%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-05-18 22:33:57
 % @LastEditTime: 2021-05-18 22:41:38
%--------------------------
function K = global_stiffness_2scale_nonlinear(F, dFdx, iK, jK, dx, global_u, global_l, lenout)

    eleNum = size(F, 2);
    sK = zeros(lenout^2, eleNum);
    jac = dx^3/8;

    for ele_ma = 1:eleNum        
        u = global_u{ele_ma};
        l = global_l{ele_ma};

        % element stiffness
        ke = 0; 
        for gp = 1:8
            Fe  = F{gp, ele_ma};    % 4 * eleNum_mi
            dFe = dFdx{gp, ele_ma}; % 4 * lenout * eleNum_mi

            dP1 = dPdF_fast_nonlinear(u, l, Fe, dFe);         % 4 * l * m
            dPT = permute(dP1, [2,1,3]);             % l * 4 * m 
            dP2 = reshape(dPT, lenout, []);          % l * 4m

            dF1 = permute(dFe, [2,1,3]); % l * 4 * eleNum_mi 
            dF2 = reshape(dF1, lenout, [])'; % 4m * l

            ke_g = dP2 * dF2;                % lenout * lenout
            ke = ke + ke_g * jac;
        end
        sK(:, ele_ma) = ke(:);
    end
    K = sparse(iK, jK, sK(:));
    K = (K + K')/2;
end