Reply to “Comment on ‘Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited’ ”

This is a Reply to the Comment by Gonis and Zhang1 on our recent paper.2 They discuss supposed issues with our “accurate and fast numerical solution of Poisson’s equation for arbitrary Voronoi polyhedra” (VP). The method of Gonis et al.3 and Vitos and Koll´ar4 correctly addresses the mathematical issues related to the solution of Poisson’s equation [and near-field corrections (NFCs)] using a spherical harmonic basis (L’s). However, as discussed in Ref. 2, their method is not numerically efficient and suffers from severe convergence issues from the multiply nested (conditionally convergent) multipole expansions to address r problems. Hence, the abstract in Ref. 2 clearly states that we provide a method to address a “fast but accurate numerical solution of the Poisson equation” for site-centered methods.