%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-07 09:13:42
 % @LastEditTime: 2022-05-10 11:12:32
%--------------------------
function [dc, dv] = sensitivity_cvt_hex(c_dH, c_interEles, c_rho, c_psi, ...
    edofMat, U, e0, e1, penal, ke0, nelx, nely, nelz, lx)

    nele = size(c_rho, 1);
    dc_local = cell(nele, 1);

    parfor ele = 1 : nele
        %% compliance sensitivity
        psi1 = c_psi{ele};             % [12, 3v, m]
        psi2 = permute(psi1, [2,1,3]); % [3v, 12, m]
        nvdofs = size(psi2, 1);

        rho = c_rho{ele};

        sK1 = reshape(ke0(:) * (e0 + rho(:)'.^penal * (e1 - e0)), [], 1);
        sK2 = reshape(sK1, 24,24,[]); % [12,12,m]

        Ke0 = mtimesx(mtimesx(psi2, sK2), psi1); % [3v,3v,m]
        Ke1 = reshape(Ke0, nvdofs, []); % [3v, 3v*m]

        edof = edofMat(ele, :);
        ue = U(edof); % [3v,1]

        dc1 = ue' * Ke1; % [1, 3v*m]
        dc2 = reshape(dc1, nvdofs, [])'; % [m,3v]
        dc_local{ele} = dc2 * ue; % [m, 1]
    end

    npnts = size(c_dH, 1);
    dcdp = zeros(npnts, 4);
    dvdp = zeros(npnts, 4);
    
    vol0 = nelx * nely * nelz * lx^3;
    vol1 = lx^3;

    parfor i = 1 : npnts
        for j = 1:4
            dH_ele = c_dH{i,j};
            interEles = c_interEles{i,j};
            nnb = length(interEles);

            for k = 1 : nnb
                ele = interEles(k);
                dcdp(i, j) = dcdp(i, j) + sum(dc_local{ele} .* dH_ele{k}); 
                dvdp(i, j) = dvdp(i, j) + sum(vol1 / vol0 .* dH_ele{k}); 
            end
        end
    end
    dc = reshape(dcdp', [], 1);
    dv = reshape(dvdp', [], 1);
end