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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/REC-html40/loose.dtd"><html><head> <title>Description of coarsening</title> <meta name="keywords" content="coarsening"> <meta name="description" content="COARSENING coarsens the current mesh"> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="m2html © 2003 Guillaume Flandin"> <meta name="robots" content="index, follow"> <link type="text/css" rel="stylesheet" href="../../m2html.css"></head><body><a name="_top"></a><!-- # AFEM@matlab --><!-- menu.html 4_Refine --><h1>coarsening</h1><h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2><div class="box"><strong>COARSENING coarsens the current mesh</strong></div><h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2><div class="box"><strong>function [mesh,eta] = coarsening(mesh,eta,theta) </strong></div><h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2><div class="fragment"><pre class="comment"> COARSENING coarsens the current mesh USAGE [mesh,eta] = coarsening(mesh,eta,theta) INPUT mesh: current mesh eta: error indicator for each triangle theta: parameter in (0,1). We mark minimal number of triangles M such that \sum_{T \in M} \eta_T < \theta*\sum\eta_T OUTPUT mesh: new mesh after refinement eta: new error indicator for each triangle NOTE Only one level coarsening REFERENCE AFEM@matlab Manual --> Algorithms --> Coarsening</pre></div><!-- crossreference --><h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>This function calls:<ul style="list-style-image:url(../../matlabicon.gif)"></ul>This function is called by:<ul style="list-style-image:url(../../matlabicon.gif)"><li><a href="../../AFEM@matlab/1_Example/Lshape.html" class="code" title="function Lshape">Lshape</a> LSHAPE solves Poisson equation in a L-shaped domain with FEM with</li><li><a href="../../AFEM@matlab/1_Example/circle.html" class="code" title="function circle">circle</a> CIRCLE simulates adaptive grids for a problem with moving circlular</li><li><a href="../../AFEM@matlab/1_Example/crack.html" class="code" title="function crack">crack</a> CRACK solves Poisson equation in a crack domain with AFEM.</li></ul><!-- crossreference --><h2><a name="_subfunctions"></a>SUBFUNCTIONS <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2><ul style="list-style-image:url(../../matlabicon.gif)"><li><a href="#_sub1" class="code">function bdEdge = updatebd(bdEdge, markedNode)</a></li></ul><h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2><div class="fragment"><pre><a name="_sub0" href="#_subfunctions" class="code">function [mesh,eta] = coarsening(mesh,eta,theta)</a><span class="comment">% COARSENING coarsens the current mesh</span><span class="comment">%</span><span class="comment">% USAGE</span><span class="comment">% [mesh,eta] = coarsening(mesh,eta,theta)</span><span class="comment">%</span><span class="comment">% INPUT</span><span class="comment">% mesh: current mesh</span><span class="comment">% eta: error indicator for each triangle</span><span class="comment">% theta: parameter in (0,1).</span><span class="comment">% We mark minimal number of triangles M such that</span><span class="comment">% \sum_{T \in M} \eta_T < \theta*\sum\eta_T</span><span class="comment">%</span><span class="comment">% OUTPUT</span><span class="comment">% mesh: new mesh after refinement</span><span class="comment">% eta: new error indicator for each triangle</span><span class="comment">%</span><span class="comment">% NOTE</span><span class="comment">% Only one level coarsening</span><span class="comment">%</span><span class="comment">% REFERENCE</span><span class="comment">% AFEM@matlab Manual --> Algorithms --> Coarsening</span><span class="comment">%</span><span class="comment">% L. Chen & C. Zhang 11-15-2006</span><span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% Construct data structure</span><span class="comment">%--------------------------------------------------------------------------</span>N = size(mesh.node,1); NT = size(mesh.elem,1);dualEdge = sparse(mesh.elem(:,[1,2,3]),mesh.elem(:,[2,3,1]),[1:NT,1:NT,1:NT]);valence = accumarray(mesh.elem(:),ones(3*NT,1),[N 1]);eta_p = accumarray(mesh.elem(:),[eta;eta;eta],[N 1]); <span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% Mark nodes for coarsen</span><span class="comment">%--------------------------------------------------------------------------</span>total = sum(eta_p); maxeta = max(eta_p);current = 0; marker = uint8(zeros(N,1)); newestNode = unique(mesh.elem(:,1)); <span class="comment">% newest vertices of all elements</span>coarseNode = find(mesh.type==1); <span class="comment">% nodes in the initial triangulation</span>newestNode = setdiff(newestNode,coarseNode);isGood = (valence(newestNode) == 2) | (valence(newestNode) == 4);goodNode = newestNode(isGood);<span class="comment">% A node is called 'good' if it can be removed without breaking the mesh</span><span class="comment">% comformity. A node is 'good' if and only if</span><span class="comment">% 0. it is not a node of marco elements in the initial triangluation;</span><span class="comment">% 1. it is the newest node in each of the elements with it as a node;</span><span class="comment">% 2. if it is an interior node, the valence is 4;</span><span class="comment">% 3. if it is on the boundary, the valence is 2.