grinprodgausnodequad Computes the gradient part of the system matrix in the quadratic basis case. The conductivity is in the linear basis. Function int=grinprodgausnodequad(g,I); computes the gradient part of the system matrix in the quadratic basis case. The conductivity is in the linear basis. INPUT g = nodes of the element I = index of the chosen node OUTPUT int = three dimensional array or 3x3 matrix of the values of integral
0001 function int=grinprodgausnodequad(g,I); 0002 0003 %grinprodgausnodequad Computes the gradient part of the system matrix 0004 %in the quadratic basis case. The conductivity is in the linear basis. 0005 % Function int=grinprodgausnodequad(g,I); 0006 % computes the gradient part of the system matrix 0007 % in the quadratic basis case. The conductivity is in the linear basis. 0008 % 0009 % INPUT 0010 % 0011 % g = nodes of the element 0012 % I = index of the chosen node 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 w=[1/6*ones(3,1)]; 0024 ip=[1/2 0;1/2 1/2;0 1/2]; 0025 0026 int=0; 0027 for ii=1:3 0028 S=[1-ip(ii,1)-ip(ii,2);ip(ii,1);ip(ii,2)]; 0029 L=[4*(ip(ii,1)+ip(ii,2))-3, -8*ip(ii,1)-4*ip(ii,2)+4, ... 0030 4*ip(ii,1)-1, 4*ip(ii,2), 0, -4*ip(ii,2); ... 0031 4*(ip(ii,1)+ip(ii,2))-3, -4*ip(ii,1), ... 0032 0, 4*ip(ii,1), 4*ip(ii,2)-1, -8*ip(ii,2)-4*ip(ii,1)+4]; 0033 Jt=L*g; 0034 iJt=inv(Jt); 0035 dJt=abs(det(Jt)); 0036 G=iJt*L; 0037 int=int+w(ii)*S(I)*G'*G*dJt; 0038 end 0039 0040 0041 0042 0043 0044 0045