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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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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa40915
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first_indexed 2018-07-03T13:45:37Z
last_indexed 2020-10-31T03:53:42Z
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spelling 2020-10-30T09:42:36.6225810 v2 40915 2018-07-03 Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2018-07-03 CIVL 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. Journal Article Journal of Computational Physics 373 304 323 0021-9991 Spectral element method, Explicit time integration, Stability, Heterogeneous media, High-order 15 11 2018 2018-11-15 10.1016/j.jcp.2018.07.002 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-10-30T09:42:36.6225810 2018-07-03T11:34:34.5202464 College of Engineering Engineering Rubén Sevilla 0000-0002-0061-6214 1 Régis Cottereau 2 0040915-06072018083920.pdf sevilla2018(2)v2.pdf 2018-07-06T08:39:20.4070000 Output 851231 application/pdf Accepted Manuscript true 2019-07-04T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true eng
title Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
spellingShingle Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
Rubén Sevilla
title_short Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
title_full Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
title_fullStr Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
title_full_unstemmed Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
title_sort Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Rubén Sevilla
Régis Cottereau
format Journal article
container_title Journal of Computational Physics
container_volume 373
container_start_page 304
publishDate 2018
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2018.07.002
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description 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.
published_date 2018-11-15T03:55:19Z
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score 10.89855