弹性动力学中的散射问题
Scattering problems in elastodynamics
摘要：
在电磁学、声学和量子力学中，散射问题通常可以通过在模拟域边界处的完全匹配层（PML）来数值求解。不幸的是，对于连续介质力学中的一般弹性动力学波动问题，这是不可能的。在本文中，我们介绍了相应的散射场的Navier方程的制定。我们推导出PMLs的基础上，复值坐标变换导致Cosserat弹性张量分布不服从次要的对称性。这些层被示出为在二维中工作，对于所有偏振和所有方向。通过自适应地选择衰减长度，深亚波长偏振模激光器可以一直使用到准静态状态。作为苛刻的例子，我们研究的有效性的圆柱形弹性动力学斗篷的Cosserat类型和近似。
英文摘要：
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.
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