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spclibs/examples/dirichlet/poisson.m
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poisson.m
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%
% @file poisson.m
%
% @brief
%
% @copyright
% Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
% SPC (Swiss Plasma Center)
%
% spclibs is free software: you can redistribute it and/or modify it under
% the terms of the GNU Lesser General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your option)
% any later version.
%
% spclibs is distributed in the hope that it will be useful, but WITHOUT ANY
% WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
%
% You should have received a copy of the GNU Lesser General Public License
% along with this program. If not, see <https://www.gnu.org/licenses/>.
%
% @authors
% (in alphabetical order)
% @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
%
file='poisson.h5';
m=3;
%
% Get data from data sets
%
r=hdf5read(file,'/xgrid');
t=hdf5read(file,'/ygrid');
sol=hdf5read(file,'/sol')';
solexact=hdf5read(file,'/solana')';
err=hdf5read(file,'/errors')';
solr=hdf5read(file,'/derivx')';
solt=hdf5read(file,'/derivy')';
[R,T]=meshgrid(r,t);
x = R.*cos(T); y= R.*sin(T);
solx = cos(T).*solr - sin(T)./R.*solt;
soly = sin(T).*solr + cos(T)./R.*solt;
figure
subplot(221)
pcolor(double(r),double(t),double(sol));
shading interp
hold on, quiver(r,t,solr,solt)
xlabel('r'); ylabel('\theta')
title('R-THETA plane')
colorbar
subplot(222)
pcolor(double(x),double(y),double(sol))
shading interp
hold on, quiver(x,y,solx,soly)
hold off, axis image
xlabel('X'); ylabel('Y')
title('X-Y plane')
colorbar
subplot(223)
surfc(double(x),double(y),double(sol))
xlabel('X'); ylabel('Y');
title('Solutions')
subplot(224)
surfc(double(x),double(y),double(err))
xlabel('X'); ylabel('Y');
title('Errors')
figure
subplot(211)
plot(r,sol(1,:),'o',r,solexact(1,:))
xlabel('r')
ylabel('Solutions at \theta=0')
grid on
subplot(212)
tt=0:0.01:2*pi;
plot(t,sol(:,end),'o',tt,cos(m.*tt))
xlabel('\theta')
ylabel('Solutions at r=1')
grid on
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