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 warning('EIDORS:deprecated','INTEGROFGRAD is deprecated as of 06-Jun-2012. ');
0017 
0018 [vr,vc] = size(vtx);
0019 [sr,sc] = size(simp);
0020 
0021 if sr ~= length(mat_ref)
0022    error('Mismatched data entered')
0023 end
0024 
0025 if sc ~= 4
0026    error('Only first order tetrahedral elements supported');
0027 end
0028 
0029 
0030 %w = [1/24*ones(4,1)];
0031 
0032 IntGrad = sparse(vr^2,sr);
0033 
0034 for i=1:size(simp,1)
0035 
0036    vv = [];
0037 
0038    for j=1:size(simp,2)
0039       vv = [vv;vtx(simp(i,j),:)];
0040    end
0041 
0042    interp_fun = [-1 1 0 0; -1 0 1 0; -1 0 0 1];
0043 
0044    Jts = interp_fun*vv;
0045    inv_Jts = inv(Jts);
0046    det_Jts = abs(det(Jts));
0047 
0048    Gs = inv_Jts*interp_fun;
0049 
0050    %int = 0;
0051    %for q=1:4
0052    %  int = int + w(q)*Gs'*Gs;
0053    %end
0054    %Inte = int*det_Jts; % or simplified
0055    % Citation: The FEM displayed G.Dhatt & G. Touzot
0056 
0057    Inte = (1/6)*Gs'*Gs*det_Jts;
0058 
0059    Local = sparse(vr,vr);
0060    Local(simp(i,:),simp(i,:))= Inte;
0061    IntGrad(:,i) = Local(:);
0062 end
0063 
0064 
0065 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0066 % This is part of the EIDORS suite.
0067 % Copyright (c) N. Polydorides 2003
0068 % Copying permitted under terms of GNU GPL
0069 % See enclosed file gpl.html for details.
0070 % EIDORS 3D version 2.0
0071 % MATLAB version 5.3 R11
0072 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%