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build_lhs2.m
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build_lhs2.m
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function [lhsmat] = build_lhs2(xs,ys)
%Builds the matrix of streamfunction contributions from cylinder.
%Matrix [A] in handout, Eqn 6.
np = length(xs)-1;
%initialise psi matrix
psip = zeros(np, np+1);
xa=repmat(xs(1:np),np,1);
ya=repmat(ys(1:np),np,1);
xb=repmat(xs(2:np+1),np,1);
yb=repmat(ys(2:np+1),np,1);
x= xa';
y= ya';
[infa, infb]=panelinf(xa,ya,xb,yb,x,y);
psip(:,1)=infa(:,1);
psip(:,2:np)=infa(:,2:np)+infb(:,1:np-1);
psip(:,np+1)=infb(:,np);
% build lhs matrix
lhsmat = zeros(np+1,np+1);
%special cases gamma 1 and gamma 0
lhsmat(1,1) = 1;
lhsmat(np+1,np+1) = 1;
i=2:np;
lhsmat(i,:)=psip(i,:)-psip(i-1,:);
end