Spectral Indicator Method for A Non-selfadjoint Steklov Eigenvalue Problem
For researchers solving non-selfadjoint eigenvalue problems, this provides an efficient numerical method to compute complex eigenvalues without a priori spectral information.
The paper proposes a spectral indicator method for computing complex eigenvalues of a non-selfadjoint Steklov eigenvalue problem, using Lagrange finite elements and a boundary reduction to lower computational cost. Numerical examples validate the method's effectiveness.
We propose an efficient numerical method for a non-selfadjoint Steklov eigenvalue problem. The Lagrange finite element is used for discretization. The convergence is proved using the spectral perturbation theory for compact operators. The non-sefadjointness of the problem leads to non-Hermitian matrix eigenvalue problem. Due to the existence of complex eigenvalues and lack of a priori spectral information, we propose a modified version of the recently developed spectral indicator method to compute (complex) eigenvalues in a given region on the complex plane. In particular, to reduce computational cost, the problem is transformed into a much smaller matrix eigenvalue problem involving the unknowns only on the boundary of the domain. Numerical examples are presented to validate the effectiveness of the proposed method.