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

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.

Keywords:

• Interior transmission eigenvalues
• method of fundamental solutions
• elastic scattering

2010 Mathematics Subject Classifications:

• 65N80
• 65N35
• 35P25

Disclosure statement

No potential conflict of interest was reported by the author(s).