Impedance eigenvalues in linear elasticity

Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265, Monk, P. and Selgas, V. (2021) Impedance eigenvalues in linear elasticity. SIAM Journal on Applied Mathematics (SIAP), 81 (6). pp. 2433-2456. ISSN 0036-1399 doi: 10.1137/21M1412955

Abstract/Summary

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid interaction problems. We first consider several possible families of eigenvalues of the elasticity problem, focusing on certain impedance eigenvalues that are an analogue of Steklov eigenvalues. We show that one of these families arises naturally in inverse scattering. We also analyse their approximation from far field measurements of the scattered pressure field in the fluid, and illustrate several alternative methods of approximation in the case of an isotropic elastic disk.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/100064
Identification Number/DOI	10.1137/21M1412955
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Fluid-solid interaction, inverse scattering, Dirichlet-to-Neumann map, linear elasticity, impedance eigenvalues
Publisher	Society for Industrial and Applied Mathematics
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