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Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions

Bao, Gang and Xu, Liwei and Yin, Tao (2019) Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions. Computer Methods in Applied Mechanics and Engineering, 354 . pp. 464-486. ISSN 0045-7825. doi:10.1016/j.cma.2019.05.027. https://resolver.caltech.edu/CaltechAUTHORS:20190528-101603856

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Abstract

In this paper, we consider the boundary integral equation (BIE) methods for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first kind. The innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper-singular boundary integral operators (BIO) associated with the time-harmonic elastic and thermoelastic wave equations. With the help of the new regularized formulations, we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations. The accuracy of the regularized formulations is demonstrated through numerical examples using the Galerkin boundary element method (BEM).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2019.05.027DOIArticle
https://arxiv.org/abs/1902.04095arXivDiscussion Paper
Additional Information:© 2019 Elsevier B.V. Received 7 December 2018, Revised 19 May 2019, Accepted 20 May 2019, Available online 28 May 2019. The work of G. Bao is supported in part by a NSFC Innovative Group Fund (No. 11621101), an Integrated Project of the Major Research Plan of NSFC (No. 91630309), and an NSFC A3 Project (No. 11421110002). The work of L. Xu is partially supported by a Key Project of the Major Research Plan of NSFC (No. 91630205), and a NSFC Grant (No. 11771068). The authors also would like to thank the referees for their constructive comments which helped to improve the paper.
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of China11621101
National Natural Science Foundation of China91630309
National Natural Science Foundation of China11421110002
National Natural Science Foundation of China91630205
National Natural Science Foundation of China11771068
Subject Keywords:Elastic wave; Thermoelastic wave; Hyper-singular boundary integral operator; Regularized formulation; Boundary element method
DOI:10.1016/j.cma.2019.05.027
Record Number:CaltechAUTHORS:20190528-101603856
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190528-101603856
Official Citation:Gang Bao, Liwei Xu, Tao Yin, Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions, Computer Methods in Applied Mechanics and Engineering, Volume 354, 2019, Pages 464-486, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2019.05.027. (http://www.sciencedirect.com/science/article/pii/S004578251930297X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95811
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 May 2019 17:26
Last Modified:16 Nov 2021 17:15

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