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potentials.m
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classdef potentials
properties
SL % Single layer
DL % Double layer
end
methods
function obj = cctor_local(obj,k,x,prt)
obj.SL = SL_potential(k,x,prt);
obj.DL = DL_potential(k,x,prt);
end
function obj = cctor(obj,k,x,geo)
for t_int = 1:geo.n_parts
prt_int = geo.get_part(t_int);
S = SL_potential(k,x,prt_int);
D = DL_potential(k,x,prt_int);
if (t_int == 1)
AS = S;
AD = D;
else
AS = [AS S];
AD = [AD D];
end
end
obj.SL = AS;
obj.DL = AD;
end
%-------------------------------------------------------------------------%
end
end
%%
function DL = DL_potential(k,x,prt_i)
Npe = numel(x(:,1));
Npi = prt_i.Np;
% Evaluation point
x1 = x(:,1);
x2 = x(:,2);
x_1 = repmat(x1,1,Npi);
x_2 = repmat(x2,1,Npi);
% Integration point
xp1 = prt_i.x(:,1);
xp2 = prt_i.x(:,2);
dxp1 = prt_i.dx(:,1);
dxp2 = prt_i.dx(:,2);
xp_1 = repmat(xp1.',Npe,1);
xp_2 = repmat(xp2.',Npe,1);
dxp_1 = repmat(dxp1.',Npe,1);
dxp_2 = repmat(dxp2.',Npe,1);
%%%
%tol = 1e-4;
r = sqrt((x_1-xp_1).^2+(x_2-xp_2).^2);
%r = r.* (r>tol) + tol*(r<=tol);
dW = repmat(prt_i.dw.',Npe,1);
DL = (1i*k/4*besselh(1,k*r)./r.*((x_1-xp_1).*dxp_2-(x_2-xp_2).*dxp_1)*pi/prt_i.N).*dW;
%% Complex interpolation
% tol = 1e-4;
%
% ind = (r<=tol);
%
% h = 2*tol;
% for n=1:size(ind,1)
%
% for m=1:size(ind,2)
%
% if ind(n,m)
%
% x_eval = x(n,:);
% x_int = prt.x(m,:);
%
% x1 = x_eval+1i*h/2*[1 1];
% r1 = sqrt((x1(1)-x_int(1)).^2+(x1(2)-x_int(2)).^2);
% A1 = besselh(1,k*r1)/r1;
%
% x2 = x_eval+1i*h/2*[-1 1];
% r2 = sqrt((x2(1)-x_int(1)).^2+(x2(2)-x_int(2)).^2);
% A2 = besselh(1,k*r2)/r2;
%
% x3 = x_eval+1i*h/2*[-1 -1];
% r3 = sqrt((x4(1)-x_int(1)).^2+(x3(2)-x_int(2)).^2);
% A3 = besselh(1,k*r3)/r3;
%
% x4 = x_eval+1i*h/2*[1 -1];
% r4 = sqrt((x4(1)-x_int(1)).^2+(x4(2)-x_int(2)).^2);
% A4 = besselh(1,k*r4)/r4;
%
% DL(n,m) = (1i/16.*(A1+A2+A3+A4)*((x_1(n,m)-xp_1(n,m))*dxp_2(n,m)-(x_2(n,m)-xp_2(n,m))*dxp_1(n,m))*pi/prt_i.N)*dW(n,m);
%
% end
%
% end
%end
end
%%
function SL = SL_potential(k,x,prt_i)
Npi = prt_i.Np;
Npe = numel(x(:,1));
x1 = x(:,1);
x2 = x(:,2);
xp1 = prt_i.x(:,1);
xp2 = prt_i.x(:,2);
dxp1 = prt_i.dx(:,1);
dxp2 = prt_i.dx(:,2);
xp_1 = repmat(xp1.',Npe,1);
xp_2 = repmat(xp2.',Npe,1);
x_1 = repmat(x1,1,Npi);
x_2 = repmat(x2,1,Npi);
dxp_1 = repmat(dxp1.',Npe,1);
dxp_2 = repmat(dxp2.',Npe,1);
tol = 1e-4;
r = sqrt((x_1-xp_1).^2+(x_2-xp_2).^2);
%r = r.* (r>tol) + tol*(r<=tol);
tau = sqrt(dxp_1.^2+dxp_2.^2);
dW = repmat(prt_i.dw.',Npe,1);
SL = (1i/4.*besselh(0,k*r) .* tau * pi/prt_i.N).*dW;
%% Complex interpolation
% tol = 1e-4;
%
% ind = (r<=tol);
%
% h = 2*tol;
%
% for n=1:size(ind,1)
%
% for m=1:size(ind,2)
%
% if ind(n,m)
%
% x_eval = x(n,:);
% x_int = prt.x(m,:);
%
% x1 = x_eval+1i*h/2*[1 1];
% r1 = sqrt((x1(1)-x_int(1)).^2+(x1(2)-x_int(2)).^2);
% A1 = besselh(0,k*r1);
%
% x2 = x_eval+1i*h/2*[-1 1];
% r2 = sqrt((x2(1)-x_int(1)).^2+(x2(2)-x_int(2)).^2);
% A2 = besselh(0,k*r2);
%
% x3 = x_eval+1i*h/2*[-1 -1];
% r3 = sqrt((x4(1)-x_int(1)).^2+(x3(2)-x_int(2)).^2);
% A3 = besselh(0,k*r3);
%
% x4 = x_eval+1i*h/2*[1 -1];
% r4 = sqrt((x4(1)-x_int(1)).^2+(x4(2)-x_int(2)).^2);
% A4 = besselh(0,k*r4);
%
% SL(n,m) = (1i/16.*(A1+A2+A3+A4)* tau(n,m) * pi/prt_i.N)*dW(n,m);
%
% end
%
% end
%
% end
end