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epsilon_FB_block.m
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function [Eout,Mout] = epsilon_FB_block(pdir,lambda2)
%THIS FUNCTION CALCULATES THE EPSILON MATRIX ELEMENT THROUGHT THE ENTIRE
%DOMAIN -
global nx ny nz NO DN NOUT dirfield file R c DPMLs DPMLe gain;
%PLOT DIRECTOR FIELD
if strcmp(pdir, 'YES')
if strcmp(dirfield, 'FILE')
dirarray = read_dir('/data/Matlab/data/141128_22_input_M3_res_dir.raw');
end
u1=zeros(nx,ny);
v1=zeros(nx,ny);
u2=zeros(nx,nz);
v2=zeros(nx,nz);
u3=zeros(ny,nz);
v3=zeros(ny,nz);
nordplot = zeros(nx);
dnplot = zeros(nx);
nordplot2 = zeros(nx);
exportdir(dirfield);
for i = 1:nx
for j = 1:ny
for k = 1:nz
% [u1(i,j),v1(i,j),~] = dir(i,j,nz-1);
% [u2(i,k),~,v2(i,k)] = dir(i,1,k);
% [~,u3(j,k),v3(j,k)] = dir(nx - 1,j,k);
[u1(i,j),v1(i,j),~] = dir(i,j,(nz+1)/2);
[u2(i,k),~,v2(i,k)] = dir(i,(nz+1)/2+1,k);
[~,u3(j,k),v3(j,k)] = dir((nz+1)/2+1,j,k);
end
end
end
[x1,y1]=meshgrid(1:nx,1:ny);
[x2,z2]=meshgrid(1:nx,1:nz);
[y3,z3]=meshgrid(1:ny,1:nz);
for i=1:nx
nordplot(i) = nord(i,3*ny/4,3*nz/4);
dnplot(i) = dn(i,3*ny/4,3*nz/4);
nordplot2(i) =nord(i,1,1);
end
f1 = figure;
set(f1,'visible','off');
quiver(x1,y1,u1',v1');
pbaspect([1 1 1]);
f2 = figure;
set(f2,'visible','off');
quiver(x2,z2,u2',v2');
pbaspect([1 1 1]);
f3 = figure;
set(f3,'visible','off');
quiver(y3,z3,u3',v3');
pbaspect([1 1 1]);
f4 = figure;
set(f4,'visible','off');
plot(nordplot);
f5 = figure;
set(f5,'visible','off');
plot(dnplot);
f6 = figure;
set(f6,'visible','off');
plot(nordplot2);
if isempty(file) == 0
out = strcat(file,'/dir');
print(f1,strcat(out,'XY'),'-dpng');
print(f2,strcat(out,'XZ'),'-dpng');
print(f3,strcat(out,'YZ'),'-dpng');
print(f4,strcat(out,'nord'),'-dpng');
print(f5,strcat(out,'dn'),'-dpng');
print(f6,strcat(out,'nord2'),'-dpng');
end
end
n = nx*ny*nz;
Di = zeros(n,1);
Dj = zeros(n,1);
Exxv = zeros(n,1);
Exyv = zeros(n,1);
Exzv = zeros(n,1);
Eyxv = zeros(n,1);
Eyyv = zeros(n,1);
Eyzv = zeros(n,1);
Ezxv = zeros(n,1);
Ezyv = zeros(n,1);
Ezzv = zeros(n,1);
Mxxv = zeros(n,1);
Myyv = zeros(n,1);
Mzzv = zeros(n,1);
Rxpi = zeros(2*n,1);
Rypi = zeros(2*n,1);
Rzpi = zeros(2*n,1);
Rxpj = zeros(2*n,1);
Rypj = zeros(2*n,1);
Rzpj = zeros(2*n,1);
Rxpv = zeros(2*n,1);
Rypv = zeros(2*n,1);
Rzpv = zeros(2*n,1);
