A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves (Communications in Computational Physics, 2022)
The paper presents a holomorphic operator function approach for thetransmission eigenvalue problem of elastic waves using the discontinuous Galerkinmethod. To use the abstract approximation theory for holomorphic operator functions,we rewrite the elastic transmission eigenvalue problem as the eigenvalue problem ofa holomorphic Fredholm operator function of index zero. The convergence for thediscontinuous Galerkin method is proved following the abstract theory of the holomorphic Fredholm operator. The spectral indicator method is employed to computethe transmission eigenvalues. Extensive numerical examples are presented to validatethe theory.
Keywords: Discontinuous Galerkin method; transmission eigenvalue problem; elastic waves; Fredholm operator.