calculate_material_component_values_2d.m

The Finite Difference Time Domain Method for Electromagnetics With MATLAB Simulations Atef Elshe

disp('filling material components arrays');

% creating temporary 1D arrays for storing 
% parameter values of material types
for ind = 1:size(material_types,2)
    t_eps_r(ind)   = material_types(ind).eps_r;
    t_mu_r(ind)    = material_types(ind).mu_r;
    t_sigma_e(ind) = material_types(ind).sigma_e;
    t_sigma_m(ind) = material_types(ind).sigma_m;
end

% assign negligibly small values to t_mu_r and t_sigma_m where they are
% zero in order to prevent division by zero error 
t_mu_r(find(t_mu_r==0)) = 1e-20;
t_sigma_m(find(t_sigma_m==0)) = 1e-20;

disp('Calculating eps_r_x');
% eps_r_x(i,j) is average of two cells 
% (i,j),(i,j-1) 
eps_r_x(1:nx,2:ny) = 0.5 * (t_eps_r(material_2d_space(1:nx,2:ny)) ...
                        + t_eps_r(material_2d_space(1:nx,1:ny-1)));

disp('Calculating eps_r_y');
% eps_r_y(i,j) is average of two cells 
% (i,j,k),(i-1,j,k) 
eps_r_y(2:nx,1:ny) = 0.5 * (t_eps_r(material_2d_space(2:nx,1:ny)) ...
                        + t_eps_r(material_2d_space(1:nx-1,1:ny)));
                    
disp('Calculating eps_r_z');
% eps_r_z(i,j) is average of four cells 
% (i,j),(i-1,j), (i,j-1), (i-1,j-1) 
eps_r_z(2:nx,2:ny) = 0.25 * (t_eps_r(material_2d_space(2:nx,2:ny)) ...
                        + t_eps_r(material_2d_space(1:nx-1,2:ny)) ...
                        + t_eps_r(material_2d_space(2:nx,1:ny-1)) ...
                        + t_eps_r(material_2d_space(1:nx-1,1:ny-1)));

disp('Calculating sigma_e_x');
% sigma_e_x(i,j) is average of two cells (i,j),(i,j-1) 
sigma_e_x(1:nx,2:ny) = 0.5 * (t_sigma_e(material_2d_space(1:nx,2:ny)) ...
                        + t_sigma_e(material_2d_space(1:nx,1:ny-1)));

disp('Calculating sigma_e_y');
% sigma_e_y(i,j) is average of two cells (i,j),(i-1,j)
sigma_e_y(2:nx,1:ny) = 0.5 * (t_sigma_e(material_2d_space(2:nx,1:ny)) ...
                        + t_sigma_e(material_2d_space(1:nx-1,1:ny)));
                    
disp('Calculating sigma_e_z');
% sigma_e_z(i,j) is average of four cells
% (i,j),(i-1,j), (i,j-1), (i-1,j-1) 
sigma_e_z(2:nx,2:ny) = 0.25 * (t_sigma_e(material_2d_space(2:nx,2:ny)) ...
                        + t_sigma_e(material_2d_space(1:nx-1,2:ny)) ...
                        + t_sigma_e(material_2d_space(2:nx,1:ny-1)) ...
                        + t_sigma_e(material_2d_space(1:nx-1,1:ny-1)));

                    
disp('Calculating mu_r_x');
% mu_r_x(i,j) is average of two cells (i,j),(i-1,j)
mu_r_x(2:nx,1:ny) = 2 * (t_mu_r(material_2d_space(2:nx,1:ny)) ...
                        .* t_mu_r(material_2d_space(1:nx-1,1:ny))) ...
                        ./(t_mu_r(material_2d_space(2:nx,1:ny)) ...
                        + t_mu_r(material_2d_space(1:nx-1,1:ny)));
                    
disp('Calculating mu_r_y');
% mu_r_y(i,j) is average of two cells (i,j),(i,j-1)
mu_r_y(1:nx,2:ny) = 2 * (t_mu_r(material_2d_space(1:nx,2:ny)) ...
                        .* t_mu_r(material_2d_space(1:nx,1:ny-1))) ...
                        ./(t_mu_r(material_2d_space(1:nx,2:ny)) ...
                        + t_mu_r(material_2d_space(1:nx,1:ny-1)));
                    
disp('Calculating mu_r_z');
% mu_r_z(i,j) is equal to one cell (i,j,k)
mu_r_z(1:nx,1:ny) = t_mu_r(material_2d_space(1:nx,1:ny));
                    
disp('Calculating sigma_m_x');
% sigma_m_x(i,j) is average of two cells (i,j),(i-1,j)
sigma_m_x(2:nx,1:ny) = 2 * (t_sigma_m(material_2d_space(2:nx,1:ny)) ...
                        .* t_sigma_m(material_2d_space(1:nx-1,1:ny))) ...
                        ./(t_sigma_m(material_2d_space(2:nx,1:ny)) ...
                        + t_sigma_m(material_2d_space(1:nx-1,1:ny)));
                    
disp('Calculating sigma_m_y');
% sigma_m_y(i,j) is average of two cells (i,j),(i,j-1)
sigma_m_y(1:nx,2:ny) = 2 * (t_sigma_m(material_2d_space(1:nx,2:ny)) ...
                        .* t_sigma_m(material_2d_space(1:nx,1:ny-1))) ...
                        ./(t_sigma_m(material_2d_space(1:nx,2:ny)) ...
                        + t_sigma_m(material_2d_space(1:nx,1:ny-1)));
                    
disp('Calculating sigma_m_z');
% sigma_m_z(i,j) is equal to one cell (i,j)
sigma_m_z(1:nx,1:ny) = t_sigma_m(material_2d_space(1:nx,1:ny));