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/* Copyright (C) 2005-2015 Massachusetts Institute of Technology.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
/* Anisotropic dispersion test program */
/* For comparison, we solve for the dispersion relation
analytically in Matlab using the fsolve command to solve
the nonlinear eigenproblem. The Matlab code is as follows.
function result = detMwk(f,k)
sigE = [ 2.92724 0.45948 0.70117;
0.45948 2.89689 0.45083;
0.70117 0.45083 2.17378; ];
epsinf = [ 2.41104 0.48709 0.41226;
0.48709 2.43172 1.62060;
0.41226 1.62060 3.61498; ];
sigH = 0;
muinf = [ 1 0 0; 0 1 0; 0 0 1; ];
f0 = 1.1; g0 = 1e-5;
epsinv = inv(epsinf + ((f0^2)/(f0^2 - f^2 -i*f*g0))*sigE);
muinv = inv(muinf + ((f0^2)/(f0^2 - f^2 -i*f*g0))*sigH);
E = [ 0 0; 1 0; 0 1; ];
kx = k * [ 0 0 0; 0 0 -1; 0 1 0; ];
result = det(E' * (f.^2*eye(3) + kx * muinv * kx * epsinv) * E);
endfunction
k = 0.813;
w1 = fsolve(@(w)detMwk(w,k),0.9);
w2 = fsolve(@(w)detMwk(w,k),w1-0.1);
*/
#include <meep.hpp>
using namespace meep;
using namespace std;
class anisodisp_material : public material_function {
public:
virtual void eff_chi1inv_row(component c, double chi1inv_row[3],
const volume &v,
double tol=DEFAULT_SUBPIXEL_TOL,
int maxeval=DEFAULT_SUBPIXEL_MAXEVAL) {
(void) v; (void) tol; (void) maxeval; // unused
if (component_direction(c) == X) {
chi1inv_row[0] = 0.432818;
chi1inv_row[1] = -0.076724;
chi1inv_row[2] = -0.014964;
}
else if (component_direction(c) == Y) {
chi1inv_row[0] = -0.076724;
chi1inv_row[1] = 0.600041;
chi1inv_row[2] = -0.260249;
}
else {
chi1inv_row[0] = -0.014964;
chi1inv_row[1] = -0.260249;
chi1inv_row[2] = 0.395003;
}
}
virtual void sigma_row(component c, double sigrow[3], const vec &r) {
(void) r; // unused
if (component_direction(c) == X) {
sigrow[0] = 2.92724;
sigrow[1] = 0.45948;
sigrow[2] = 0.70117;
}
else if (component_direction(c) == Y) {
sigrow[0] = 0.45948;
sigrow[1] = 2.89689;
sigrow[2] = 0.45083;
}
else {
sigrow[0] = 0.70117;
sigrow[1] = 0.45083;
sigrow[2] = 2.17378;
}
}
};
int main(int argc, char **argv) {
initialize mpi(argc, argv);
bool ok = true;
// we can only use one process for this 1-pixel simulation
if (0 == divide_parallel_processes(count_processors())) {
quiet = true;
const double res = 200;
grid_volume gv = vol3d(0,0,0, res);
gv.center_origin();
anisodisp_material anisodispmat;
structure s(gv, anisodispmat);
s.add_susceptibility(anisodispmat, E_stuff,
lorentzian_susceptibility(1.1,1e-5));
fields f(&s);
f.use_bloch(vec(0.813,0,0));
f.add_point_source(Ez, 0.5, 1.0, 0.0, 4.0, vec(0,0,0));
double T = f.last_source_time();
int iT = T / f.dt;
while (f.t < iT) {
if (f.t % (iT / 10) == 0)
master_printf("%g%% done with source\n", f.time()/T * 100);
f.step();
}
double T2 = 200;
int iT2 = T2 / f.dt;
complex<double> *vals = new complex<double>[iT2];
while (f.t - iT < iT2) {
if ((f.t - iT) % (iT2 / 10) == 0)
master_printf("%g%% done with harminv\n", (f.t - iT) * 100.0 / iT2);
vals[f.t - iT] = f.get_field(Ez, vec(0.,0.,0.));
f.step();
}
complex<double> amps[8];
double freqs_re[8], freqs_im[8];
master_printf("done with timestepping, running harminv...\n");
int num = do_harminv(vals, iT2, f.dt, 0.0, 1.0, 8,
amps, freqs_re, freqs_im);
// compute the error compared to analytical solution
int i0 = 0;
for (int i=0;i<num;i++) {
master_printf("freq %d is %0.6g, %0.6g\n",i,freqs_re[i],freqs_im[i]);
if (fabs(freqs_re[i]-0.41562) < fabs(freqs_re[i0]-0.41562))
i0 = i;
}
master_printf("err. real: %g\n",fabs(freqs_re[i0]-0.41562)/0.41562);
master_printf("err. imag: %g\n",fabs(freqs_im[i0]+4.8297e-07)/4.8297e-7);
ok = fabs(freqs_re[i0]-0.41562)/0.41562 < 1e-4
&& fabs(freqs_im[i0]+4.8297e-07)/4.8297e-7 < 0.2;
}
end_divide_parallel();
return !and_to_all(ok);
}
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