function Int=FEintegrate2D(CtrlVar,MUA,f)

Int=FEintegrate2D(CtrlVar,MUA,f) calculates the integral of a nodal variable
f over each of the elements of the FE mesh.

CtrlVar can be entered as an empty variable.

Examples:

Ice volume:

Int=FEintegrate2D([],MUA,h);
TotalIceVolume=sum(Int)

Grounded area:

Int=FEintegrate2D([],MUA,GF.node); GroundedArea=sum(Int);

Integrated surface mass balance over grounded areas (i.e. upstream of grounding lines):

M=sum(FEintegrate2D(CtrlVar,MUA,F.as.*F.GF.node)) ;

ndim=2;

fnod=reshape(f(MUA.connectivity,1),MUA.Nele,MUA.nod);

% [points,weights]=sample('triangle',MUA.nip,ndim);

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=fnod*fun;
    Int=Int+fint.*detJw;

end

end

Published with MATLAB® R2021a