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Optimized first-order absorbing boundary conditions for anisotropic elastodynamics

机译：各向异性弹性动力学优化的一阶吸收边界条件

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摘要

We propose new forms of low-order absorbing boundary conditions (ABC) for time-dependent elastic waves in isotropic and anisotropic media. The configuration considered is that of a two-dimensional elastic waveguide. The ABC shares with the widely-known Lysmer-Kuhlemeyer (LK) boundary condition the ease of implementation, especially in a finite-element (FE) setting, while offering gains in accuracy over the LK-like condition (or the LK condition in the isotropic case). The new conditions are proved to be energy-stable, even in the case when inverse modes are present, for which the normal components of the phase and group velocities have an opposite direction. The developed ABCs are particularly convenient to use in a Finite Element setting as they preserve the symmetry and positivity of the formulation and are simple to implement. The ABC features several parameters, which are optimized for accuracy. The optimization criterion is based on the notion of the energy-rate reflection coefficient. We test the performance of the scheme via a numerical example. While the gain in accuracy is found to be moderate (around 20% relative to the LK condition), the main result of this investigation lies in the development of ABCs for anisotropic elastodynamics that are proved to be stable from the outset, and are amenable for accuracy optimization. We plan to design in a future study analogous stable and optimized high-order ABCs using the methodology developed here. (C) 2019 Elsevier B.Y. All rights reserved.
机译：我们为各向同性和各向异性介质中的时间依赖性弹性提出了新的低阶吸收边界条件（ABC）。所考虑的配置是二维弹性波导的配置。 ABC股份与广泛的Lysmer-Kuhlemeyer（LK）边界条件的易于实现，特别是在有限元（FE）设置，同时在LK样条件（或LK条件中）提供提升的准确性各向同性案例）。证明了新的条件是节能的，即使在存在逆模式时，即使在存在逆模式时，相位和群速度的正常分量具有相反的方向。开发的ABC在有限元环境中使用特别方便，因为它们保持配方的对称性和积极性并且易于实施。 ABC具有多种参数，可针对精度进行优化。优化标准基于能量率反射系数的概念。我们通过数值示例测试方案的性能。虽然发现准确性的增益适中（相对于LK条件约为20％），但该研究的主要结果在于ABC的发展，用于从一开始就被证明是稳定的，并且适用于准确性优化。我们计划在未来的研究中设计类似于此处开发的方法的类似稳定和优化的高阶ABC。 （c）2019年Elsevier B.Y.版权所有。

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