论文标题
复杂波导中近似DTN图的光谱分解方法
A spectral decomposition method to approximate DtN maps in complicated waveguides
论文作者
论文摘要
在本文中，我们提出了一种新的光谱分解方法，以模拟复杂波导中传播的波。对于波导散射问题的数值解决方案，重要的任务是有效地近似dirichlet到neumann地图。从以前的结果来看，物理解决方案可以分解为广义本征函数的家族，因此我们可以通过这些函数明确地编写Dirichlet到Neumann地图。从广义本征函数的指数衰减中，我们通过有限的截断来近似dirichlet到neumann（DTN）图，并证明近似值被证明是呈指数收敛的。借助截短的DTN映射，将未结合的域截断为有限的域，并在此界面域中设置了问题的变性公式。然后通过有限元方法解决截断的问题。还为数值算法提供了误差估计，并显示了数值示例以说明算法的效率。
In this paper, we propose a new spectral decomposition method to simulate waves propagating in complicated waveguides. For the numerical solutions of waveguide scattering problems, an important task is to approximate the Dirichlet-to-Neumann map efficiently. From previous results, the physical solution can be decomposed into a family of generalized eigenfunctions, thus we can write the Dirichlet-to-Neumann map explicitly by these functions. From the exponential decay of the generalized eigenfunctions, we approximate the Dirichlet-to-Neumann (DtN) map by a finite truncation and the approximation is proved to converge exponentially. With the help of the truncated DtN map, the unbounded domain is truncated into a bounded one, and a variational formulation for the problem is set up in this bounded domain. The truncated problem is then solved by a finite element method. The error estimation is also provided for the numerical algorithm and numerical examples are shown to illustrate the efficiency of the algorithm.
