%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                       Matlab-Tutorium: PDE Toolbox                      %
%                                                                         %
%                                Aufgabe 4                                %
%                                                                         %
%                            Michael Pokojovy                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[pde_fig,ax] = pdeinit;
pdetool('appl_cb', 1);
pdetool('snapon', 'on');
set(ax, 'DataAspectRatio', [1 1 1]);
set(ax, 'PlotBoxAspectRatio', [1.5 1 1]);
set(ax, 'XLim', [-5 5]);
set(ax, 'YLim', [-2 2]);
set(ax, 'XTickMode', 'auto');
set(ax, 'YTickMode', 'auto');
pdetool('gridon', 'on');

% Geometrie des Gebietes Omega:
pderect([-3 3 -2 2], 'R');
pdeellip(-3, 0, 2, 2, 0,  'E1');
pdeellip( 3, 0, 2, 2, 0,  'E2');
pdeellip( 0, 0, 2, 1, pi/6, 'E3');

% Mengenformel (set formula):
set(findobj(get(pde_fig,'Children'),'Tag','PDEEval'), 'String', '(R+E1+E2)-E3')

% Randbedingungen
% Gamma_1 : Dirichletsche Randbedingungen
pdetool('changemode', 0);
I = [1 3 5 8 10 11];
for k = 1:6
    pdesetbd(I(k), 'dir', 1, '1', '1');     
end

% Gamma_2 : Robinsche Randbedingungen
for k = 13:18
    pdesetbd(k, 'neu', 1, '1', '0');     
end

% Erstellung der Triangulierung:
refine_count = 1;
setuprop(pde_fig, 'Hgrad', 1.6);
setuprop(pde_fig, 'refinemethod', 'regular');
pdetool('initmesh')
for k = 1:refine_count
    pdetool('refine')
end
 
% Koeffizienten der PDG:
funktion = '1/4*(x.*x + y.*y)';
pdeseteq(1, str2mat('2', '0', '0', '5'), '1', funktion, '1.0', '0:10', '0.0', '0.0', '[0 100]')

setuprop(pde_fig, 'currparam', ['1.0'; '0.0'; '0  '; '1.0'])
 
% Parameter fuer "solve":
setuprop(pde_fig,'solveparam',...
str2mat('0', '1176', '10', 'pdeadworst', '0.5', 'longest', '0', '1E-4', '', 'fixed', 'Inf'))
 
% Darstellungsparameter:
setuprop(pde_fig,'plotflags', [1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1]);
setuprop(pde_fig,'colstring','');
setuprop(pde_fig,'arrowstring','');
setuprop(pde_fig,'deformstring','');
setuprop(pde_fig,'heightstring','');

% Loesung der PDG:
pdetool('solve')
title('\it u(x, y)')