Recursive integral method for transmission eigenvalues
For researchers in inverse scattering and nondestructive testing, this method provides a self-correcting, robust way to compute transmission eigenvalues without requiring initial approximations.
The paper proposes a recursive integral method for computing transmission eigenvalues from a finite element discretization, overcoming difficulties of existing methods by using eigenprojectors of compact operators. Numerical examples demonstrate effectiveness and robustness.
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this paper, we propose a recursive integral method for computing transmission eigenvalues from a finite element discretization of the continuous problem. The method, which overcomes some difficulties of existing methods, is based on eigenprojectors of compact operators. It is self-correcting, can separate nearby eigenvalues, and does not require an initial approximation based on some a priori spectral information. These features make the method well suited for the transmission eigenvalue problem whose spectrum is complicated. Numerical examples show that the method is effective and robust.