SquareMesh.m

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function Th=SquareMesh(N)
% function Th=SquareMesh(N)
% Initialization of the Mesh structure for a square domain
%
% Square domain is `[0,1]\times[0,1]`.<br/>
%
% This mesh has 4 boundary labels :
%   - label 1 : boundary `y=0`
%   - label 2 : boundary `x=1`
%   - label 3 : boundary `y=1`
%   - label 4 : boundary `x=0` <br/>
% There are N+1 points on each boundary.
%
% Parameters:
%  N: integer, number of elements on a boundary
%
% Return values:
%  Th: mesh structure
%
% See also
%  #ComputeAreaOpt, EdgeLengthOpt
%
% OptFEM2DP1 [V1.0d] -    Copyright (C) 2013  CJS (LAGA)
%
%   This file is part of OptFEM2DP1.
%   OptFEM2DP1 is free software: you can redistribute it and/or modify
%   it under the terms of the GNU General Public License as published by
%   the Free Software Foundation, either version 3 of the License, or
%   (at your option) any later version.
%
%   OptFEM2DP1 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 General Public License
%   along with this program.  If not, see <http://www.gnu.org/licenses/>.
  h=1/N;t=0:h:1;
  if isOctave()
    mesh=msh2m_structured_mesh(t,t,1,1:4); % package msh
    me=mesh.t(1:3,:);
    q=mesh.p;
  else
    [x,y] = meshgrid(t,t);
    q=[x(:) y(:)]';
    tri = delaunay(x,y);
    me=tri';
  end
  
  nq=length(q);
  nme=length(me);
  
  ql=zeros(1,nq);
  be=zeros(2,4*N);
  bel=zeros(1,4*N);
  % Points du bord
  ql=zeros(1,nq);
  I=find(q(2,:)==0);
  ql(I)=1;
  be(:,1:N)=[I(1:end-1);I(2:end)];
  bel(:,1:N)=1;
  I=find(q(1,:)==1);
  ql(I)=2;
  be(:,N+1:2*N)=[I(1:end-1);I(2:end)];
  bel(:,N+1:2*N)=2;
  I=find(q(2,:)==1);
  ql(I)=3;
  I=fliplr(I);
  be(:,2*N+1:3*N)=[I(1:end-1);I(2:end)];
  bel(:,2*N+1:3*N)=3;
  I=find(q(1,:)==0);
  ql(I)=4;
  I=fliplr(I);
  be(:,3*N+1:4*N)=[I(1:end-1);I(2:end)];
  bel(:,3*N+1:4*N)=4;
  
  Th=struct('q',q,'me',me,'ql',ql,'mel',zeros(1,nme),'be',be,'bel',bel, ...
            'nq',size(q,2), ...
            'nme',size(me,2), ...
            'nbe',size(be,2), ...
            'areas',ComputeAreaOpt(q,me),...
            'lbe',EdgeLengthOpt(be,q));