论文标题
关于弹性动力学中向后波的精确截断
On exact truncation of backward waves in elastrodynamics
论文作者
论文摘要
对于无限的各向异性介质中的弹性波散射问题，向后波的存在使经典截断技术完全失败。本文与一种精确的截断技术有关，用于终止向后弹性波。我们基于傅立叶变换的方法并设计了两个基本原理，以确保其物理正确性，从而得出了一种闭合形式的Elastronanic Green的张量。我们提出了一种严格的理论，可以完全对格林张量的传播行为进行分类，从而证明了Bécache，Fauqueux和Joly（J。Comp。Phys。，188，2003）提出的一种猜想，内容涉及向后波的不存在的必要条件。使用Green的张量，我们提出了一种新的辐射条件，以表征无穷大处的散布波。这导致了确切的透明边界条件（TBC），以截断无界的域，无论是否存在向后波。我们开发了一种快速算法来评估格林的张量和一个高智能方案，以离散TBC。进行了许多实验，以验证新TBC的正确性和效率。
For elastic wave scattering problems in unbounded anisotropic media, the existence of backward waves makes classic truncation techniques fail completely. This paper is concerned with an exact truncation technique for terminating backward elastic waves. We derive a closed form of elastrodynamic Green's tensor based on the method of Fourier transform and design two fundamental principles to ensure its physical correctness. We present a rigorous theory to completely classify the propagation behavior of Green's tensor, thus proving a conjecture posed by Bécache, Fauqueux and Joly (J. Comp. Phys., 188, 2003) regarding a necessary and suffcient condition of the non-existence of backward waves. Using Green's tensor, we propose a new radiation condition to characterize anistropic scattered waves at infinity. This leads to an exact transparent boundary condition (TBC) to truncate the unbounded domain, regardless the existence of backward waves or not. We develop a fast algorithm to evaluate Green's tensor and a high-accuracy scheme to discretize the TBC. A number of experiments are carried out to validate the correctness and efficiency of the new TBC.
