%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-01-22 17:09:20
 % @LastEditTime: 2021-01-22 17:09:31

 % init macro U with singal stiffer material ke
 % init micro u for loop=1, when n = 0
%--------------------------
function [U, U_cell, Umi_cell] = init_macro_U(nelx, nely, ke, optDesign, vF, lx, microx, bdofs, multi_edofMat, alldofs)
    [iK, jK, edofMat, ~] = forAssemble(nelx, nely);
    sK = repmat(ke(:), nelx*nely, 1);
    K = sparse(iK, jK, sK);

    [freedofs, ~, fext, ~] = designDomain(optDesign, nelx, nely, vF);
    U0 = zeros(2*(nelx+1)*(nely+1), 1);
    U0(freedofs) = K(freedofs,freedofs)\fext(freedofs);

    % interpolation to get the macro-U on the borders
    N_b = interpolate_N_4nodes(lx, microx, bdofs);

    alldofs_mi = 1 : 2*(microx+1)^2;
    N_i = interpolate_N_4nodes(lx, microx, alldofs_mi);
    
    U = zeros(alldofs, 1);
    U_cell = cell(nelx*nely, 1);
    Umi_cell = cell(nelx*nely, 1);
    
    for ele = 1:nelx*nely        
        edof = edofMat(ele, :);
        uc = U0(edof);
        ub = N_b * uc;
        
        multi_edof = multi_edofMat(ele, :);
        U(multi_edof) = [uc; ub];
        
        ui = N_i * uc;
        Umi_cell{ele} = ui;

%         U(multi_edof) = 0;
        U_cell{ele} = U(multi_edof); 
    end
end