function [dfdx,dfdy,xint,yint]=calcFEderivativesMUA(f,MUA)

[dfdx,dfdy,xint,yint]=calcFEderivativesMUA(f,MUA,CtrlVar)

calculates x and y derivatives of a nodal variable at integration points

f          :  a nodal quantity
dfdx, dfdy :  x and y derivatitves of f
xint, yint :  x, y locations of the elements of dfdx and dfdy

CtrlVar    : optional, can be left empty.

Note: On input f is a nodal variable, ie defined at nodes On return dfdx and dfdy are integration-point variables, ie defined at the integration points xint and yint.

Example:

load("PIG-TWG-RestartFile.mat","CtrlVarInRestartFile","MUA","F","RunInfo")
[dsdxInt,dsdyInt,xint,yint]=calcFEderivativesMUA(F.s,MUA) ;
[dsdx,dsdy]=ProjectFintOntoNodes(MUA,dsdxInt,dsdyInt) ;
SurfaceGradient=sqrt(dsdx.*dsdx+dsdy.*dsdy);
FindOrCreateFigure("surface gradient")
UaPlots(CtrlVarInRestartFile,MUA,F,SurfaceGradient) ;

See also: ProjectFintOntoNodes

narginchk(2,2)

ndim=2;
% [points,weights]=sample('triangle',MUA.nip,ndim);

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

dfdx=zeros(MUA.Nele,MUA.nip); dfdy=zeros(MUA.Nele,MUA.nip);


% f is a vector with nod values
% the derivative at a given integration point is
% dfds=Dx f   ( [Nele x nod] * [nod]
% Dx=Deriv(:,1,:)  which is Nele x nod
% dfdx(nEle)=Dx

for Iint=1:MUA.nip

    Deriv=MUA.Deriv(:,:,:,Iint);

    for I=1:MUA.nod
        dfdx(:,Iint)=dfdx(:,Iint)+Deriv(:,1,I).*fnod(:,I);
        dfdy(:,Iint)=dfdy(:,Iint)+Deriv(:,2,I).*fnod(:,I);
    end

end

if nargout>2

    xint=zeros(MUA.Nele,MUA.nip) ; yint=zeros(MUA.Nele,MUA.nip);
    coox=reshape(MUA.coordinates(MUA.connectivity,1),MUA.Nele,MUA.nod);
    cooy=reshape(MUA.coordinates(MUA.connectivity,2),MUA.Nele,MUA.nod);

    for Iint=1:MUA.nip
        fun=shape_fun(Iint,ndim,MUA.nod,MUA.points) ;

        xint(:,Iint)=coox*fun;
        yint(:,Iint)=cooy*fun;

    end
else
    xint=[] ; yint=[];
end

end

Published with MATLAB® R2022b