Elastic interior transmission eigenvalues and their computation via the method of fundamental solutions

TL;DR

This paper introduces a stabilized fundamental solution method for efficiently computing complex elastic interior transmission eigenvalues in 2D, applicable to various PDE eigenproblems, with supporting analysis and numerical validation.

Contribution

It presents a new stabilized algorithm for elastic eigenvalue computation that is simple to implement and adaptable to similar PDE problems, along with theoretical and numerical validation.

Findings

Successful computation of complex elastic interior transmission eigenvalues

The method is stable and easy to implement

Numerical examples confirm the approach's feasibility

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 without voids. Its algorithm can be implemented very shortly and adopts to many similar PDE-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.