Finite element method and isogeometric analysis in electronic structure calculations: convergence study

TL;DR

This paper compares the convergence properties of isogeometric analysis and finite element method in electronic structure calculations, focusing on their application to key sub-problems in density functional theory.

Contribution

It provides a systematic convergence comparison between IGA and FEM for ab-initio electronic structure calculations, including a benchmark on nitrogen atom.

Findings

IGA shows comparable or improved convergence over FEM.

Convergence behavior is analyzed on Poisson and eigenvalue problems.

The iterative algorithm for charge density fixed point is outlined and tested.

Abstract

We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The convergence is studied on simple sub-problems that appear within the density functional theory approximation to the Schr\"odinger equation: the Poisson problem and the generalized eigenvalue problem. We also outline the complete iterative algorithm seeking a fixed point of the charge density of a system of atoms or molecules, and study IGA/FEM convergence on a benchmark problem of nitrogen atom.