Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array

2023/04/28 by Qiang Du, Du, Qiang, Huaiyu Li +5
Computer Science · Earth and Planetary Sciences · Engineering · #35C07 #35L40 #65M12 #65M60 #78A40 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.00072

openalex publication_date 2023/04/28 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28

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 L² norm. We provide numerical experiments that validate and illustrate the effectiveness of our proposed numerical methods.

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