integrofgrad

function [IntGrad] = integrofgrad(vtx,simp,mat_ref);

function that calculates the integral of the gradients for first order 
tetrahedral elements. Required for the calculation of the Jacobian. 



vtx     = The vertices matrix
simp    = The simplices matrix
mat_ref = The reference conductivity vector
IntGrad = The intgral of the gradients

0001 function [IntGrad] = integrofgrad(vtx,simp,mat_ref);
0002 %function [IntGrad] = integrofgrad(vtx,simp,mat_ref);
0003 %
0004 %function that calculates the integral of the gradients for first order
0005 %tetrahedral elements. Required for the calculation of the Jacobian.
0006 %
0007 %
0008 %
0009 %vtx     = The vertices matrix
0010 %simp    = The simplices matrix
0011 %mat_ref = The reference conductivity vector
0012 %IntGrad = The intgral of the gradients
0013 
0014 
0015 
0016 [vr,vc] = size(vtx);
0017 [sr,sc] = size(simp);
0018 
0019 if sr ~= length(mat_ref)
0020    error('Mismatched data entered')
0021 end
0022 
0023 if sc ~= 4
0024    error('Only first order tetrahedral elements supported');
0025 end
0026 
0027 
0028 %w = [1/24*ones(4,1)];
0029 
0030 IntGrad = sparse(vr^2,sr);
0031    
0032    for i=1:size(simp,1)
0033       
0034       vv = [];
0035        
0036       for j=1:size(simp,2)
0037       vv = [vv;vtx(simp(i,j),:)];
0038       end
0039       
0040       interp_fun = [-1 1 0 0; -1 0 1 0; -1 0 0 1];
0041       
0042       Jts = interp_fun*vv;
0043       inv_Jts = inv(Jts);
0044       det_Jts = abs(det(Jts));
0045       
0046       Gs = inv_Jts*interp_fun;
0047       
0048       %int = 0;
0049       %for q=1:4
0050        %  int = int + w(q)*Gs'*Gs;
0051       %end
0052       %Inte = int*det_Jts; % or simplified
0053       % Citation: The FEM displayed G.Dhatt & G. Touzot
0054       
0055       Inte = (1/6)*Gs'*Gs*det_Jts;
0056             
0057       Local = sparse(vr,vr);
0058       Local(simp(i,:),simp(i,:))= Inte;
0059       IntGrad(:,i) = Local(:);
0060    end
0061  
0062    
0063 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0064 % This is part of the EIDORS suite.
0065 % Copyright (c) N. Polydorides 2003
0066 % Copying permitted under terms of GNU GPL
0067 % See enclosed file gpl.html for details.
0068 % EIDORS 3D version 2.0
0069 % MATLAB version 5.3 R11
0070 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%