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

Creators: Bao, Gang; Xu, Liwei; Yin, Tao

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).

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.

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