Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations

TL;DR

This paper develops and analyzes a multi-patch discontinuous Galerkin isogeometric method for solving full-potential electronic structure problems, providing error estimates and numerical validation.

Contribution

It introduces a novel multi-patch DG-IGA approach with rigorous error analysis for elliptic eigenvalue problems in electronic structure calculations.

Findings

The method achieves optimal convergence rates.

Numerical experiments confirm theoretical error estimates.

The approach effectively handles complex domain decompositions.

Abstract

In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the wavefunction separately using B-spline basis functions, possibly with different degrees, on varying mesh sizes, and then combine them by DG methods. We also provide a rigorous {\em a priori} error analysis of the DG-IGA approximations for linear eigenvalue problems. Furthermore, this work offers a unified analysis framework for the DG-IGA method applied to a class of elliptic eigenvalue problems. Finally, we present several numerical experiments to verify our theoretical results.