 6; ++i) { fprintf(fpout, "%8.4f", UOUT(1, i, 1)); fprintf(fpout, i%6 == 0 || i == 6?"\n":""); } fprintf(fpout, " u(2)"); for (i = 1; i <= 6; ++i) { fprintf(fpout, "%8.4f", UOUT(2, i, 1)); fprintf(fpout, i%6 == 0 || i == 6?"\n":""); } } /* Print integration statistics */ fprintf(fpout, "\n"); fprintf(fpout, " Number of integration steps in time "); fprintf(fpout, "%4ld\n", isave[0]); fprintf(fpout, " Number of residual evaluations of resulting ODE system "); fprintf(fpout, "%4ld\n", isave[1]); fprintf(fpout, " Number of Jacobian evaluations "); fprintf(fpout, "%4ld\n", isave[2]); fprintf(fpout, " Number of iterations of nonlinear solver "); fprintf(fpout, "%4ld\n", isave[4]); END: if (fpout != stdout) fclose(fpout); if (rsave) NAG_FREE(rsave); if (u) NAG_FREE(u); if (uout) NAG_FREE(uout); if (x) NAG_FREE(x); if (isave) NAG_FREE(isave); return exit_status; } static int NAG_CALL uinit(double *u, double *x, Integer npde, Integer npts, double alpha) { /* PDE initial conditon */ Integer i; for (i = 1; i <= npts; ++i) { U(1, i) = alpha*2.0*x[i-1]; U(2, i) = 1.0; } return 0; } static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[], const double ux[], double p[], double q[], double r[], Integer *ires, Nag_Comm *comm) { /* PDE coefficients */ double *alpha = (double *) comm->p; q[0] = *alpha*4.0*(u[1]+x*ux[1]); q[1] = 0.0; r[0] = x*ux[0]; r[1] = ux[1] - u[0] * u[1]; P(1, 1) = 0.0; P(1, 2) = 0.0; P(2, 1) = 0.0; P(2, 2) = 1.0-x*x; return; } static void NAG_CALL bndary(Integer npde, double t, const double u[], const double ux[], Integer ibnd, double beta[], double gamma[], Integer *ires, Nag_Comm *comm) { /* Boundary conditions */ if (ibnd == 0) { beta[0] = 0.0; beta[1] = 1.0; gamma[0] = u[0]; gamma[1] = -u[0]*u[1]; } else { beta[0] = 1.0; beta[1] = 0.0; gamma[0] = -u[0]; gamma[1] = u[1]; } return; }