Analysis of a Fourier–Galerkin Method for the Transmission Eigenvalue Problem based on a Boundary Integral Formulation

Document Type

Article

Publication Date

4-10-2023

Department

Department of Mathematical Sciences

Abstract

We consider the computation of the transmission eigenvalue problem based on a boundary integral formulation. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function. A Fourier–Galerkin method is proposed for the integral equations. The approximation properties of the associated discrete operators are analyzed and some convergence results of the eigenvalues are obtained. We present the details of the implementation and employ the spectral projection method to compute the eigenvalues. Numerical examples validate the effectiveness and accuracy of the proposed method.

Publication Title

Journal of Scientific Computing

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