论文标题
各向异性介质的传输特征值的有限元近似
Finite Element Approximation of Transmission Eigenvalues for Anisotropic Media
论文作者
论文摘要
传播特征值问题来自不均匀培养基的反散射理论，并且在许多定性方法中具有重要的应用。该问题被发布为一个由两个二阶偏微分方程的系统，本质上是非线性，非偏爱和更高阶的系统。开发有效的数值方法和收敛的证明是不利的。在本文中，我们制定了各向异性介质的传输特征值问题，作为索引零的全体形态Fredholm操作员功能的特征值问题。 Lagrange有限元用于离散化，并且使用塑形操作员功能的抽象近似理论证明了收敛性。开发了一种光谱指标方法来计算特征值。提出了数值示例以进行验证。
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is posted as a system of two second order partial differential equations and is essentially nonlinear, non-selfadjoint, and of higher order. It is nontrivial to develop effective numerical methods and the proof of convergence is challenging. In this paper, we formulate the transmission eigenvalue problem for anisotropic media as an eigenvalue problem of a holomorphic Fredholm operator function of index zero. The Lagrange finite elements are used for discretization and the convergence is proved using the abstract approximation theory for holomorphic operator functions. A spectral indicator method is developed to compute the eigenvalues. Numerical examples are presented for validation.
