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#include <math.h>
#include "meep_internals.hpp"
/* This file contains routines to compute the "average" or "effective"
dielectric constant for a pixel, using an anisotropic averaging
procedure described in an upcoming paper (similar to the one in
MPB). */
namespace meep {
////////////////////////////////////////////////////////////////////////////
#include "sphere-quad.h"
static vec sphere_pt(const vec ¢, double R, int n, double &weight) {
switch (cent.dim) {
case D1:
{
weight = sphere_quad[0][n][3];
vec pt(sphere_quad[0][n][2]);
return cent + pt * R;
}
case D2:
{
weight = sphere_quad[1][n][3];
vec pt(sphere_quad[1][n][0], sphere_quad[1][n][1]);
return cent + pt * R;
}
case D3:
{
weight = sphere_quad[2][n][3];
vec pt(sphere_quad[2][n][0], sphere_quad[2][n][1],
sphere_quad[2][n][2]);
return cent + pt * R;
}
case Dcyl:
{
weight = sphere_quad[1][n][3];
return cent
+ veccyl(sphere_quad[1][n][0], sphere_quad[1][n][1]) * R;
}
default:
abort("unknown dimensions in sphere_pt\n");
}
}
////////////////////////////////////////////////////////////////////////////
vec material_function::normal_vector(field_type ft, const volume &v)
{
vec gradient(zero_vec(v.dim));
vec p(v.center());
double R = v.diameter();
for (int i = 0; i < num_sphere_quad[number_of_directions(v.dim)-1]; ++i) {
double weight;
vec pt = sphere_pt(p, R, i, weight);
gradient += (pt - p) * (weight * chi1p1(ft,pt));
}
return gradient;
}
/* default: simple numerical integration of surfaces/cubes, relative
tolerance 'tol'. This is superseded by the routines in the libctl
interface, which either use a semi-analytical average or can
use a proper adaptive cubature. */
void material_function::eff_chi1inv_row(component c, double chi1inv_row[3],
const volume &v,
double tol, int maxeval) {
field_type ft = type(c);
if (!maxeval) {
trivial:
chi1inv_row[0] = chi1inv_row[1] = chi1inv_row[2] = 0.0;
chi1inv_row[component_direction(c) % 3] = 1/chi1p1(ft,v.center());
return;
}
vec gradient(normal_vector(ft, v));
if (abs(gradient) < 1e-8) goto trivial;
double meps=1, minveps=1;
vec d = v.get_max_corner() - v.get_min_corner();
int ms = 10;
double old_meps=0, old_minveps=0;
int iter = 0;
switch(v.dim) {
case D3:
while ((fabs(meps - old_meps) > tol*fabs(old_meps)) && (fabs(minveps - old_minveps) > tol*fabs(old_minveps))) {
old_meps=meps; old_minveps=minveps;
meps = minveps = 0;
for (int k=0; k < ms; k++)
for (int j=0; j < ms; j++)
for (int i=0; i < ms; i++) {
double ep = chi1p1(ft,v.get_min_corner() + vec(i*d.x()/ms, j*d.y()/ms, k*d.z()/ms));
if (ep < 0) goto trivial;
meps += ep; minveps += 1/ep;
}
meps /= ms*ms*ms;
minveps /= ms*ms*ms;
ms *= 2;
if (maxeval && (iter += ms*ms*ms) >= maxeval) goto done;
}
break;
case D2:
while ((fabs(meps-old_meps) > tol*old_meps) && (fabs(minveps-old_minveps) > tol*old_minveps)) {
old_meps=meps; old_minveps=minveps;
meps = minveps = 0;
for (int j=0; j < ms; j++)
for (int i=0; i < ms; i++) {
double ep = chi1p1(ft,v.get_min_corner() + vec(i*d.x()/ms, j*d.y()/ms));
if (ep < 0) goto trivial;
meps += ep; minveps += 1/ep;
}
meps /= ms*ms;
minveps /= ms*ms;
ms *= 2;
if (maxeval && (iter += ms*ms) >= maxeval) goto done;
}
break;
case Dcyl:
while ((fabs(meps-old_meps) > tol*old_meps) && (fabs(minveps-old_minveps) > tol*old_minveps)) {
