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Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria

Régis Cottereau, Rubén Sevilla Orcid Logo

International Journal for Numerical Methods in Engineering

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.5922

Abstract

This paper considers the stability of an explicit Leap‐Frog time marching scheme for the simulation of acoustic wave propagation in heterogeneous media with high‐order spectral elements. The global stability criterion is taken as a minimum over local element stability criteria, obtained through the...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40878
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first_indexed 2018-06-29T13:30:10Z
last_indexed 2018-09-10T12:56:03Z
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spelling 2018-09-10T11:03:37.8190074 v2 40878 2018-06-29 Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2018-06-29 CIVL This paper considers the stability of an explicit Leap‐Frog time marching scheme for the simulation of acoustic wave propagation in heterogeneous media with high‐order spectral elements. The global stability criterion is taken as a minimum over local element stability criteria, obtained through the solution of element‐borne eigenvalue problems. First, an explicit stability criterion is obtained for the particular case of a strongly‐heterogeneous and/or rapidly‐fluctuating medium using asymptotic analysis. This criterion is only dependent upon the maximum velocity at the vertices of the mesh elements, and not on the velocity at the interior nodes of the high‐order elements. Second, in a more general setting, bounds are derived using statistics of the coefficients of the elemental dispersion matrices. Different bounds are presented, discussed and compared. Several numerical experiments show the accuracy of the proposed criteria in one‐dimensional test cases as well as in more realistic large scale 3D problems. Journal Article International Journal for Numerical Methods in Engineering 00295981 explicit time integration, heterogeneous media, high‐order spectral element method, stability 31 12 2018 2018-12-31 10.1002/nme.5922 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-09-10T11:03:37.8190074 2018-06-29T10:48:26.7293956 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Régis Cottereau 1 Rubén Sevilla 0000-0002-0061-6214 2 0040878-29062018105213.pdf cottereau2018.pdf 2018-06-29T10:52:13.7600000 Output 4898043 application/pdf Accepted Manuscript true 2019-07-04T00:00:00.0000000 true eng
title Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
spellingShingle Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
Rubén Sevilla
title_short Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
title_full Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
title_fullStr Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
title_full_unstemmed Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
title_sort Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Régis Cottereau
Rubén Sevilla
format Journal article
container_title International Journal for Numerical Methods in Engineering
publishDate 2018
institution Swansea University
issn 00295981
doi_str_mv 10.1002/nme.5922
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description This paper considers the stability of an explicit Leap‐Frog time marching scheme for the simulation of acoustic wave propagation in heterogeneous media with high‐order spectral elements. The global stability criterion is taken as a minimum over local element stability criteria, obtained through the solution of element‐borne eigenvalue problems. First, an explicit stability criterion is obtained for the particular case of a strongly‐heterogeneous and/or rapidly‐fluctuating medium using asymptotic analysis. This criterion is only dependent upon the maximum velocity at the vertices of the mesh elements, and not on the velocity at the interior nodes of the high‐order elements. Second, in a more general setting, bounds are derived using statistics of the coefficients of the elemental dispersion matrices. Different bounds are presented, discussed and compared. Several numerical experiments show the accuracy of the proposed criteria in one‐dimensional test cases as well as in more realistic large scale 3D problems.
published_date 2018-12-31T03:52:05Z
_version_ 1763752568578637824
score 11.016235

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