# A discontinuous Galerkin scheme for full-potential electronic structure calculations

## TL;DR

This paper introduces an efficient discontinuous Galerkin scheme for full-potential electronic structure calculations, combining different basis functions in atomic and interstitial regions with spectral convergence.

## Contribution

It develops a novel DG-based numerical scheme with spectral convergence for periodic electronic structure calculations, inspired by (L)APW methods.

## Key findings

- Scheme achieves spectral convergence rate
- Provides rigorous a priori error analysis
- Demonstrates effectiveness through numerical simulations

## Abstract

In this paper, we construct an efficient numerical scheme for full-potential electronic structure calculations of periodic systems. In this scheme, the computational domain is decomposed into a set of atomic spheres and an interstitial region, and different basis functions are used in different regions: radial basis functions times spherical harmonics in the atomic spheres and plane waves in the interstitial region. These parts are then patched together by discontinuous Galerkin (DG) method. Our scheme has the same philosophy as the widely used (L)APW methods in materials science, but possesses systematically spectral convergence rate. We provide a rigorous a priori error analysis of the DG approximations for the linear eigenvalue problems, and present some numerical simulations in electronic structure calculations.