EIGENVALUE PROBLEM IN A SOLID WITH MANY INCLUSIONS: ASYMPTOTIC ANALYSIS



Maz'ya, VG, Movchan, AB and Nieves, MJ
(2017) EIGENVALUE PROBLEM IN A SOLID WITH MANY INCLUSIONS: ASYMPTOTIC ANALYSIS. MULTISCALE MODELING & SIMULATION, 15 (2). pp. 1003-1047.

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Abstract

We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterized by a small parameter which is much larger when compared with the nominal size of inclusions. Remainder estimates for the approximations to the first eigenvalue and associated eigenfield are presented. Numerical illustrations are given to demonstrate the efficiency of the asymptotic approach compared to conventional numerical techniques, such as the finite element method, for three-dimensional solids containing clusters of small inclusions.

Item Type: Article
Additional Information: 55 pages, 5 figures
Uncontrolled Keywords: singular perturbations, clouds of inclusions, asymptotic approximations, eigenvalue problem, Helmholtz equation
Depositing User: Symplectic Admin
Date Deposited: 19 Jan 2018 14:52
Last Modified: 19 Jan 2023 06:46
DOI: 10.1137/16M1079348
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3014629