ElemStiffMat3DP1D0.m

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function [Elem]=ElemStiffMat3DP1D0(ql,V)
% NAME 
%  [Elem]=ElemStiffMat3DP1D0(ql,V)
% INPUTS 
%  area         : double (element volume)
%  ql           : matrix 3x4
%                 ql(:,il) ...
% OUTPUTS 
%  Elem         : matrix 4x4
% DESCRIPTION
%  Compute P1-Lagrange elementary Stiff matrix.
%  Numbering of local points in reference element is :
%    P=[(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1)]
%----------------------------------------
% Automatic generation with sage
% (c) Cuvelier F. email:cuvelier@math.univ-paris13.fr
% Copyright:
%   See \ref license
D12=ql(:,1)-ql(:,2);
D13=ql(:,1)-ql(:,3);
D14=ql(:,1)-ql(:,4);
D23=ql(:,2)-ql(:,3);
D24=ql(:,2)-ql(:,4);
D34=ql(:,3)-ql(:,4);
M=zeros(3,4);
M(1,1)=-D23(2)*D24(3) + D23(3)*D24(2);
M(2,1)=D23(1)*D24(3) - D23(3)*D24(1);
M(3,1)=-D23(1)*D24(2) + D23(2)*D24(1);
M(1,2)=D13(2)*D14(3) - D13(3)*D14(2);
M(2,2)=-D13(1)*D14(3) + D13(3)*D14(1);
M(3,2)=D13(1)*D14(2) - D13(2)*D14(1);
M(1,3)=-D12(2)*D14(3) + D12(3)*D14(2);
M(2,3)=D12(1)*D14(3) - D12(3)*D14(1);
M(3,3)=-D12(1)*D14(2) + D12(2)*D14(1);
M(1,4)=D12(2)*D13(3) - D12(3)*D13(2);
M(2,4)=-D12(1)*D13(3) + D12(3)*D13(1);
M(3,4)=D12(1)*D13(2) - D12(2)*D13(1);
G=M'*M;
Elem=[ ...
[ +1*G(1,1), +1*G(1,2), +1*G(1,3), +1*G(1,4)]; ...
[ +1*G(1,2), +1*G(2,2), +1*G(2,3), +1*G(2,4)]; ...
[ +1*G(1,3), +1*G(2,3), +1*G(3,3), +1*G(3,4)]; ...
[ +1*G(1,4), +1*G(2,4), +1*G(3,4), +1*G(4,4)]]/(36*V);