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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

孙继广 研究员, Michigan Technological University

Inviter: 季霞
Title:
Direct and Inverse Steklov Eigenvalue Problems
Time & Venue:
2018.1.8 10:00-11:00 Z311
Abstract:
We study the direct and inverse non-selfadjoint Steklov eigenvalue problems.
An efficient numerical method for a non-selfadjoint Steklov eigenvalue problem is proposed. 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.
Steklov eigenvalues are associated with the inverse scattering problem of inhomogeneous media. Some technique to reconstruct Steklov eigenvalues is discussed. These eigenvalues can further be used to obtain information of the physical property of the scatterer using certain statistical method.
 

 

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