  We present an explicit solver of the three-dimensional screened and
unscreened Poisson's 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.
