%% Example for 4D singular integrals arising in IE formulations
% Licensing: This code is distributed under the GNU LGPL license.
% Modified: 8 February 2013
% Author: Athanasios Polimeridis
% References
% A. G. Polimeridis, ?Direct evaluation method in computational electromagnetics (DEMCEM) package,? 2011.
% [Online]. Available: http://lema.epfl.ch/Members/thanos/Software.html
% A. G. Polimeridis and T. V. Yioultsis, “On the direct evaluation of weakly singular
% integrals in Galerkin mixed potential integral equation formulations,” IEEE Trans.
% Antennas Propag., vol. 56, no. 9, pp. 3011-3019, Sep. 2008.
% A. G. Polimeridis and J. R. Mosig, “Complete semi-analytical treatment of weakly
% singular integrals on planar triangles via the direct evaluation method,” Int. J.
% Numerical Methods Eng., vol. 83, pp. 1625-1650, 2010.
% A. G. Polimeridis, J. M. Tamayo, J. M. Rius and J. R. Mosig, “Fast and accurate
% computation of hyper-singular integrals in Galerkin surface integral equation
% formulations via the direct evaluation method,” IEEE Trans.
% Antennas Propag., vol. 59, no. 6, pp. 2329-2340, Jun. 2011.
% A. G. Polimeridis and J. R. Mosig, “On the direct evaluation of surface integral
% equation impedance matrix elements involving point singularities,” IEEE Antennas
% Wireless Propag. Lett., vol. 10, pp. 599-602, 2011.
% INPUT DATA
% f = working frequency
% dx, dy = dimensions of rectangle
% Np_1D = order of the Gauss-Legendre quadrature rule
% OUTPUT DATA
% I_ST = Singular Galerkin inner product for coincident
% elements, where the kernel is just the free-space Green's
% function (or Helmholtz fundamental solution), i.e.,
% G = exp(-j*k*r) / (4*pi*r)
%
clear all
close all
global ko
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% INPUT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f = 300e6; % working frequency
dx = 1e-6; % dx,dy = edge lengths for the rectangle
dy = dx;
Np_1D = 10; % Order of 1D Gauss quadrature
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EM basic parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mu = 4*pi*1e-7;
co = 299792458;
eo = 1/co^2/mu;
%
omega = 2 * pi * f;
lambda = co/f;
%
ko = 2*pi/lambda % wavenumber
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Compute Self-Term
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[I_ST] = DEMCEM_ST(Np_1D,dx,dy);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PRINT RESULTS %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fprintf('Np_1D: %d \n', Np_1D)
fprintf('I_ST: (%4.16e, %4.16e) \n', real(I_ST),imag(I_ST))