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convergence_cyl_waveguide.cpp
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convergence_cyl_waveguide.cpp
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#include <stdio.h>
#include <meep.hpp>
using namespace meep;
#include "config.h"
using std::complex;
double eps(const vec &pt) { return ((pt.r() < 0.5 + 1e-6) ? 9.0 : 1.0); }
#define MINRES 10
#define MAXRES 25
#define RESSTEP 3 // should be odd
int find_exponent(double a_mean, double a_meansqr, double a2_mean, double a2_meansqr,
const char *name) {
// Verdict on convergence
double a_sigma, a2_sigma;
a_sigma = sqrt(a_meansqr - a_mean * a_mean);
a2_sigma = sqrt(a2_meansqr - a2_mean * a2_mean);
master_printf("%s a's: ", name);
if (a2_sigma / a2_mean < 0.15) {
master_printf("converged as %3.1e / (a*a)\n", a_mean);
return 2;
}
else if (a_sigma / a_mean < 0.15) {
master_printf("converged as %3.1e / a\n", a_mean);
return 1;
}
else {
master_printf("Not clear if it converges...\n");
return 0;
}
}
void test_convergence_without_averaging() {
double w0 = 0.2858964; // exact to last digit
int n[2] = {0, 0};
double a_mean[2] = {0, 0}, a_meansqr[2] = {0, 0}, a2_mean[2] = {0, 0}, a2_meansqr[2] = {0, 0};
for (int a = MINRES; a <= MAXRES; a += RESSTEP) {
grid_volume vol = volcyl(1.0, 0.0, a);
structure s(vol, eps);
fields f(&s, 1);
f.use_bloch(0.1);
f.set_boundary(High, R, Metallic);
f.add_point_source(Hr, w0, 2.0, 0.0, 5.0, veccyl(0.2, 0.0));
while (f.time() < f.last_source_time())
f.step();
int t_harminv_max = 2500; // try increasing this in case of failure
complex<double> *mon_data = new complex<double>[t_harminv_max];
int t = 0;
monitor_point mp;
while (t < t_harminv_max) {
f.step();
f.get_point(&mp, veccyl(0.2, 0.0));
mon_data[t] = mp.get_component(Er);
t++;
}
int maxbands = 10, nfreq;
complex<double> *amps = new complex<double>[maxbands];
;
double *freq_re = new double[maxbands], *freq_im = new double[maxbands];
double *errors = new double[maxbands];
nfreq = do_harminv(mon_data, t_harminv_max - 1, f.dt, 0.10, 0.50, maxbands, amps, freq_re,
freq_im, errors);
double w = 0.0;
for (int jf = 0; jf < nfreq; jf++)
if (abs(freq_re[jf] - w0) < abs(w - w0)) w = freq_re[jf];
double e = -(w - w0) / w0, ea = e * a, ea2 = e * a * a; // to check 1/a and 1/(a*a) convergence
// master_printf("Using a = %d ...\n", a);
// master_printf("a = %3d\tw = %g \t(w-w0)/w0*a = %4.2e \t(w-w0)/w0*a*a = %4.2e\n", a, w, ea,
// ea2);
master_printf("noavg:, %d, %g, %g\n", a, w, fabs(e));
// Statistical analysis
int index = (2 * (a / 2) == a) ? 0 : 1; // even / odd
a_mean[index] += ea;
a_meansqr[index] += ea * ea;
a2_mean[index] += ea2;
a2_meansqr[index] += ea2 * ea2;
n[index]++;
}
for (int i = 0; i < 2; i++)
a_mean[i] /= n[i];
for (int i = 0; i < 2; i++)
a_meansqr[i] /= n[i];
for (int i = 0; i < 2; i++)
a2_mean[i] /= n[i];
for (int i = 0; i < 2; i++)
a2_meansqr[i] /= n[i];
/* Note: in older versions of Meep, even with "no averaging" there
was some funny averaging that happened to give quadratic convergence
