Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Computational Physics Year : 2022

Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes

Abstract

Two different Perfectly Matched Layer (PML) formulations with efficient pseudospectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential integrator scheme for a firstorder formulation and a linearly implicit preconditioned finite-difference scheme for a secondorder formulation are proposed and analyzed. To obtain a high spatial accuracy, new regularized Bermúdez type absorption profiles are introduced for the PML. It is shown that the two schemes are efficient, but the linearly implicit scheme should be preferred for accuracy purpose when used within the framework of pseudo-spectral methods combined with the regularized Bermúdez type functions. In addition, in the non-relativistic regime, numerical examples lead to the conclusion that the error related to regularized Bermúdez type absorption functions is insensitive to the small parameter ε involved in the NKGE. The paper ends by a two-dimensional example showing that the strategy extends to the rotating NKGE where the vortex dynamics is very well-reproduced.
Fichier principal
Vignette du fichier
PML_for_Klein_Gordon_equation.pdf (1.89 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03102303 , version 1 (07-01-2021)

Identifiers

Cite

Xavier Antoine, Xiaofei Zhao. Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes. Journal of Computational Physics, 2022, 448, pp.110728. ⟨10.1016/j.jcp.2021.110728⟩. ⟨hal-03102303⟩
80 View
70 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More