Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

Hoke, Kurt

On the numerics of the 3D Kohn-Sham system

The Schrödinger-Poisson system with exchange-correlation potential (Kohn-Sham system) in three dimensions is solved using the fixed point iteration scheme proposed by Kerkhoven. This scheme goes in line with the analytical description used by H.-Chr. Kaiser and J. Rehberg as a fixed point mapping. It separates in two parts, which intend to stabilize and accelerate the pure fixed point iteration. First, underrelaxation with some carefully adapted relaxation-factor is used for stabilization. Secondly, acceleration is reached by switching to Newton's method and applying a derivative-free version of the GMRES method.