A multiwavelet approach to the direct solution of the Poisson equation: implementation and optimization

Abstract

This work is presenting a fully numerical approach for the direct solution of the Poisson equation for the electrostatic potential given by an arbitrary charge density. Efficient solution of this equation is important in many fields of science, where the current work is dealing with nuclear and electronic potential calculations, used in the field of computational chemistry. The equation is solved using the mathematical framework of multiwavelets, which is a theory that enables us to represent functions and operators with rigorous error control. The multiwavelet basis is well suited to treat the multiple length scales present in the calculation of electronic structure. A prototype implementation of the solution of the Poisson equation using the multiwavelet formalism has previously been obtained by the computational chemistry group at the University of Tromso¸, and the current work is dealing with optimization of the existing code and with the development of the code into new areas of applicability, specifically to the calculation of electronic structure using the framework of density functional theory