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Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods

Rubén Sevilla Orcid Logo, Régis Cottereau

Journal of Computational Physics, Volume: 373, Pages: 304 - 323

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1016/j.jcp.2018.07.002

Abstract

This paper presents a mathematical analysis of the stability of high-order spectral elemetns with explicit time marching for the solution of acoustic wave propagation in heterogeneous media. Using a Von Neumann stability analysis, the origin for the instability that is often observed when the stabil...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa40915
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Abstract: This paper presents a mathematical analysis of the stability of high-order spectral elemetns with explicit time marching for the solution of acoustic wave propagation in heterogeneous media. Using a Von Neumann stability analysis, the origin for the instability that is often observed when the stability limit derived for homegenous media is adapted for heterogeneous media. In large scale projects such as the simulation of seismic wave propagation, this known issue results either in simulations that are too expensive due to a conservative choice of the time step or to simulations that lead to unstable results due to the inability to predict the suitability of the time step. The proposed work not only explain the mathematical origin of this problem but also derives exact stability bounds are given for cases when the heterogeneity is periodic.
Keywords: Spectral element method, Explicit time integration, Stability, Heterogeneous media, High-order
College: Faculty of Science and Engineering
Start Page: 304
End Page: 323

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