A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves

Abstract

The paper presents a holomorphic operator function approach for the transmission eigenvalue problem of elastic waves using the discontinuous Galerkin method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the elastic transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for the discontinuous Galerkin method is proved following the abstract theory of the holomorphic Fredholm operator. The spectral indicator method is employed to compute the transmission eigenvalues. Extensive numerical examples are presented to validate the theory.