% NOTE: edofMat is for micro eles in this macro ele
function mu = adjoint_mu(subx, suby, den2, k0, iK, jK, rightF, freedofs)

    mu = zeros(size(rightF)); % for one micro-ele 8*9

    K = assembleK(k0, den2, iK, jK, subx, suby);
    mu(freedofs,:) = K(freedofs,freedofs)\rightF(freedofs,:);    
end

function K = assembleK(k0, den2, iK, jK, subx, suby)

    globalK = zeros(64, suby, subx);
    
    % which coarse ele in this sub
    for i = 1:subx
        for j = 1:suby            
            globalK(:,j,i) = k0(:) * den2(j,i);
        end
    end
    sK = globalK(:);
    K = sparse(iK, jK, sK); 
    K = (K + K') / 2;
end