%FILL THE ARRAYS OF EPSILON COMPONENTS
for i = 1:nx
for j = 1:ny
for k = 1:nz
[D1,DM1] = eblock(i,j,k);
% epsilon and mu blocks are all diagonal matrices
Di(ind(i,j,k)) = ind(i,j,k);
Dj(ind(i,j,k)) = ind(i,j,k);
%dielectric tensor
Exxv(ind(i,j,k)) = D1(1,1);
Exyv(ind(i,j,k)) = D1(1,2);
Exzv(ind(i,j,k)) = D1(1,3);
Eyxv(ind(i,j,k)) = D1(2,1);
Eyyv(ind(i,j,k)) = D1(2,2);
Eyzv(ind(i,j,k)) = D1(2,3);
Ezxv(ind(i,j,k)) = D1(3,1);
Ezyv(ind(i,j,k)) = D1(3,2);
Ezzv(ind(i,j,k)) = D1(3,3);
%permeability matrix with PML
Mxxv(ind(i,j,k)) = DM1(1,1);
Myyv(ind(i,j,k)) = DM1(2,2);
Mzzv(ind(i,j,k)) = DM1(3,3);
%espilon interpolation matrices
Rxpi(2*ind(i,j,k)-1) = ind(i,j,k); %diagonalni
Rxpj(2*ind(i,j,k)-1) = ind(i,j,k); %diagonalni
Rypi(2*ind(i,j,k)-1) = ind(i,j,k); %diagonalni
Rypj(2*ind(i,j,k)-1) = ind(i,j,k); %diagonalni
Rzpi(2*ind(i,j,k)-1) = ind(i,j,k); %diagonalni
Rzpj(2*ind(i,j,k)-1) = ind(i,j,k); %diagonalni
Rxpi(2*ind(i,j,k)-0) = ind(i,j,k); %izvendiagonalni
Rxpj(2*ind(i,j,k)-0) = ind(i+1,j,k); %izvendiagonalni
Rypi(2*ind(i,j,k)-0) = ind(i,j,k); %izvendiagonalni
Rypj(2*ind(i,j,k)-0) = ind(i,j+1,k); %izvendiagonalni
Rzpi(2*ind(i,j,k)-0) = ind(i,j,k); %izvendiagonalni
Rzpj(2*ind(i,j,k)-0) = ind(i,j,k+1); %izvendiagonalni
if i == nx
Rxpv(2*ind(i,j,k)-1) = 1; %maybe2??; %diagonalni
Rxpv(2*ind(i,j,k)-0) = 0; %diagonalni
else
Rxpv(2*ind(i,j,k)-1) = 1; %diagonalni
Rxpv(2*ind(i,j,k)-0) = 1; %izvendiagonalni
end
if j == ny
Rypv(2*ind(i,j,k)-1) = 1; %maybe2??; %diagonalni
Rypv(2*ind(i,j,k)-0) = 0; %diagonalni
else
Rypv(2*ind(i,j,k)-1) = 1; %diagonalni
Rypv(2*ind(i,j,k)-0) = 1; %izvendiagonalni
end
if k == nz
Rzpv(2*ind(i,j,k)-1) = 1; %maybe2??; %diagonalni
Rzpv(2*ind(i,j,k)-0) = 0; %diagonalni
else
Rzpv(2*ind(i,j,k)-1) = 1; %diagonalni
Rzpv(2*ind(i,j,k)-0) = 1; %izvendiagonalni
end
end
end
end
Exx = sparse(Di,Dj,Exxv);
Exy = sparse(Di,Dj,Exyv);
Exz = sparse(Di,Dj,Exzv);
Eyx = sparse(Di,Dj,Eyxv);
Eyy = sparse(Di,Dj,Eyyv);
Eyz = sparse(Di,Dj,Eyzv);
Ezx = sparse(Di,Dj,Ezxv);
Ezy = sparse(Di,Dj,Ezyv);
Ezz = sparse(Di,Dj,Ezzv);
Mxx = sparse(Di,Dj,Mxxv);
Myy = sparse(Di,Dj,Myyv);
Mzz = sparse(Di,Dj,Mzzv);
Rxp = 1/2*sparse(Rxpi,Rxpj,Rxpv);
Ryp = 1/2*sparse(Rypi,Rypj,Rypv);
Rzp = 1/2*sparse(Rzpi,Rzpj,Rzpv);
Rxp = Rxp(1:nx*ny*nz,1:nx*ny*nz);
Ryp = Ryp(1:nx*ny*nz,1:nx*ny*nz);
Rzp = Rzp(1:nx*ny*nz,1:nx*ny*nz);
