INTEGARTION OF BESSELH function
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george veropoulos
on 19 Nov 2024
Commented: Walter Roberson
on 22 Nov 2024
Hi
i make a code where i integrate the hankel function besselh(0, 2)
function z = Escat(r,phi)
[f,N,ra,k0,Z0] =parameter();
[Is]=currentMoM()
Phim=zeros(N+1);
FINAL=0;
for jj=1:N
%Phi0(jj)=(jj-1).*(pi./N);
Phi0(jj)=(jj-1).*(2.*pi./N);
FINAL=FINAL-(k0.*Z0./4).*Is(jj).*ra.*integral(@(xx)besselh(0,2,k0.*sqrt(ra.^2+r.^2-2.*r.*ra.*(phi-xx))),Phi0(jj),2*pi/N+Phi0(jj));
end
z=FINAL;
end
when i plot the function in the range φ=0 : 2π with r=const the valus of Escat are extremely big value ...
clear all
clc
[f,N,ra,k0,Z0] = parameter();
%ph_i=pi/2;
rho=10.*ra ;
phi=0:pi/180:2*pi;
Es=zeros(length(phi));
%phi=0:pi/200:pi/3
for jj=1:length(phi)
Es(jj)=abs(Escat(rho,phi(jj)));
end
plot(phi*(180./pi),Es,'b--')
hold on
%plot(phi*(180./pi),abs(integ),'b--')
plot(phi,abs(Escattheory_new(rho,phi)),'r-')
xlabel('$\phi$','Interpreter','latex')
ylabel('$|E_{s}|$','Interpreter','latex' )
%legend('MoM', 'Theory')
hold off
can i check if the the integration is ok ?
the parameter fucntion is
function [f,N,ra,k0,Z0] = parameter()
%UNTITLED Summary of this function goes here
c0=3e8;
Z0=120.*pi;
ra=1;
N=80;
f=300e6;
lambda=c0./f;
k0=2*pi./lambda;
end
thank you
6 Comments
Steven Lord
on 20 Nov 2024
If you're adding information, please put it as a comment rather than a separate answer. Leave the answer for posts that may be a solution to the problem, to make them easier to distinguish from commentary.
Walter Roberson
on 22 Nov 2024
Note that function e_n leaves y undefined in the case where k is NaN.
If k cannot be NaN then there is no point in using elseif -- just use else
Accepted Answer
David Goodmanson
on 22 Nov 2024
Edited: David Goodmanson
on 22 Nov 2024
Hi george,
I don't know what the values of your parameters are, but it appears that the problem with Escat is that
besselh(0,2,k0.*sqrt(ra.^2+r.^2-2.*r.*ra.*(phi-xx)))
is missing a cosine factor and should be
besselh(0,2,k0.*sqrt(ra.^2+r.^2-2.*r.*ra.*cos(phi-xx)))
Without the cosine, it's possible for the argument of the sqrt to become negative, which causes the argument of besselh to become imaginary, which leads to very large values in the result.
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