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We present an explicit solver of the three-dimensional screened andunscreened Poisson's equation which combines accuracy, computational efficiencyand versatility. The solver, based on a mixed plane-wave / interpolatingscaling function representation, can deal with any kind of periodicity (alongone, two, or three spatial axes) as well as with fully isolated boundaryconditions. It can seamlessly accommodate a finite screening length,non-orthorhombic lattices and charged systems. This approach is particularlyadvantageous because convergence is attained by simply refining the real spacegrid, namely without any adjustable parameter. At the same time, the numericalmethod features O(N log N) scaling of the computational cost (N being thenumber of grid points) very much like plane-wave methods. The methodology,validated on model systems, is tailored for leading-edge computer simulationsof materials (including ab initio electronic structure computations), but itmight as well be beneficial for other research domains.

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