compact_topology_optimization/2d/util_trimesh/optimize_t_trimesh.m

%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-11-02 15:18:36
 % @LastEditTime: 2021-11-04 15:56:57

 % Ke is [6,6,faces_num]
%--------------------------
function optimize_t_trimesh(Ke, nodes, faces, nodes_cell, faces_cell, MMCs, MMCs_max, MMCs_min, radius, p, ...
    edofMat, iK, jK, freedofs, F, nidx_cell, fidx_cell, MMCs_num, volfrac)

    nele_global = size(faces, 1);

    cvt_num = size(MMCs, 1);
    pn = 16; % for pnorm

    U = zeros(size(nodes,1)*2, 1);
    [xval, xold1, xold2, xmin, xmax, low, upp, m_mma, c_mma, d_mma, a0_mma, a_mma] = MMA_paras1(MMCs, MMCs_min, MMCs_max, MMCs_num);

    loop = 1; change = 1; maxloop = 100;
    while loop < maxloop && change > 1e-4

        %% MMC-part
        [H, dH_global, denk_global, den_global, v_local] = project_MMC(nodes_cell, faces_cell, MMCs, radius, p, nidx_cell, fidx_cell);
        figure(1); clf; trisurf(faces, nodes(:,1), nodes(:,2), H);

        %% simulation
        [dcdH, comp] = simulation_MMC_trimesh(edofMat, iK, jK, freedofs, U, F, Ke, denk_global, den_global);

        cons_v_micro = (mean(v_local.^pn))^(1/pn);

        %% Sensitivities 
        dpnorm = 1/cvt_num * (mean(v_local.^pn))^(1/pn-1) * (v_local.^(pn-1)); % [cvy_num,1]
        dpn_expand = zeros(nele_global, 1);
        for i = 1 : cvt_num
            dpn_expand(fidx_cell(i,1) : fidx_cell(i,2)) = dpnorm(i);
        end
        dvdH  = ones(nele_global, 1) / nele_global .* dpn_expand;

        dc = zeros(MMCs_num, 3);
        dv = zeros(MMCs_num, 3);
        idx = 0;
        for i = 1 : cvt_num
            % NOTE: each MMC only effects its own cell
            dH = dH_global{i};
            edges_num = size(MMCs{i}, 2);
            
            dcdt = zeros(edges_num, 3);
            dvdt = zeros(edges_num, 3);
            for e = 1 : edges_num
                dHdt = squeeze(dH(e, :, :))'; % [m,3]
                dcdt(e, :) = dcdH(:)' * dHdt; % [1,m]*[m,3] -> [1,3]
                dvdt(e, :) = dvdH(:)' * dHdt; 
            end
            dc(idx+1 : idx+edges_num, :) = dcdt;
            dv(idx+1 : idx+edges_num, :) = dvdt;
        end
        dc = dc'; % change to [3, MMCs_num]
        dv = dv';
        
        %% optimization-part
        f0val= comp; 
        df0dx= -dc(:) / max(abs(dc(:))); 
        fval = cons_v_micro - volfrac;
        dfdx = dv(:) / max(abs(dv(:))); 
        [xmma, ~, ~, ~, ~, ~, ~, ~, ~,low, upp]= mmasub_mmc(m_mma, nn, Loop, xval(:), xmin, xmax, xold1,...
            xold2, f0val, df0dx, fval, dfdx', low, upp, a0_mma, a_mma, c_mma, d_mma);
        xold2 = xold1; xold1 = xval; 
        change  = max(abs(xval-xmma));

        % update MMCs
        MMCs = update_MMC(xval, MMCs);
    end
end

%% utils
function [dcdH, comp] = simulation_MMC_trimesh(edofMat, iK, jK, freedofs, U, F, Ke, denk, den)
    
    sKe = reshape(Ke, 36, []); % [36,m]
    sK = sKe .* denk(:)';

    K = sparse(iK(:),jK(:),sK(:)); K=(K+K')/2; 
    U(freedofs,:) = K(freedofs,freedofs) \ F(freedofs,:); 
    
    % Energy of element 
    u0 = U(edofMat)'; % [6,m]
    u1(1,:,:) = u0;   % [1,6,m]
    u2(:,1,:) = u0;   % [6,1,m]
    energy = squeeze(mtimesx(mtimesx(u1, Ke), u2)); % [m,1]
    dcdH = 2 * energy(:) .* den(:); % [m,1]

    comp = F'*U; 
end

function [H_global, dH_global, denk_global, den_global, v_local] = project_MMC(nodes_cell, faces_cell, MMCs, radius, p, nidx_cell, fidx_cell)

    cvt_num = size(MMCs, 1);
    denk_global = zeros(fidx_cell(end), 1);
    den_global  = zeros(fidx_cell(end), 1);
    v_local   = zeros(cvt_num, 1); % for volume-pnorm

