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%                       Matlab-Tutorium: PDE Toolbox                      %
%                                                                         %
%                                Aufgabe 2                                %
%                                                                         %
%                            Michael Pokojovy                             %
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[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', [-2 2]);
set(ax, 'YLim', [-2 2]);
set(ax, 'XTickMode', 'auto');
set(ax, 'YTickMode', 'auto');
pdetool('gridon', 'on');

% Geometrie des Gebietes Omega:
pdecirc(0, 0, 2, 'C1');
pderect([-1 1 -1 1], 'SQ1');

% Mengenformel (set formula):
set(findobj(get(pde_fig,'Children'), 'Tag', 'PDEEval'), 'String', 'C1-SQ1');

% Randbedingungen:
% Gamma_2 : Rand des Quadrats, Dirichletsche Randbedingungen
pdetool('changemode', 0);
rb = 'sqrt(x.*x + y.*y)';
for k = 1:4
     pdesetbd(k, 'dir', 1, '1', rb)     
end

% Gamma_1 : Rand des Kreises, Dirichletsche Randbedingungen
rb = '1';
for k = 5:8
     pdesetbd(k, 'dir', 1, '1', rb)     
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 = 'cos(x.*x + y.*y)';
pdeseteq(1, str2mat('1', '1/2', '1/2', '1'), '-1.0', 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)')