Isogeometric analysis in electronic structure calculations

TL;DR

This paper introduces the use of isogeometric analysis (IGA) with Bézier extraction in electronic structure calculations to improve the continuity of discretized functions, enhancing the accuracy of derivative computations.

Contribution

It presents a novel integration of IGA into existing FEM-based electronic structure codes using Bézier extraction, enabling better derivative calculations.

Findings

IGA achieves higher continuity than FEM in discretized functions.

Benchmark comparisons show improved accuracy with IGA.

Numerical results demonstrate the effectiveness of IGA in electronic state calculations.

Abstract

In electronic structure calculations, various material properties can be obtained by means of computing the total energy of a system as well as derivatives of the total energy w.r.t. atomic positions. The derivatives, also known as Hellman-Feynman forces, require, because of practical computational reasons, the discretized charge density and wave functions having continuous second derivatives in the whole solution domain. We describe an application of isogeometric analysis (IGA), a spline modification of finite element method (FEM), to achieve the required continuity. The novelty of our approach is in employing the technique of B\'ezier extraction to add the IGA capabilities to our FEM based code for ab-initio calculations of electronic states of non-periodic systems within the density-functional framework, built upon the open source finite element package SfePy. We compare FEM and IGA in benchmark problems and several numerical results are presented.