Rxm = Rxp';
Rym = Ryp';
Rzm = Rzp';
Eout = [Exx Rxp*Rym*Exy Rxp*Rzm*Exz; Ryp*Rxm*Eyx Eyy Ryp*Rzm*Eyz; Rzp*Rxm*Ezx Rzp*Rym*Ezy Ezz];
Mout = [Mxx sparse(n,n) sparse(n,n); sparse(n,n) Myy sparse(n,n); sparse(n,n) sparse(n,n) Mzz];
%define space dependance of refractive index
function f = nord(i,j,k)
TW = tukeywin(200, 0.4);
if r(i,j,k,c) < R
f = NO; %NOUT + (NO - NOUT)*TW(round(100*(1-r(i,j,k,c)/R)+1));
else
f = NOUT;
end
end
function f = dn(i,j,k)
f = DN;
% TW = tukeywin(200, 0.4);
% if r(i,j,k,c) < R
% f = DN; %*TW(round(100*(1-r(i,j,k,c)/R)+1));
% else
% f = 0;
% end
end
function f = ind(i,j,k)
f = (k-1)*nx*ny + (j-1)*nx + (i-1) + 1;
end
%SELECT DIRECTOR FIELD
function [f1,f2,f3] = dir(i,j,k)
%RANDOM
if strcmp(dirfield, 'RANDOM')
f11 = rand;
f21 = rand;
f31 = rand;
f1 = f11/sqrt(f11^2+f21^2+f31^2);
f2 = f21/sqrt(f11^2+f21^2+f31^2);
f3 = f31/sqrt(f11^2+f21^2+f31^2);
%ISOTROPIC
elseif strcmp(dirfield, 'ISOTROPIC')
f1 = 1;
f2 = 1;
f3 = 1;
% f1 = -(i-c(1))/(sqrt((i-c(1))^2 + (j-c(2))^2 )+1E-12);
% f2 = -(j-c(2))/(sqrt((i-c(1))^2 + (j-c(2))^2 )+1E-12);
% f3 = 0;
%RADIAL DROPLET
elseif strcmp(dirfield, 'ISOSPHERE')
if r(i,j,k,c) < R
f1 = 1;
f2 = 0;
f3 = 0;
else
f1 = 0;
f2 = 0;
f3 = 0;
end
%ZERO
elseif strcmp(dirfield, 'ZERO')
f1 = 0;
f2 = 0;
f3 = 0;
% HELICONICAL
elseif strcmp(dirfield, 'HELICONIC')
f1 = cos(pi/4);
f2 = sin(2*pi*i/(nx))*sin(pi/4);
f3 = cos(2*pi*i/(nx))*sin(pi/4);
%HELICONICAL XY DIAGONAL
elseif strcmp(dirfield,'HELICONICXY')
pitch = nx*sqrt(2)/2;
f1 = cos(pi/4)*cos(pi/4) - sin(phi(i*cos(pi/4)+j*(sin(pi/4)),pitch)) * sin(pi/4) * sin(pi/4);
f2 = cos(pi/4)*sin(pi/4) + sin(phi(i*cos(pi/4)+j*(sin(pi/4)),pitch)) * sin(pi/4) * cos(pi/4);
f3 = cos(phi(i*cos(pi/4)+j*(sin(pi/4)),pitch))*sin(pi/4);
%HELICONICAL XZ DIAGONAL
elseif strcmp(dirfield, 'HELICONICXZ')
theta = pi/4;
pitch = nx*sqrt(2)/2;
f1 = cos(theta)*cos(pi/4) - cos(phi(i*cos(pi/4)+k*(sin(pi/4)),pitch))*sin(theta) * sin(pi/4);
f2 = sin(phi(i*cos(pi/4)+k*(sin(pi/4)),pitch)) * sin(theta);
f3 = cos(theta)*sin(pi/4) + cos(phi(i*cos(pi/4)+k*(sin(pi/4)),pitch))*sin(theta) * cos(pi/4);
%HELICONICAL YZ DIAGONAL
elseif strcmp(dirfield, 'HELICONICYZ')
theta = pi/4;
pitch = ny*sqrt(2)/2;
f1 = cos(theta)*cos(pi/4) - cos(phi(j*cos(pi/4)+k*(sin(pi/4)),pitch))*sin(theta) * sin(pi/4);
f2 = sin(phi(j*cos(pi/4)+k*(sin(pi/4)),pitch)) * sin(theta);
