% ALTTST
%
% example of alternating Schwarz iteration
% for -u_xx - u_yy = f
% 
%
stats=zeros(10,3);
for p=1:3
mp=p+4;
m=2^mp-1; h=1/(m+1);
x=1:m; x=x'*h; y=x;
%
% overlap = fraction of m means convergence rate is independent of h
%         = constant means convergence rate increases as h decreases
%
%overlap=floor(m/10);
overlap=3;
%
% Fix the right side so that the solution is
%
% u(x,y) = sin(pi x) sin(pi y) e^x
%
        wx=sin(pi*x); wxp=pi*cos(pi*x); wxpp=-pi*pi*wx;
        wy=wx; wypp=wxpp;
        u=(wx.*exp(x))*wy';
        wxx=(wx + 2*wxp + wxpp).*exp(x); uxx=wxx*wy';
        wyy=wypp; uyy=(wx.*exp(x))*wyy';
	rhs2d=-(uxx+uyy);
%
%
%
uin=zeros(m,m);
[u2d,stats(:,p)]=altsw(m,rhs2d,uin,overlap);
u1=u2d(:); r1=rhs2d(:); err=norm(lapmf(u1)-r1,inf)
end
%
% look at the convergence reates
%
stats(2:10,:)./stats(1:9,:)