for the even-resolution cylindrical case here. We no longer do this
-- "no averaging" really means no averaging now. */
if (find_exponent(a_mean[0], a_meansqr[0], a2_mean[0], a2_meansqr[0], "Even") != 1)
abort("Failed even convergence test with no fancy averaging!\n");
if (find_exponent(a_mean[1], a_meansqr[1], a2_mean[1], a2_meansqr[1], "Odd") != 1)
abort("Failed odd convergence test with no fancy averaging!\n");
master_printf("Passed convergence test with no fancy averaging!\n");
}
void test_convergence_with_averaging() {
double w0 = 0.2858964; // exact to last digit
int n[2] = {0, 0};
double a_mean[2] = {0, 0}, a_meansqr[2] = {0, 0}, a2_mean[2] = {0, 0}, a2_meansqr[2] = {0, 0};
for (int a = MINRES; a <= MAXRES; a += RESSTEP) {
grid_volume vol = volcyl(1.0, 0.0, a);
structure s(vol, eps);
s.set_epsilon(eps);
fields f(&s, 1);
f.use_bloch(0.1);
f.set_boundary(High, R, Metallic);
f.add_point_source(Hr, w0, 2.0, 0.0, 5.0, veccyl(0.2, 0.0));
while (f.time() < f.last_source_time())
f.step();
int t_harminv_max = 2500; // try increasing this in case of failure
complex<double> *mon_data = new complex<double>[t_harminv_max];
int t = 0;
monitor_point mp;
while (t < t_harminv_max) {
f.step();
f.get_point(&mp, veccyl(0.2, 0.0));
mon_data[t] = mp.get_component(Er);
t++;
}
int maxbands = 10, nfreq;
complex<double> *amps = new complex<double>[maxbands];
;
double *freq_re = new double[maxbands], *freq_im = new double[maxbands],
*errors = new double[maxbands];
nfreq = do_harminv(mon_data, t_harminv_max - 1, f.dt, 0.10, 0.50, maxbands, amps, freq_re,
freq_im, errors);
double w = 0.0;
for (int jf = 0; jf < nfreq; jf++)
if (abs(freq_re[jf] - w0) < abs(w - w0)) w = freq_re[jf];
double e = -(w - w0) / w0, ea = e * a, ea2 = e * a * a; // to check 1/a and 1/(a*a) convergence
// master_printf("Using a = %d ...\n", a);
// master_printf("a = %3d\tw = %g \t(w-w0)/w0*a = %4.2e \t(w-w0)/w0*a*a = %4.2e\n", a, w, ea,
// ea2);
master_printf("avg:, %d, %g, %g\n", a, w, fabs(e));
// Statistical analysis
int index = (2 * (a / 2) == a) ? 0 : 1; // even / odd
a_mean[index] += ea;
a_meansqr[index] += ea * ea;
a2_mean[index] += ea2;
a2_meansqr[index] += ea2 * ea2;
n[index]++;
}
for (int i = 0; i < 2; i++)
a_mean[i] /= n[i];
for (int i = 0; i < 2; i++)
a_meansqr[i] /= n[i];
for (int i = 0; i < 2; i++)
a2_mean[i] /= n[i];
for (int i = 0; i < 2; i++)
a2_meansqr[i] /= n[i];
if (find_exponent(a_mean[0], a_meansqr[0], a2_mean[0], a2_meansqr[0], "Even") != 2)
abort("Failed convergence test with anisotropic dielectric averaging!\n");
if (find_exponent(a_mean[1], a_meansqr[1], a2_mean[1], a2_meansqr[1], "Odd") != 2)
abort("Failed convergence test with anisotropic dielectric averaging!\n");
master_printf("Passed convergence test with anisotropic dielectric averaging!\n");
}
int main(int argc, char **argv) {
initialize mpi(argc, argv);
verbosity = 0;
#ifdef HAVE_HARMINV
master_printf("Testing convergence of a waveguide mode frequency...\n");
test_convergence_without_averaging();
test_convergence_with_averaging();
#endif
return 0;
}