Efficient and accurate solver of the three-dimensional screened and unscreened Poissons equation with generic boundary conditions

摘要

We present an explicit solver of the three-dimensional screened and unscreened Poissons equation, which combines accuracy, computational efficiency, and versatility. The solver, based on a mixed plane-wave/interpolating scaling function representation, can deal with any kind of periodicity (along one, two, or three spatial axes) as well as with fully isolated boundary conditions. It can seamlessly accommodate a finite screening length, non-orthorhombic lattices, and charged systems. This approach is particularly advantageous because convergence is attained by simply refining the real space grid, namely without any adjustable parameter. At the same time, the numerical method features O(N _(log)N) scaling of the computational cost (N being the number of grid points) very much like plane-wave methods. The methodology, validated on model systems, is tailored for leading-edge computer simulations of materials (including ab initio electronic structure computations), but it might as well be beneficial for other research domains.