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The inverse electromagnetic scattering problem for anisotropic media plays a special role in inverse scattering theory due to the fact that the (matrix) index of refraction is not uniquely determined from the far field pattern of the scattered field even if multi-frequency data is available. In this paper we describe how transmission eigenvalues can be(More)
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)
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)
We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting cavity from measurement of scattered electric field due to electric dipole sources on a surface inside the cavity. We prove a reciprocity relation for the scattered electric field and a uniqueness theorem for the inverse problem. Then the near field(More)
In this paper we consider the transmission eigenvalue problem corresponding to the scattering problem for an anisotropic magnetic materials with voids, i.e. subregion with refractive index the same as the background. Under weak assumptions on the material properties, we show that the transmission eigenvalues can be determined from the far field(More)
We consider the exterior transmission eigenvalue problem for spherically stratified media in R 3 and consider the case of axially symmetric eigenfunctions. The exterior transmission eigenvalue problem is then reduced to a problem in ordinary differential equations. We first determine conditions on the index of refraction which guarantee the existence of(More)