The method of fundamental solutions for computing acoustic interior transmission eigenvalues. (1st February 2018)

• Record Type: Journal Article
• Authors: Kleefeld, Andreas; Pieronek, Lukas
• Is Part Of: Inverse problems. Volume 34:Number 3(2018:Mar.)
• Publication Date: 2018-02-01
• Subjects: interior transmission eigenvalues -- method of fundamental solutions -- non-linear eigenvalue problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa72d
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.