f3 = cos(theta)*sin(pi/4) + cos(phi(j*cos(pi/4)+k*(sin(pi/4)),pitch))*sin(theta) * cos(pi/4);
%RADIAL DROPLET
elseif strcmp(dirfield, 'RADIALD')
if r(i,j,k,c) < R
f1 = -(i-c(1))/(r(i,j,k,c)+1E-12);
f2 = -(j-c(2))/(r(i,j,k,c)+1E-12);
f3 = -(k-c(3))/(r(i,j,k,c)+1E-12);
else
f1 = 0;
f2 = 0;
f3 = 0;
end
%QUARTER OF A DROPLET
elseif strcmp(dirfield, 'RADIALD_QTR')
if r_qrt(i,j,k) < R
f1 = -(i)/(r_qrt(i,j,k)+1E-12);
f2 = -(j)/(r_qrt(i,j,k)+1E-12);
f3 = -(k)/(r_qrt(i,j,k)+1E-12);
else
f1 = 0;
f2 = 0;
f3 = 0;
end
%ESCAPED CYLINDER GUIDE
elseif strcmp(dirfield, 'ESCAPEDC')
if sqrt((i-nx/2)^2 + (j-ny/2)^2) < nx/4
f1 = -sin(2*pi*(i-nx/2)/nx);
f2 = -sin(2*pi*(j-ny/2)/nx);
f3 = sqrt(1-f1^2-f2^2);
else
f1 = -(i-nx/2)/sqrt((i-nx/2)^2 + (j-ny/2)^2 +1E-12);
f2 = -(j-ny/2)/sqrt((i-nx/2)^2 + (j-ny/2)^2 +1E-12);
f3 = 0;
end
%BIPOLAR DROPLET
elseif strcmp(dirfield, 'BIPOLAR')
if r(i,j,k,c) < R
th = (k-c(3))/(R*r(i/R,j/R,k/R,c/R));
ph = atan2((j-c(2))/R,(i-c(1))/R);
f1 = cos(th)*cos(ph) / sqrt(cos(th)^2 + sin(th)^2);
f2 = cos(th)*sin(ph) / (cos(th)^2 + sin(th)^2);
f3 = -sin(th) / sqrt(cos(th)^2 + sin(th)^2);
else
f1 = 0;
f2 = 0;
f3 = 0;
end
%BIPOLAR DROPLET in x direction
elseif strcmp(dirfield, 'BIPOLARX')
if r(i,j,k,c) < R
th = (i-c(3))/(R*r(i/R,j/R,k/R,c/R));
ph = atan2((j-c(2))/R,(k-c(3))/R);
f3 = -cos(th)*cos(ph) / sqrt(cos(th)^2 + sin(th)^2);
f2 = cos(th)*sin(ph) / (cos(th)^2 + sin(th)^2);
f1 = -sin(th) / sqrt(cos(th)^2 + sin(th)^2);
else
f1 = 0;
f2 = 0;
f3 = 0;
end
%read DIR from file
elseif strcmp(dirfield, 'FILE')
f1 = dirarray(3*ind(i,j,k)-2);
f2 = dirarray(3*ind(i,j,k)-1);
f3 = dirarray(3*ind(i,j,k)-0);
else
disp('ERROR: Unknown analytical director field');
return;
end
end
%phi angle for heliconics and cholesterics
function f = phi(l,pitch)
f = 2*pi*l/(pitch);
end
%radius for droplets
function f = r(i,j,k,c)
f = sqrt((i-c(1))^2 + (j-c(2))^2 + (k-c(3))^2);
end
%radius for droplets
function f = r_qrt(i,j,k)
f = sqrt((i)^2 + (j)^2 + (k)^2);
end
%calculates eps_o and deps
function f = epsO(i,j,k)
if abs(gain) > 0 && r(i,j,k,c) < R
f = ((nord(i,j,k)+dn(i,j,k))^2 + 2*nord(i,j,k)^2)/3 - gain^2/4;
else
f = ((nord(i,j,k)+dn(i,j,k))^2 + 2*nord(i,j,k)^2)/3;
end
end
function f = deps(i,j,k)
f = (nord(i,j,k)+dn(i,j,k))^2 - nord(i,j,k)^2;
% TW = tukeywin(2*nx/4, 0.4);
