% periodic boundary conditions
function [wfixed,ufixed,d1,d2,d3,d4,testNum] = microPBC(nelx,nely,lx,ly)  

    nodenrs = reshape(1:(1 + nelx) * (1 + nely), 1 + nely, 1 + nelx);
    
    e0 = eye(3);
    ufixed = zeros(8, 3);    
    
    alldofs = 1:2 * (nely + 1) * (nelx + 1);

    % four corner points
    n1 = [nodenrs(end, [1, end]), nodenrs(1, [end, 1])];
    d1 = reshape([2 * n1 - 1; 2 * n1], 1, 8); 

    % left+bottom boundaries
    n3 = [nodenrs(2:end - 1, 1)', nodenrs(end, 2:end - 1)];
    d3 = reshape([2 * n3 - 1; 2 * n3], 1, 2 * (nelx + nely - 2)); 

    % right+up boundaries
    n4 = [nodenrs(2:end - 1, end)', nodenrs(1, 2:end - 1)];
    d4 = reshape([2 * n4 - 1; 2 * n4], 1, 2 * (nelx + nely - 2)); 

    d2 = setdiff(alldofs, [d1, d4, d3]);   
    
    for j = 1:3
        ufixed(3:4, j) = [e0(1, j), e0(3, j) / 2; e0(3, j) / 2, e0(2, j)] * [lx; 0]; % set lx=ly=1
        ufixed(7:8, j) = [e0(1, j), e0(3, j) / 2; e0(3, j) / 2, e0(2, j)] * [0; ly]; % down->up,-nely
        ufixed(5:6, j) = ufixed(7:8, j) + ufixed(3:4, j);
    end

    wfixed = [repmat(ufixed(3:4, :), nely - 1, 1); repmat(ufixed(7:8, :), nelx - 1, 1)];
    
    testNum = 3;
end