function Int=FEintegrateProduct2D(CtrlVar,MUA,varargin)

Int=FEintegrateProduct2D(CtrlVar,MUA,varargin)

calculates the integral of the product of the nodal variable
varargin over each of the elements of the FE mesh.

Example: To calculate the product of h and s over the mesh:

Int=FEintegrateProduct2D(CtrlVar,MUA,h,s)

Testing integration using different quadrature rules of different degrees

coordinates=[0 0 ; 0 1 ; 1 1 ; 1 0];
connectivity=[1 2  4 ; 4 2 3 ];
CtrlVar=Ua2D_DefaultParameters;
CtrlVar.TriNodes=3;
MUA=CreateMUA(CtrlVar,connectivity,coordinates);

CtrlVar.TriNodes=10; MUA=UpdateMUA(CtrlVar,MUA);
x=MUA.coordinates(:,1);  y=MUA.coordinates(:,2) ;
p=4;
f=(1+x+y).^p;

I=0 ;

F=nan(10,1);
D=nan(10,1);
for Degree=1:10

   MUA.QuadratureRuleDegree=Degree;
   Q=quadtriangle(Degree,'Type','nonproduct','Points','inside','Domain',[0 0 ; 1 0 ; 0 1]) ;
   MUA.nip=size(Q.Points,1);
   MUA.niph=size(Q.Points,1);
   CtrlVar.nip=MUA.nip;
   CtrlVar.niph=MUA.niph;
   MUA.points=Q.Points;
   MUA.weights=Q.Weights;
   [MUA.Deriv,MUA.DetJ]=CalcMeshDerivatives(CtrlVar,MUA.connectivity,MUA.coordinates,MUA.nip,MUA.points);

   Int=FEintegrateProduct2D(CtrlVar,MUA,x,y,f,f,f,f,f,f,f,f,f) ;

   Int=sum(Int);
   fprintf(' Degree %i \t  nip %i  \t Int=%f \n ',Degree,MUA.nip,Int)
   I=I+1 ; F(I)=Int; D(I)=Degree;

end

figure ; plot(D,F,'-x')
xlabel('Degree')
ylabel('Fint')

%%

ndim=2;


Int=zeros(MUA.Nele,1);

for Iint=1:MUA.nip

    fun=shape_fun(Iint,ndim,MUA.nod,MUA.points) ;
    detJ=MUA.DetJ(:,Iint);
    detJw=detJ*MUA.weights(Iint);

    fint=1;
    for k=1:numel(varargin)

        f=varargin{k};
        fnod=reshape(f(MUA.connectivity,1),MUA.Nele,MUA.nod);
        fint=fnod*fun.*fint;

    end

    Int=Int+fint.*detJw;

end

end

Published with MATLAB® R2024b