Journal article

Wave propagation along periodic layers

Abstract:: Solutions for waves travelling transversely in a layered medium satisfy an exact recurrence relation when the transit time across each of the layers is the same. Using such solutions in an alternating-direction splitting method, high accuracy solutions can also be computed for wave propagation parallel to the layers. An asymptotic analysis uncovers the remarkable result that dispersion of waves parallel to the layers is very similar to the dispersion observed in the transverse case. This result is confirmed by the numerical solutions. The results are in general agreement with similar observations reported in the literature using di↵erent numerical and analytical methods.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Farmer, C., Ockendon, H., & Ockendon, J. (2018). Wave propagation along periodic layers. SIAM Journal on Applied Mathematics, 78(4), 2154–2175.

MLA Style

Farmer, C., et al. “Wave Propagation along Periodic Layers.” SIAM Journal on Applied Mathematics, vol. 78, no. 4, Society for Industrial and Applied Mathematics, 2018, pp. 2154–75.

Chicago Style

Farmer, C, H Ockendon, and J Ockendon. 2018. “Wave Propagation along Periodic Layers.” SIAM Journal on Applied Mathematics 78 (4): 2154–75.
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Files:: waves_2D_accepted_4th_June_2018.pdf

(Preview, Accepted manuscript, pdf, 4.1MB, Terms of use)

Publisher copy:: 10.1137/17M115092X

Authors

+ Farmer, C More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Ockendon, H More by this author

Institution:: University of Oxford
Division:: MPLS Division
Department:: Mathematical Institute
Role:: Author

+ Ockendon, J More by this author

Institution:: University of Oxford
Division:: MPLS Division
Department:: Mathematical Institute
Role:: Author

Publisher:: Society for Industrial and Applied Mathematics
Journal:: SIAM Journal on Applied Mathematics More from this journal
Volume:: 78
Issue:: 4
Pages:: 2154–2175
Publication date:: 2018-08-14
Acceptance date:: 2018-06-04
DOI:: 10.1137/17M115092X
EISSN:: 1095-712X
ISSN:: 0036-1399

Keywords:: dispersion

wave propagation

periodic media

homogenization

multiple scales
Pubs id:: pubs:856134
UUID:: uuid:ea1b5b04-99e9-45a9-af47-8a5189dba3f0
Local pid:: pubs:856134
Source identifiers:: 856134
Deposit date:: 2018-06-06

Terms of use

Copyright holder:: Society for Industrial and Applied Mathematics
Copyright date:: 2018
Notes:: Copyright © 2018, Society for Industrial and Applied Mathematics. This is the accepted manuscript version of the article. The final version is available online from SIAM at: https://doi.org/10.1137/17M115092X

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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