% if r(i,j,k)<nx/4
% f = (nord(i,j,k)+TW(round(r(i,j,k))+nx/4)*dn(i,j,k))^2 - nord(i,j,k)^2;
% else
% f = (nord(i,j,k)+dn(i,j,k))^2 - nord(i,j,k)^2;
% end
end
%calculates components of epsilon from director field, accounts for Yee
%lattice shifts
function [eps,mu] = eblock(i,j,k)
if abs(gain) > 0 && r(i,j,k,c) < R
G = - 1i * gain * NO;
else
G = 0;
end
%PML factors
if DPMLs(1) == 0
sxs = 1;
elseif i <= abs(DPMLs(1))
sxs = s(i,nx,-DPMLs(1));
else
sxs = 1;
end
if DPMLs(2) == 0
sys = 1;
elseif j <= abs(DPMLs(2))
sys = s(j,ny,-DPMLs(2));
else
sys = 1;
end
if DPMLs(3) == 0
szs = 1;
elseif k <= abs(DPMLs(3))
szs = s(k,nz,-DPMLs(3));
else
szs = 1;
end
if DPMLe(1) == 0
sxe = 1;
elseif i > nx - DPMLe(1)
sxe = s(i,nx,DPMLe(1));
else
sxe = 1;
end
if DPMLe(2) == 0
sye = 1;
elseif j > ny - DPMLe(2)
sye = s(j,ny,DPMLe(2));
else
sye = 1;
end
if DPMLe(3) == 0
sze = 1;
elseif k > nz - DPMLe(3)
sze = s(k,nz,DPMLe(3));
else
sze = 1;
end
%i+1/2 for exx eyx ezx
[dir1,dir2,dir3]=dir(i + 1/2,j,k);
% Qxx = (3*dir1*dir1 * (1 + 2*G/(3*deps(i+1/2,j,k))) -1)/2;
% Qxy = (3*dir1*dir2 * (1 + 2*G/(3*deps(i+1/2,j,k))))/2;
% Qxz = (3*dir1*dir3 * (1 + 2*G/(3*deps(i+1/2,j,k))))/2;
% Qyy = (3*dir2*dir2 * (1 + 2*G/(3*deps(i+1/2,j,k))) -1)/2;
% Qyz = (3*dir2*dir3 * (1 + 2*G/(3*deps(i+1/2,j,k))))/2;
% Qzz = (3*dir3*dir3 * (1 + 2*G/(3*deps(i+1/2,j,k))) -1)/2;
Qxx = (dir1*dir1 * 3 -1)/2;
Qxy = (dir1*dir2 * 3)/2;
Qxz = (dir1*dir3 * 3)/2;
Qyy = (dir2*dir2 * 3 -1)/2;
Qyz = (dir2*dir3 * 3)/2;
Qzz = (dir3*dir3 * 3 -1)/2;
Qten = [Qxx Qxy Qxz; Qxy Qyy Qyz; Qxz Qyz Qzz];
% [TQ,DQ] = eig(Qten);
% [TQ,DQ] = sortem(TQ,DQ);
% DQ(1,1) = DQ(1,1) * (1 + G/(DQ(1,1)*deps(i+1/2,j,k)));
% DQ(2,2) = DQ(2,2) * (1 + G/(DQ(2,2)*deps(i+1/2,j,k)));
% DQ(3,3) = DQ(3,3) * (1 + G/(DQ(3,3)*deps(i+1/2,j,k)));
% Qten = TQ * DQ * TQ';
epsX = (deps(i + 1/2,j,k) * Qten + (epsO(i + 1/2,j,k)+deps(i + 1/2,j,k)/3) * eye (3));
epsX(1,1) = epsX(1,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsX(1,2) = epsX(1,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsX(1,3) = epsX(1,3) * (sxs*sys/szs) * (sxe*sye/sze);
epsX(2,1) = epsX(2,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsX(2,2) = epsX(2,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsX(2,3) = epsX(2,3) * (sxs*sys/szs) * (sxe*sye/sze);