old_meps=meps; old_minveps=minveps;
meps = minveps = 0;
double sumvol = 0;
for (int j=0; j < ms; j++)
for (int i=0; i < ms; i++) {
double r = v.get_min_corner().r() + i*d.r()/ms;
double ep = chi1p1(ft,v.get_min_corner() + veccyl(i*d.r()/ms, j*d.z()/ms));
if (ep < 0) goto trivial;
sumvol += r;
meps += ep * r; minveps += r/ep;
}
meps /= sumvol;
minveps /= sumvol;
ms *= 2;
if (maxeval && (iter += ms*ms) >= maxeval) goto done;
}
break;
case D1:
while ((fabs(meps-old_meps) > tol*old_meps) && (fabs(minveps-old_minveps) > tol*old_minveps)) {
old_meps=meps; old_minveps=minveps;
meps = minveps = 0;
for (int i=0; i < ms; i++) {
double ep = chi1p1(ft,v.get_min_corner() + vec(i*d.z()/ms));
if (ep < 0) {
meps = chi1p1(ft,v.center());
minveps = 1/meps;
goto done;
}
meps += ep; minveps += 1/ep;
}
meps /= ms;
minveps /= ms;
ms *= 2;
if (maxeval && (iter += ms*ms) >= maxeval) goto done;
}
break;
}
done:
{
double n[3] = {0,0,0};
double nabsinv = 1.0/abs(gradient);
LOOP_OVER_DIRECTIONS(gradient.dim, k)
n[k%3] = gradient.in_direction(k) * nabsinv;
/* get rownum'th row of effective tensor
P * minveps + (I-P) * 1/meps = P * (minveps-1/meps) + I * 1/meps
where I is the identity and P is the projection matrix
P_{ij} = n[i] * n[j]. */
int rownum = component_direction(c) % 3;
for (int i=0; i<3; ++i)
chi1inv_row[i] = n[rownum] * n[i] * (minveps - 1/meps);
chi1inv_row[rownum] += 1/meps;
}
}
void structure_chunk::set_chi1inv(component c,
material_function &medium,
bool use_anisotropic_averaging,
double tol, int maxeval) {
if (!is_mine() || !gv.has_field(c)) return;
field_type ft = type(c);
if (ft != E_stuff && ft != H_stuff) abort("only E or H can have chi");
medium.set_volume(gv.pad().surroundings());
if (!use_anisotropic_averaging) maxeval = 0;
const double smoothing_diameter = 1.0; // FIXME: make user-changable?
// may take a long time in 3d, so prepare to print status messages
int npixels = 0, ipixel = 0;
int loop_npixels = 0;
LOOP_OVER_VOL(gv, c, i) {
loop_npixels = loop_n1 * loop_n2 * loop_n3;
goto breakout; // hack to use loop-size computation from LOOP_OVER_VOL
}
breakout: npixels += loop_npixels;
double last_output_time = wall_time();
FOR_FT_COMPONENTS(ft,c2) if (gv.has_field(c2)) {
direction d = component_direction(c2);
if (!chi1inv[c][d]) chi1inv[c][d] = new realnum[gv.ntot()];
if (!chi1inv[c][d]) abort("Memory allocation error.\n");
}
direction dc = component_direction(c);
direction d0 = X, d1 = Y, d2 = Z;
if (gv.dim == Dcyl) { d0 = R; d1 = P; }
int idiag = component_index(c);
bool trivial[3] = {true,true,true};
double trivial_val[3] = {0,0,0};
trivial_val[idiag] = 1.0;
ivec shift1(unit_ivec(gv.dim,component_direction(c))
* (ft == E_stuff ? 1 : -1));
LOOP_OVER_VOL(gv, c, i) {
double chi1invrow[3], chi1invrow_offdiag[3];
IVEC_LOOP_ILOC(gv, here);
medium.eff_chi1inv_row(c, chi1invrow,
gv.dV(here,smoothing_diameter), tol,maxeval);
medium.eff_chi1inv_row(c, chi1invrow_offdiag,
gv.dV(here-shift1,smoothing_diameter), tol,maxeval);
if (chi1inv[c][d0]) {
chi1inv[c][d0][i] = (d0 == dc) ? chi1invrow[0] : chi1invrow_offdiag[0];
trivial[0] = trivial[0] && (chi1inv[c][d0][i] == trivial_val[0]);
}
if (chi1inv[c][d1]) {
chi1inv[c][d1][i] = (d1 == dc) ? chi1invrow[1] : chi1invrow_offdiag[1];
