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.

翻译：本文研究了用于全势电子结构计算的多片间断伽辽金等几何分析（DG-IGA）近似方法。我们将物理域分解为若干子域，在每个子域上使用B样条基函数（允许具有不同阶次和网格尺寸）分别表示波函数的各个部分，然后通过间断伽辽金方法将其组合。我们还为线性特征值问题的DG-IGA近似提供了严格的先验误差分析。此外，这项工作为应用于一类椭圆型特征值问题的DG-IGA方法提供了一个统一的分析框架。最后，我们通过若干数值实验验证了理论结果。