    H_global    = zeros(nidx_cell(end), 1);
    dH_global   = cell(cvt_num, 1);

    step = radius / 2;
    
    for i = 1:cvt_num
        mmc = MMCs{i}; % [7, edges_num]
        nodes = nodes_cell{i};
        faces = faces_cell{i};

        edges_num = size(mmc,2); % edges_num
        each_phi  = cell(edges_num, 1);
        phi0 = 0;
        for j = 1 : edges_num 
            tmpPhi = tPhi(mmc(:,j), nodes(:,1), nodes(:,2));
            each_phi{j} = tmpPhi;
            phi0 = phi0 + exp(p * tmpPhi);
        end
        phi_max = log(phi0) / p;
        H = Heaviside_simply(phi_max, radius);
        H_global(nidx_cell(i,1) : nidx_cell(i,2)) = H;

        edofMat0 = [2*faces-1, 2*faces]; % [n,6]
        edofMat  = edofMat0(:, [1,4,2,5,3,6]);
        EleNodesID = edofMat(:, 2:2:6) ./ 2; 
        denk= sum(H(EleNodesID).^2, 2) / 3; % 3 for tiangle
        den = sum(H(EleNodesID), 2) / 3;    % [m,1]
        denk_global(fidx_cell(i,1) : fidx_cell(i,2)) = denk;
        den_global(fidx_cell(i,1) : fidx_cell(i,2))  = den;

        v_local(i) = mean(den);

%         figure(3); clf; trimesh(faces, nodes(:,1), nodes(:,2), H);

        faces_num = size(faces, 1);
        dH_global{i} = sensitivity_MMC(edges_num, mmc, step, nodes, p, each_phi, radius, EleNodesID, faces_num);
    end
end

function dH = sensitivity_MMC(edges_num, mmc, step, nodes, p, each_phi, radius, EleNodesID, faces_num)

    dH = zeros(edges_num, 3, faces_num);

    for j = 1 : edges_num

        mmc_j = mmc(:,j);        

        for ti = 1 : 3
            mmc_plus = mmc_j;
            mmc_minus = mmc_j;
        
            mmc_plus(ti) = mmc_j(ti) + step;
            phi_plus0 = tPhi(mmc_plus, nodes(:,1), nodes(:,2));
            phi_plus = exp(p * phi_plus0);
            for j1 = 1 : j-1
                phi_plus = phi_plus + exp(p * each_phi{j1});
            end
            for j2 = j+1 : edges_num
                phi_plus = phi_plus + exp(p * each_phi{j2});
            end
            phi_plus_blend = log(phi_plus) / p;

            mmc_minus(ti) = mmc_j(ti) - step;
            phi_minus0 = tPhi(mmc_minus, nodes(:,1), nodes(:,2));
            phi_minus = exp(p * phi_minus0);
            for j1 = 1 : j-1
                phi_minus = phi_minus + exp(p * each_phi{j1});
            end
            for j2 = j+1 : edges_num
                phi_minus = phi_minus + exp(p * each_phi{j2});
            end
            phi_minus_blend = log(phi_minus) / p;

            H_plus  = Heaviside_simply(phi_plus_blend, radius);
            H_minus = Heaviside_simply(phi_minus_blend, radius);
            dHi = (H_plus - H_minus) / (2 * step); % [n,1]
            
            dH(j, ti, :) = sum(dHi(EleNodesID), 2) / 3; % [n,1] -> [m,1]
            % CHECK: need dH/dH_e ? from node to ele

%             figure(1); clf; trimesh(faces, nodes(:,1), nodes(:,2), H_plus);
%             figure(2); clf; trimesh(faces, nodes(:,1), nodes(:,2), H_minus);
        end
    end
end

function MMCs = update_MMC(xval, MMCs)

    cvt_num = size(MMCs, 1);
    idx = 0;
    for i = 1:cvt_num
        mmc = MMCs{i};
        edges_num = size(mmc, 2);
        MMCs{i}(1:3, :) = xval(:, idx+1 : idx+edges_num);
    end
end

function [xval, xold1, xold2, xmin, xmax, low, upp, m_mma, c_mma, d_mma, a0_mma, a_mma] = MMA_paras1(MMCs, MMCs_min, MMCs_max, MMCs_num)

    xval  = zeros(3, MMCs_num);
    xmin  = zeros(3, MMCs_num);
    xmax  = zeros(3, MMCs_num);

    cvt_num = size(MMCs, 1);
    idx = 0;
    for i = 1 : cvt_num
        mmc = MMCs{i};
        edges_num = size(mmc, 2);
        xval(:, idx+1 : idx+edges_num) = mmc(1:3, :);
        xmin(:, idx+1 : idx+edges_num) = MMCs_min{i}(1:3, :);
        xmax(:, idx+1 : idx+edges_num) = MMCs_max{i}(1:3, :);
    end

    % variables are t1,t2,t3
    xval = xval(:);
    xold1= xval; xold2 = xval; 
    xmin = xmin(:); xmax = xmax(:);
    low  = xmin; upp = xmax; 

    m_mma = 1; % number of constrainm 
    c_mma = 1000*ones(m_mma,1); d_mma = zeros(m_mma,1); a0_mma = 1; a_mma = zeros(m_mma,1); 
end