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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)

- Jiguang Sun
- SIAM J. Numerical Analysis
- 2011

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 refraction, of the scattering target. Despite considerable effort devoted to the existence and estimation for the transmission eigenvalues, the numerical treatment is limited. Since… (More)

- Hongrui Geng, Xia Ji, Jiguang Sun, Liwei Xu
- J. Sci. Comput.
- 2016

We investigate the C interior penalty Galerkin (C IPG) method for biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn-Hilliard type. We prove the convergence of the method and present numerical results to illustrate its performance. We also compare the C IPG method with the Argyris C… (More)

- Jing Li, Zhaofa Zeng, Jiguang Sun, Fengshan Liu
- IEEE Geosci. Remote Sensing Lett.
- 2012

- Xia Ji, Jiguang Sun, Tiara Turner
- ACM Trans. Math. Softw.
- 2012

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)

- Peter Monk, Jiguang Sun
- SIAM J. Scientific Computing
- 2012

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)

- Fioralba Cakoni, Peter Monk, Jiguang Sun
- Comput. Meth. in Appl. Math.
- 2014

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)

- Jiguang Sun, Liwei Xu
- 2013

We present an iterative method to compute the Maxwell’s transmission eigenvalue problem which has importance in non-destructive testing of anisotropic materials. The transmission eigenvalue problem is first written as a quad-curl eigenvalue problem. Then we show that the real transmission eigenvalues are the roots of a non-linear function whose value is the… (More)

- Jiguang Sun
- Numerische Mathematik
- 1999