A Multi-level Mixed Element scheme of the two dimensional helmholtz transmission eigenvalue problem
This work provides an efficient numerical method for solving transmission eigenvalue problems on irregular domains, which is important for applications in inverse scattering and non-destructive testing.
The paper presents a multi-level mixed element scheme for solving the Helmholtz transmission eigenvalue problem on polygonal domains, achieving optimal convergence rates and computational cost.
In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by rectangle grids. We first construct an equivalent linear mixed formulation of the transmission eigenvalue problem and then discretize it with Lagrangian finite elements of low regularities. The proposed scheme admits a natural nested discretization, based on which we construct a multi-level scheme. Optimal convergence rate and optimal com- putational cost can be obtained with the scheme.