Computation of Maxwell’s transmission eigenvalues and its applications in inverse medium problems
Computation of Maxwell’s transmission eigenvalues and its applications in inverse medium problems
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DOI：
10.1088/0266-5611/29/10/104013
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发表时间：
2013-10
期刊：
影响因子：
2.1
通讯作者：
Jiguang Sun;Liwei Xu
中科院分区：
文献类型：
--
作者：
Jiguang Sun;Liwei Xu
提出了一种迭代计算麦克斯韦传输本征值问题的方法，该问题在各向异性材料的无损检测中具有重要意义。传输本征值问题首先被写成一个四卷曲本征值问题。然后，我们证明了实传输本征值是一个非线性函数的根，该非线性函数的值是一个相关的自伴四卷曲本征值问题的广义本征值，该问题是用混合有限元方法计算的。用割线法计算非线性函数的根。数值算例验证了该方法的有效性。此外，还利用该方法研究了传输本征值与各向异性的关系，并对非均匀介质的折射率进行了重建。
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 nonlinear function whose value is the generalized eigenvalue of a related self-adjoint quad-curl eigenvalue problem which is computed using a mixed finite element method. A secant method is used to compute the roots of the nonlinear function. Numerical examples are presented to validate the method. Moreover, the method is employed to study the dependence of the transmission eigenvalue on the anisotropy and to reconstruct the index of refraction of an inhomogeneous medium.