Recursive integral method for transmission eigenvalues

Transmission eigenvalue problems arise from inverse scattering theory for inhomogeneous media. These non-selfadjoint problems are numerically challenging because of a complicated spectrum. In this paper, we propose a novel recursive contour integral method for matrix eigenvalue problems from finite element discretizations of transmission eigenvalue problems. The technique tests (using an approximate spectral projection) if a region contains eigenvalues. Regions that contain eigenvalues are subdivided and tested recursively until eigenvalues are isolated with a specified precision. The method is fully parallel and requires no a priori spectral information. Numerical examples show the method is effective and robust.