%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-06-16 14:52:29
 % @LastEditTime: 2022-04-25 12:47:51

 % compute NH of \Omega_{\alpha}
 % input: interpolation matrix R:[ndofs, v], which is ordered as col by col
 % output: surface NH on this fine mesh, [nnodes_mi, 2, 2, nnodes_ma]
%--------------------------
function NH = NH_alpha(edofMat, nn_ma, Nh, R, nnodes)

    % nn_mi = size(Nh, 1);

    NH = zeros(nnodes, 2, 2, nn_ma); % [n,2,2,v]
    
    for ele_mi = 1:size(edofMat, 1)
        edof = edofMat(ele_mi, :);

        Nhe = Nh(ele_mi, :, :); % [3,3]
        Nh2 = kron(permute(Nhe,[2,3,1]), eye(2));% [6,6]

        NH1 = Nh2 * R(edof, :);         % [2*3,6] * [6, 2v] = [6,2v]
        NH2 = reshape(NH1', 2, [], 6);  % [2, v, 6]
        NH3 = permute(NH2, [3,1,2]);    % [6,2,v]
        NH4 = reshape(NH3, 2, 3, 2, []);% [2, 3, 2, v]
        NH5 = permute(NH4, [2,1,3,4]);  % [3, 2, 2, v]
                    
        NH(edof(2:2:end)/2, :, :, :) = NH5;
    end
end