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Regularized integral equation methods for elastic scattering problems in three dimensions

Bruno, Oscar P. and Yin, Tao (2020) Regularized integral equation methods for elastic scattering problems in three dimensions. Journal of Computational Physics, 410 . Art. No. 109350. ISSN 0021-9991.

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This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an extension to the elastic context of the efficient high-order singular-integration methods [13] introduced recently for the acoustic case. In order to obtain formulations leading to iterative solvers (GMRES) which converge in small numbers of iterations we investigate, theoretically and computationally, the character of the spectra of various operators associated with the elastic-wave Calderón relation—including some of their possible compositions and combinations. In particular, by relying on the fact that the eigenvalues of the composite operator NS are bounded away from zero and infinity, new uniquely-solvable, low-GMRES-iteration integral formulation for the closed-surface case are presented. The introduction of corresponding low-GMRES-iteration equations for the open-surface equations additionally requires, for both spectral quality as well as accuracy and efficiency, use of weighted versions of the classical integral operators to match the singularity of the unknown density at edges. Several numerical examples demonstrate the accuracy and efficiency of the proposed methodology.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2020 Elsevier Inc. Received 28 September 2019, Revised 10 February 2020, Accepted 17 February 2020, Available online 3 March 2020. This work was supported by NSF and AFOSR through contracts DMS-1714169 and FA9550-15-1-0043, respectively, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0043
National Security Science and Engineering Faculty FellowshipN00014-16-1-2808
Vannever Bush Faculty FellowshipUNSPECIFIED
Subject Keywords:Elastic waves; Combined field integral equations; Calderón relation; Hyper-singular operator; High-order methods
Record Number:CaltechAUTHORS:20191216-160134658
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Official Citation:Oscar P. Bruno, Tao Yin, Regularized integral equation methods for elastic scattering problems in three dimensions, Journal of Computational Physics, Volume 410, 2020, 109350, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100317
Deposited By: Tony Diaz
Deposited On:17 Dec 2019 00:06
Last Modified:20 Mar 2020 23:24

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