grinprodgausnode Computes the gradient part of the system matrix in the linear basis case. The conductivity is also in the linear basis. Function int=grinprodgausnode(g,I); computes the gradient part of the system matrix in the linear basis case. The conductivity is also in the linear basis. INPUT g = nodes of the element I = index of the chosen node (optional) OUTPUT int = three dimensional array or 3x3 matrix of the values of integral
0001 function int=grinprodgausnode(g,I); 0002 0003 %grinprodgausnode Computes the gradient part of the system matrix 0004 %in the linear basis case. The conductivity is also in the linear basis. 0005 % Function int=grinprodgausnode(g,I); 0006 % computes the gradient part of the system matrix 0007 % in the linear basis case. The conductivity is also in the linear basis. 0008 % 0009 % INPUT 0010 % 0011 % g = nodes of the element 0012 % I = index of the chosen node (optional) 0013 % 0014 % OUTPUT 0015 % 0016 % int = three dimensional array or 3x3 matrix of the values of integral 0017 0018 % P. Ronkanen and M. Vauhkonen 10.5. 1996. Modified by M. Vauhkonen for EIDORS 0019 % 11.5.2000. 0020 % University of Kuopio, Department of Applied Physics, PO Box 1627, 0021 % FIN-70211 Kuopio, Finland, email: Marko.Vauhkonen@uku.fi 0022 0023 0024 0025 w=[1/6*ones(3,1)]; 0026 ip=[1/2 0;1/2 1/2;0 1/2]; 0027 L=[-1 1 0;-1 0 1]; 0028 Jt=L*g; 0029 iJt=inv(Jt); 0030 dJt=abs(det(Jt)); 0031 G=iJt*L; 0032 GdJt=G'*G*dJt; 0033 msg=max(size(g)); 0034 0035 if nargin > 1 0036 S=[[1-ip(1,1)-ip(1,2);ip(1,1);ip(1,2)],[1-ip(2,1)-ip(2,2);ip(2,1);ip(2,2)],[1-ip(3,1)-ip(3,2);ip(3,1);ip(3,2)]]*w; 0037 int=S(I)*GdJt; 0038 else 0039 int=zeros(msg,msg,3); 0040 S=[[1-ip(1,1)-ip(1,2);ip(1,1);ip(1,2)],[1-ip(2,1)-ip(2,2);ip(2,1);ip(2,2)],[1-ip(3,1)-ip(3,2);ip(3,1);ip(3,2)]]*w; 0041 for jj=1:3 0042 int(:,:,jj)=S(jj)*GdJt; 0043 end 0044 end 0045 0046 0047 0048 0049 0050