Transmission eigenvalues have important applications in inverse scattering theory. They can be used to obtain useful information of the physical properties, such as the index of refrac-tion, of the scattering target. Despite considerable effort devoted to the existence and estimation for the transmission eigenvalues, the numerical treatment is limited.… (More)
Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method has two major advantages: 1) the… (More)
Partition of Unity Finite Element Method (PUFEM) is a very powerful tool to deal overlapping grids. It is flexible and keeps the global continuity. In this paper, we consider PUFEM for Poisson equation for minimal overlapping grids. We present details of the implementation of Poisson equation in 2D for two overlapping domains using triangular meshes.
The transmission eigenvalue problem plays a critical role in the theory of qualitative methods for inhomogeneous media in inverse scattering theory. Efficient computational tools for transmission eigenvalues are needed to motivate improvements to theory, and, more importantly as part of inverse algorithms for estimating material properties. In this paper,… (More)
In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the… (More)
The interior transmission problem (ITP) is a boundary value problem arising in inverse scattering theory which has important applications in qualitative methods. In this paper, we propose a coupled boundary element and finite element method for the ITP. The coupling procedure is realized by applying the direct boundary integral equation method to define the… (More)