function varargout=ProjectFintOntoNodes(MUA,varargin)

varargout=ProjectFintOntoNodes(MUA,varargin)

Projects element variables defined at integration points onto nodes. Does this by solving:

        min_{Fnod_p} || Fnod_p N_P - Fint||_{L2}

->  <Fnod_p N_p - Fint , N_q >_{L2}=0
->  <N_p,N_q> Fnod_p = <Fint,N_q>
      M Fnod = <Fint,n_q>

No limit on number of input/output fields.

Example:

[exxNod,eyyNod,exyNod,eNod]=ProjectFintOntoNodes(MUA,exx,eyy,exy,e)

where exx, eyy, exy, e, are defined at intergration points gives corresponding fields defined at nodes.

Note: This projection will not always preserve positivity! Even if element quantity is positive everywere, it is nevertheless possible that the projection on the nodes can be (slightly) negative.

nVarargs = length(varargin);
varargout = cell(nVarargs);


% check input dimentions
for I=1:nVarargs
    [N,M]=size(varargin{I});
    if N~=MUA.Nele || M~=MUA.nip
        fprintf('Incorrect dimensions: Must be an element variable defined at all elements and all integration points\n')
        return
    end
end

% create mass matrix

b=zeros(MUA.Nnodes,nVarargs);

% factorize
% [L,~,P]=chol(A,'lower');
for I=1:nVarargs
      b(:,I)=InnerProduct_FormFunctions_with_EleIntegrationPointVariable(MUA,varargin{I});
%      varargout{I}= P*(L' \(L \(P'*b(:,I))));
end

%A=MassMatrix2D1dof(MUA);
%sol=A\b;

if ~isfield(MUA,'M')
    MUA.M=MassMatrix2D1dof(MUA);
end

sol=MUA.M\b;

for I=1:nVarargs
    varargout{I}=sol(:,I);
end

Not enough input arguments.

Error in ProjectFintOntoNodes (line 45)
b=zeros(MUA.Nnodes,nVarargs);

end

Published with MATLAB® R2020b