Recursive Integral Method for the Nonlinear Non-Self-Adjoint Transmission Eigenvalue Problem (Journal of Computational Mathematics, 2021)
The transmission eigenvalue problem is an eigenvalue problem that arises in the scattering of time-harmonic waves by an inhomogeneous medium of compact support. Based on a fourth order formulation, the transmission eigenvalue problem is discretized by the Morley element. For the resulting quadratic eigenvalue problem, a recursive integral method is used to compute real and complex eigenvalues in prescribed regions in the complex plane. Numerical examples are presented to demonstrate the effectiveness of the proposed method.
Keywords: Transmission eigenvalue problem; Nonlinear eigenvalue problem; Contour integrals.