epsX(3,1) = epsX(3,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsX(3,2) = epsX(3,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsX(3,3) = epsX(3,3) * (sxs*sys/szs) * (sxe*sye/sze);
%j+1/2 for exy eyy ezy
[dir1,dir2,dir3]=dir(i,j+ 1/2,k);
Qxx = (dir1*dir1 * 3 -1)/2;
Qxy = (dir1*dir2 * 3)/2;
Qxz = (dir1*dir3 * 3)/2;
Qyy = (dir2*dir2 * 3 -1)/2;
Qyz = (dir2*dir3 * 3)/2;
Qzz = (dir3*dir3 * 3 -1)/2;
Qten = [Qxx Qxy Qxz; Qxy Qyy Qyz; Qxz Qyz Qzz];
% [TQ,DQ] = eig(Qten);
% [TQ,DQ] = sortem(TQ,DQ);
% DQ(1,1) = DQ(1,1) * (1 + G/(DQ(1,1)*deps(i,j+1/2,k)));
% DQ(2,2) = DQ(2,2) * (1 + G/(DQ(2,2)*deps(i,j+1/2,k)));
% DQ(3,3) = DQ(3,3) * (1 + G/(DQ(3,3)*deps(i,j+1/2,k)));
% Qten = TQ * DQ * TQ';
epsY = (deps(i,j+ 1/2,k) * Qten + (epsO(i,j+ 1/2,k)+deps(i,j+ 1/2,k)/3) * eye (3));
epsY(1,1) = epsY(1,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsY(1,2) = epsY(1,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsY(1,3) = epsY(1,3) * (sxs*sys/szs) * (sxe*sye/sze);
epsY(2,1) = epsY(2,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsY(2,2) = epsY(2,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsY(2,3) = epsY(2,3) * (sxs*sys/szs) * (sxe*sye/sze);
epsY(3,1) = epsY(3,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsY(3,2) = epsY(3,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsY(3,3) = epsY(3,3) * (sxs*sys/szs) * (sxe*sye/sze);
%k+1/2 for exz eyz ezz
[dir1,dir2,dir3]=dir(i,j,k+ 1/2);
Qxx = (dir1*dir1 * 3 -1)/2;
Qxy = (dir1*dir2 * 3)/2;
Qxz = (dir1*dir3 * 3)/2;
Qyy = (dir2*dir2 * 3 -1)/2;
Qyz = (dir2*dir3 * 3)/2;
Qzz = (dir3*dir3 * 3 -1)/2;
Qten = [Qxx Qxy Qxz; Qxy Qyy Qyz; Qxz Qyz Qzz];
% [TQ,DQ] = eig(Qten);
% [TQ,DQ] = sortem(TQ,DQ);
% DQ(1,1) = DQ(1,1) * (1 + G/(DQ(1,1)*deps(i,j,k+1/2)));
% DQ(2,2) = DQ(2,2) * (1 + G/(DQ(2,2)*deps(i,j,k+1/2)));
% DQ(3,3) = DQ(3,3) * (1 + G/(DQ(3,3)*deps(i,j,k+1/2)));
% Qten = TQ * DQ * TQ';
epsZ = (deps(i,j,k+ 1/2) * Qten + (epsO(i,j,k+ 1/2)+deps(i,j,k+ 1/2)/3) * eye (3));
epsZ(1,1) = epsZ(1,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsZ(1,2) = epsZ(1,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsZ(1,3) = epsZ(1,3) * (sxs*sys/szs) * (sxe*sye/sze);
epsZ(2,1) = epsZ(2,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsZ(2,2) = epsZ(2,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsZ(2,3) = epsZ(2,3) * (sxs*sys/szs) * (sxe*sye/sze);
