A boundary integral equation for the transmission eigenvalue problem for Maxwell equation
Abstract
We propose a new integral equation formulation to characterize and compute transmission eigenvalues in electromagnetic scattering. As opposed to the approach that was recently developed by Cakoni, Haddar and Meng (2015) which relies on a two‐by‐two system of boundary integral equations, our analysis is based on only one integral equation in terms of the electric‐to‐magnetic boundary trace operator that results in a simplification of the theory and in a considerable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further, we use the numerical algorithm for analytic nonlinear eigenvalue problems that was recently proposed by Beyn (2012) for the numerical computation of the transmission eigenvalues via this new integral equation.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 04, 2018
- Source ID
- 10.1002/mma.4664
Entities
People
- F. Cakoni
- F. Le Louër
- O. Ivanyshyn Yaman
- Rainer Kreß
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- Rutgers University
- Simons Foundation
- Sorbonne University
- University of Göttingen
- İzmir Institute of Technology