A Multilevel Correction Method for Interior Transmission Eigenvalue Problem
For researchers in computational electromagnetics and inverse scattering, this method offers a more efficient numerical scheme for solving transmission eigenvalue problems, though it is an incremental improvement over existing finite element approaches.
The paper proposes a multilevel correction method for solving the interior transmission eigenvalue problem using finite elements, which transforms the problem into a sequence of linear problems and low-dimensional eigenvalue solves, improving computational efficiency. Numerical examples validate the method's efficiency.
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction method can transform the transmission eigenvalue solving in the finest finite element space to a sequence of linear problems and some transmission eigenvalue solving in a very low dimensional spaces. Since the main computational work is to solve the sequence of linear problems, the multilevel correction method improves the overfull efficiency of the transmission eigenvalue solving. Some numerical examples are provided to validate the theoretical results and the efficiency of the proposed numerical scheme.