Hardy空间无限元用于时谐二维弹性波导问题
Hardy space infinite elements for time-harmonic two-dimensional elastic waveguide problems
AI总结：
本文提出一种基于拉普拉斯变换的Hardy空间无限元方法，用于解决二维弹性波导问题中的时谐弹性方程，通过分离变换后的解空间实现正确离散化，避免传统PML和Hardy空间无限元方法的不足。
摘要：
我们考虑包含二维半无限条带的时谐线弹性方程。由于此类问题存在群速和相速符号不同的模式，标准完美匹配层（PML）以及标准Hardy空间无限元方法失效。我们应用一种 recently developed 的无限元方法，该方法基于传播方向的拉普拉斯变换，将变换后的解空间分离为入射和出射函数空间，两者均为特定的Hardy空间。该方法不使用模态分离，适用于频率区间，这些区间内的操作符频率无关，从而在计算共振时形成线性本征值问题。数值实验包括收敛性测试和共振问题。
英文摘要：
We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips. Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer (PML) as well as standard Hardy space infinite element methods fail. We apply a recently developed infinite element method for a physically correct discretization of such waveguide problems which is based on a Laplace transform in propagation direction. In the Laplace domain the space of transformed solutions can be separated into a sum of a space of incoming and a space of outgoing functions where both function spaces are certain Hardy spaces. The Hardy space is chosen such that the construction of a simple infinite element is possible. The method does not use a modal separation and works on intervals of frequencies. On those intervals the involved operators are frequency independent and hence lead to linear eigenvalue problems when computing resonances. Numerical experiments containing convergence tests and resonance problems are included.
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