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Markus Schmidt 2026-01-06 14:05:44 +01:00
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% Square:
% flatpak run org.octave.Octave <filename>
% or
% octave --no-window-system --no-gui -qf <filename>
clear all
clc
% %% L-shape
% g=[2 0 2 0 0 1 0; % #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
% 2 2 2 0 1 1 0;
% 2 2 1 1 0.5 1 0;
% 2 1 1 0.5 2 1 0;
% 2 1 0 2 2 1 0;
% 2 0 0 2 0 1 0]';
%% square
% g=[2 0 1 0 0 1 0; % #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
% 2 1 1 0 1 1 0;
% 2 1 0 1 1 1 0;
% 2 0 0 1 0 1 0]';
% %% 2 squares
% g=[2 0 1 0 0 1 0; % 1 #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
% 2 1 1 0 1 1 2;
% 2 1 0 1 1 1 0;
% 2 0 0 1 0 1 0;
% 2 1 2 0 0 2 0; % 2 #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
% 2 2 2 0 1 2 0;
% 2 2 1 1 1 2 0
% ]';
%% 4 squares
g=[2 0 1 0 0 1 0; % 1 #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
2 1 1 0 1 1 2;
2 1 0 1 1 1 3;
2 0 0 1 0 1 0;
2 1 2 0 0 2 0; % 2 #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
2 2 2 0 1 2 0;
2 2 1 1 1 2 4;
% 2 1 1 1 0 2 1;
% 2 0 1 1 1 3 1; % 3 #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
2 1 1 1 2 3 4;
2 1 0 2 2 3 0;
2 0 0 2 1 3 0;
% 2 1 2 1 1 4 2; % 4 #vertices,v_1x, v_2x, v_1y, v_2y, subdomain_left, subdomain_right
2 2 2 1 2 4 0;
2 2 1 2 2 4 0
% 2 1 1 2 1 4 3
]';
%% Generate mesh from geometry
%
[p,e,t] = initmesh(g,'hmax',1); % works correctly
% p(1,15) = 1.51; %% angle in trangle > pi/2 ==> now the second refinement produces irregular meshes!
% p(1,15) = 1.7; %% angle in trangle > pi/2 ==> now the second refinement produces irregular meshes!
% ??
% https://de.mathworks.com/help/pde/ug/mesh-data-pet-triples.html
% generateMesh(...)
% mesh2Pet(...)
%
% [p,e,t] = initmesh(g); % problems in solution after 2 refinements
% [p,e,t] = initmesh(g,'hmax',0.5); % problems in solution after 2 refinements (peaks with h=0.5, oscillations in (1,1) for h=0.1
% [p,e,t] = initmesh(g,'hmax',0.1/4); % no problems in solution with 0 refinemnet steps
%% Show mesh
pdemesh(p,e,t)
% pdemesh(p,e,t,'NodeLabels','on')
%% Improve mesh
% min(pdetriq(p,t))
% p = jigglemesh(p,e,t,'opt','minimum','iter',inf);
% min(pdetriq(p,t))
% pdemesh(p,e,t)
%% Refine mesh, see comments in "Generate mesh from geometry"
%
% nrefine=8;
nrefine=2; %
for k=1:nrefine
[p,e,t] = refinemesh(g,p,e,t);
% p = jigglemesh(p,e,t,'opt','minimum','iter',inf); % improve mesh
min(pdetriq(p,t))
fprintf('refinement: %i nodes: %i triangles: %i \n', k, size(p,2), size(t,2))
end
% figure; pdemesh(p,e,t,'NodeLabels','on')
%
%% GH
% output from <https://de.mathworks.com/help/pde/ug/initmesh.html initmesh>
%
% coordinates p: [2][nnode]
% connectivity t: [4][nelem] with t(4,:) are the subdomain numbers
% edges e: [7][nedges] boundary edges
% e([1,2],:) - start/end vertex of edge
% e([3,4],:) - start/end values
% e(5,:) - segment number
% e([6,7],:) - left/right subdomain
ascii_write_mesh( p, t, e, mfilename);
ascii_write_subdomains( p, t, e, mfilename);
% tmp=t(1:3,:)