Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array
Numerical Analysis
2023-05-23 v2 Numerical Analysis
Mathematical Physics
math.MP
Abstract
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 norm. We provide numerical experiments that validate and illustrate the effectiveness of our proposed numerical methods.
Cite
@article{arxiv.2305.00072,
title = {Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array},
author = {Qiang Du and Huaiyu Li and Michael Weinstein and Lu Zhang},
journal= {arXiv preprint arXiv:2305.00072},
year = {2023}
}