trivial[1] = trivial[1] && (chi1inv[c][d1][i] == trivial_val[1]);
}
if (chi1inv[c][d2]) {
chi1inv[c][d2][i] = (d2 == dc) ? chi1invrow[2] : chi1invrow_offdiag[2];
trivial[2] = trivial[2] && (chi1inv[c][d2][i] == trivial_val[2]);
}
if (!quiet && (ipixel+1) % 1000 == 0
&& wall_time() > last_output_time + MIN_OUTPUT_TIME) {
master_printf("subpixel-averaging is %g%% done, %g s remaining\n",
ipixel * 100.0 / npixels,
(npixels - ipixel) *
(wall_time() - last_output_time) / ipixel);
last_output_time = wall_time();
}
++ipixel;
}
direction ds[3]; ds[0] = d0; ds[1] = d1; ds[2] = d2;
for (int i = 0; i < 3; ++i) {
trivial_chi1inv[c][ds[i]] = trivial[i];
if (i != idiag && trivial[i]) { // deallocate trivial offdiag
delete[] chi1inv[c][ds[i]];
chi1inv[c][ds[i]] = 0;
}
}
// only deallocate trivial diag if entire tensor is trivial
if (trivial[0] && trivial[1] && trivial[2]) {
delete[] chi1inv[c][dc];
chi1inv[c][dc] = 0;
}
medium.unset_volume();
}
void structure_chunk::add_susceptibility(material_function &sigma,
field_type ft,
const susceptibility &sus)
{
if (ft != E_stuff && ft != H_stuff)
abort("susceptibilities must be for E or H fields");
sigma.set_volume(gv.pad().surroundings());
susceptibility *newsus = sus.clone();
newsus->next = NULL;
newsus->ntot = gv.ntot();
// get rid of previously allocated sigma, normally not the case here:
FOR_COMPONENTS(c) FOR_DIRECTIONS(d) if (newsus->sigma[c][d]) {
delete[] newsus->sigma[c][d];
newsus->sigma[c][d] = NULL;
newsus->trivial_sigma[c][d] = true;
}
// if we own this chunk, set up the sigma array(s):
if (is_mine()) FOR_FT_COMPONENTS(ft,c) if (gv.has_field(c)) {
FOR_FT_COMPONENTS(ft,c2) if (gv.has_field(c2)) {
direction d = component_direction(c2);
if (!newsus->sigma[c][d]) newsus->sigma[c][d] = new realnum[gv.ntot()];
if (!newsus->sigma[c][d]) abort("Memory allocation error.\n");
}
bool trivial[3] = {true, true, true};
direction dc = component_direction(c);
direction d0 = X, d1 = Y, d2 = Z;
if (gv.dim == Dcyl) { d0 = R; d1 = P; }
int idiag = component_index(c);
realnum *s0 = newsus->sigma[c][d0];
realnum *s1 = newsus->sigma[c][d1];
realnum *s2 = newsus->sigma[c][d2];
vec shift1(gv[unit_ivec(gv.dim,component_direction(c))
* (ft == E_stuff ? 1 : -1)]);
LOOP_OVER_VOL(gv, c, i) {
double sigrow[3], sigrow_offdiag[3];
IVEC_LOOP_LOC(gv, here);
sigma.sigma_row(c, sigrow, here);
sigma.sigma_row(c, sigrow_offdiag, here - shift1);
sigrow[(idiag+1) % 3] = sigrow_offdiag[(idiag+1) % 3];
sigrow[(idiag+2) % 3] = sigrow_offdiag[(idiag+2) % 3];
if (s0 && (s0[i] = sigrow[0]) != 0.) trivial[0] = false;
if (s1 && (s1[i] = sigrow[1]) != 0.) trivial[1] = false;
if (s2 && (s2[i] = sigrow[2]) != 0.) trivial[2] = false;
}
direction ds[3]; ds[0] = d0; ds[1] = d1; ds[2] = d2;
for (int i = 0; i < 3; ++i) {
newsus->trivial_sigma[c][ds[i]] = trivial[i];
if (i != idiag && trivial[i]) { // deallocate trivial offdiag
delete[] newsus->sigma[c][ds[i]];
newsus->sigma[c][ds[i]] = 0;
}
}
// only deallocate trivial diag if entire tensor is trivial
if (trivial[0] && trivial[1] && trivial[2]) {
delete[] newsus->sigma[c][dc];
newsus->sigma[c][dc] = 0;
}
}
// finally, add to the beginning of the chiP list:
newsus->next = chiP[ft];
chiP[ft] = newsus;
sigma.unset_volume();
}
} // namespace meep
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