epsZ(3,1) = epsZ(3,1) * (sys*szs/sxs) * (sye*sze/sxe);
epsZ(3,2) = epsZ(3,2) * (sxs*szs/sys) * (sxe*sze/sye);
epsZ(3,3) = epsZ(3,3) * (sxs*sys/szs) * (sxe*sye/sze);
eps = [epsX(1,1) epsY(1,2) epsZ(1,3); epsX(2,1) epsY(2,2) epsZ(2,3); epsX(3,1) epsY(3,2) epsZ(3,3)];
%mu tensor
mxx = sqrt((sxs/(sys*szs)) * (sxe/(sye*sze)) );
myy = sqrt((sys/(sxs*szs)) * (sye/(sxe*sze)) );
mzz = sqrt((szs/(sxs*sys)) * (sze/(sxe*sye)) );
%only mu^(-1/2) is needed in calculations
mu = [mxx 0 0; 0 myy 0; 0 0 mzz];
end
%PML FUNCTIONS
function sout = s(l,n,PML)
sigma1 = 10*2*lambda2/(4*pi*abs(PML));
sout = psi(l,n,PML) - 1i * sigma1 * eta(l,n,PML);
end
%coordinate stretching
function psiout = psi(l,n,PML)
psiout = 1;
% if PML > 0
% if l > R
% psiout = ((n-l)/(n-R))^2;
% else
% psiout = 1;
% end
% elseif PML < 0
% if l < R
% psiout = ((l)/(R))^2;
% else
% psiout = 1;
% end
% else
% psiout = 1;
% end
end
function etaout = eta(l,n,PML)
if PML < 0 && l <= abs(PML)
etaout = (abs((l-abs(PML)))/abs(PML))^3;
elseif PML > 0 && l > n - PML
etaout = (abs((l-(n-PML)))/PML)^3;
else
etaout = 0;
end
end
function [P2,D2]=sortem(P,D)
% this function takes in two matrices P and D, presumably the output
% from Matlab's eig function, and then sorts the columns of P to
% match the sorted columns of D (going from largest to smallest)
%
% EXAMPLE:
%
% D =
% -90 0 0
% 0 -30 0
% 0 0 -60
% P =
% 1 2 3
% 1 2 3
% 1 2 3
%
% [P,D]=sortem(P,D)
% P =
% 2 3 1
% 2 3 1
% 2 3 1
% D =
% -30 0 0
% 0 -60 0
% 0 0 -90
D2=diag(sort(diag(D),'descend')); % make diagonal matrix out of sorted diagonal values of input D
[~, ind]=sort(diag(D),'descend'); % store the indices of which columns the sorted eigenvalues come from
P2=P(:,ind); % arrange the columns in this order
end
function A = read_dir(filename)
fileID = fopen(filename,'r');
A = fread(fileID,'float');
fclose(fileID);
end
function [] = exportdir(name)
dirx = zeros(nx,ny,nz);
diry = zeros(nx,ny,nz);
dirz = zeros(nx,ny,nz);
for di = 1:nx
for dj = 1:ny
for dk = 1:nz
[dirx(di,dj,dk),diry(di,dj,dk),dirz(di,dj,dk)] = dir(di,dj,dk);
end
end
end
dirout = cat(4,dirx,diry,dirz);
dirout = permute(dirout, [4,1,2,3]);
outvec = strcat(num2str(file),'_DIR_',name,'_',num2str(nx),'_',num2str(ny),'_',num2str(nz),'.raw');
fid = fopen(outvec,'w');
fwrite(fid,dirout,'float');
fclose(fid);
end
end