Multigrid method for electrostatic computations in numerical density functional theory

A multigrid method is presented for the real space numerical solution of the Poisson equation arising in ab-initio quantum computations. The specific algorithm presented is designed to compute the total electrostatic potential in real space density functional theory electronic structure calculations. Using a high-order finite difference approximation for the Laplacian and representing the nuclei as distributed charges, accurate electrostatic potentials due to both nuclei and electrons are obtained simultaneously in contrast to separate calculations for each component. Computations are presented for finite and periodic model problems in order to illustrate the accuracy of the approximation in addition to the speed and linear scaling properties of the algorithm.