Elastic transmission eigenvalues and their computation via the method of fundamental solutions. Issue 16 (10th December 2021)

• Record Type: Journal Article
• Authors: Kleefeld, A.; Pieronek, L.
• Is Part Of: Applicable analysis. Volume 100:Issue 16(2021)
• Page Start: 3445
• Page End: 3462
• Publication Date: 2021-12-10
• Subjects: Interior transmission eigenvalues -- method of fundamental solutions -- elastic scattering; 65N80 -- 65N35 -- 35P25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1721473
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.