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Lukas Drescher

A mortar finite element method for full-potential Kohn-Sham density functional theory

Master's thesis (ETH Zürich)

Date: July 2014

Supervisors: Prof. Dr. Matthias Troyer (ETH Zürich), Prof. Dr. Reinhold Schneider, Dr. Kersten Schmidt

Abstract

Based on a recent regularity analysis, we develop a non-conforming discretization for the Kohn-Sham equations in density functional theory. For this purpose, we decompose the computational domain into a set of atomic spheres and an intermediate region. These domains are discretized separately using spherical harmonics tensored with radial polynomials on spheres and finite elements in the intermediate domain. The discretizations are coupled at the spherical interfaces using the mortar element method. Based on assumptions on the smoothness of the exchange-correlation potential this allows us to derive an a priori error estimate for the linearized Kohn-Sham problem.

We proceed with the implementation of the described mortar discretization in the hp-finite element solver Concepts. In particular, we resolve the mortaring conditions for the coupling of two discretization spaces in an abstract framework, which results in a generic algorithm for the construction of the mortar space. We implement this algorithm subsequently in Concepts. To study the Kohn-Sham equations in the self-consistent limit, we formulate and implement a version of the optimal damping algorithm for the extended Kohn-Sham model. This facilitates the robust computation of the self-consistent density, which will be used in our final numerical experiment to verify our a priori error estimate on a mono-atomic system.

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