Discontinuous Galerkin Methods for a First-Order Semi-Linear Hyperbolic Continuum Model of a Topological Resonator Dimer Array

被引：0
|
作者：
Du, Qiang [1 ]
Li, Huaiyu [1 ]
Weinstein, Michael [1 ]
Zhang, Lu [2 ,3 ]
机构：
[1] Department of Applied Physics and Applied Mathematics, and Data Science Institute, Columbia University, NewYork,NY,10027, United States
[2] Department of Computational Applied Mathematics and Operations Research, Rice University, Houston,TX,77098, United States
[3] Ken Kennedy Institute, Rice University, Houston,TX,77005, United States
来源：
Journal of Scientific Computing | 2024年 / 101卷 / 03期
基金：
美国国家科学基金会;
关键词：
35c07 - 35l40 - 65m12 - 65m60 - 78a40 - Coherent structure - Discontinuous galerkin - Dynamic of coherent structure - Error estimates - First-order hyperbolic systems - Topological resonator;
D O I：
10.1007/s10915-024-02675-2
中图分类号：
学科分类号：
摘要：
We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dimer lattice of topological resonators. We examine the energy-conserving or energy-dissipating property in relation to the choices of simple, mesh-independent numerical fluxes. We demonstrate that, with certain numerical flux choices, our DG method achieves optimal convergence in the L2 norm. We provide numerical experiments that validate and illustrate the effectiveness of our proposed numerical methods. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
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