</span>[temp,ix] = sort(eta_p(goodNode));<span class="keyword">for</span> i = 1:length(goodNode) p = goodNode(ix(i)); <span class="keyword">if</span> (eta_p(p) > 0.2*maxeta), <span class="keyword">break</span>; <span class="keyword">end</span> <span class="comment">% only coarsen where error small</span> <span class="keyword">if</span> (current + eta_p(p) > theta*total), <span class="keyword">break</span>; <span class="keyword">end</span> marker(p) = 1; <span class="comment">% mark p to be removed</span> mesh.type(p) = 0; <span class="comment">% node p is non active now</span> current = current + eta_p(p);<span class="keyword">end</span><span class="keyword">if</span> (sum(marker)==0), <span class="keyword">return</span>; <span class="keyword">end</span> <span class="comment">% no node can be coarsened</span><span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% Coarsen the mesh by removing marked nodes</span><span class="comment">%--------------------------------------------------------------------------</span><span class="keyword">for</span> t = 1:NT <span class="keyword">if</span> (mesh.elem(t,1)>0) <span class="comment">% otherwise t is already deleted</span> p = mesh.elem(t,1); <span class="keyword">if</span> (marker(p)==1) <span class="comment">% p is a marked good point</span> brother = dualEdge(mesh.elem(t,2),p); mesh.elem(t,1) = mesh.elem(t,2); mesh.elem(t,2) = mesh.elem(t,3); mesh.elem(t,3) = mesh.elem(brother,2); mesh.elem(brother,1) = 0; <span class="comment">% brother is going to be deleted</span> eta(t) = eta(t) + eta(brother); <span class="comment">% new eta = eta_t + eta_brother</span> <span class="keyword">end</span> <span class="comment">% endif for all markd good nodes</span> <span class="keyword">end</span><span class="keyword">end</span> <span class="comment">% end of for loop on all elements</span><span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% Clear element and eta arrarys</span><span class="comment">%--------------------------------------------------------------------------</span>ix = (mesh.elem(:,1) == 0); mesh.elem(ix,:) = []; eta(ix,:) = [];<span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% Update boundary edges</span><span class="comment">%--------------------------------------------------------------------------</span>markedNode = goodNode((marker(goodNode)==1)&(valence(goodNode)==2));mesh.Dirichlet = <a href="#_sub1" class="code" title="subfunction bdEdge = updatebd(bdEdge, markedNode)">updatebd</a>(mesh.Dirichlet, markedNode);mesh.Neumann = <a href="#_sub1" class="code" title="subfunction bdEdge = updatebd(bdEdge, markedNode)">updatebd</a>(mesh.Neumann, markedNode);<span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% End of function COARSENING</span><span class="comment">%--------------------------------------------------------------------------</span><span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% Sub functions called by COARSENING</span><span class="comment">%--------------------------------------------------------------------------</span><a name="_sub1" href="#_subfunctions" class="code">function bdEdge = updatebd(bdEdge, markedNode)</a><span class="comment">% UPDATEDBD coarsen the boundary edges</span><span class="comment">%</span><span class="comment">% USAGE</span><span class="comment">% bdEdge = updatebd(bdEdge, markedNode)</span><span class="comment">%</span><span class="comment">% INPUT</span><span class="comment">% bdEdge: old boundary edges</span><span class="comment">% markedNode: node marked for coarsening</span><span class="comment">%</span><span class="comment">% OUTPUT</span><span class="comment">% bdEdge: new boundary edges after coarsening</span><span class="comment">%</span><span class="keyword">if</span> (isempty(bdEdge) || isempty(markedNode)), <span class="keyword">return</span>; <span class="keyword">end</span>NB = size(bdEdge,1); neig = sparse(bdEdge,ones(NB,1)*[2,1],[1:NB,1:NB]);<span class="comment">% skeleton of edges around a node</span><span class="keyword">for</span> k = 1: length(markedNode) i = neig(markedNode(k),1); j = neig(markedNode(k),2); <span class="comment">% o --- i --- o --- j --- o</span> <span class="comment">% ^</span> <span class="comment">% noActive(k)</span> bdEdge(i,2) = bdEdge(j,2); bdEdge(j,1) = 0;<span class="keyword">end</span>ix = (bdEdge(:,1)==0); bdEdge(ix,:) = [];<span class="comment">%--------------------------------------------------------------------------</span><span class="comment">% End of function UPDATEDBD</span><span class="comment">%--------------------------------------------------------------------------</span></pre></div><hr><address>Generated on Fri 17-Nov-2006 11:02:53 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/" target="_parent">m2html</a></strong> © 2003</address></body></html>⌨️ 快捷键说明
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