The PBC is handled at two levels. At the first 'wrap-around' level, cells are shifted about the cell of interest up to the size of the simulation box and treated in the same way as the nonperiodic system. After that, the entire wrapped-around box repeats until the calculated force on the atom becomes accurate within the target accuracy. As the repeat number for a box increases, the size of the assigned cubature decreases, which makes the PBC calculation affordable for electrically neutral systems. The GLST algorithm has a number of desirable characteristics, including O(N) scaling, tunability of the target accuracy, the simplicity and economy in organizing cells for PBC, and adaptability to non-cubic systems. We thus anticipate GLST to be a competitive algorithm to use for MD simulations in practice.