标题： 弹性动力学中的散射问题 显示英文标题

标题： Scattering problems in elastodynamics

摘要： 在电磁学、声学和量子力学中，借助于仿真域边界处的完全匹配层（PMLs），散射问题可以常规地被数值求解。然而，在连续介质力学中，广义的弹性波问题却无法做到这一点。本文中，我们针对Navier方程引入了相应的散射场公式。我们基于复值坐标变换推导出PMLs，这些层所对应的Cosserat弹性张量分布不服从小对称性。这些层被证明在二维情况下，对于所有偏振态和所有方向均有效。通过自适应选择衰减长度，这种深亚波长PMLs可用于准静态区域。作为具有挑战性的例子，我们研究了Cosserat型和近似型圆柱弹性波隐形衣的有效性。 显示英文摘要

摘要： In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this paper, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasi-static regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.