AI 中文总结
本文提出一种适用于二维和三维的层状介质多粒子弹性散射快速求解器，结合Sommerfeld积分、边界积分公式与快速多极方法，经数值实验验证可用于直接及逆散射应用。
AI 中文摘要
本文提出一种用于求解嵌入层状介质中多粒子的时谐弹性散射问题的快速求解器，粒子表面可施加Dirichlet或Neumann边界条件。这类问题出现在复合材料优化、无损检测、地下成像等重要应用中，因粒子间强多次散射相互作用及层状界面的影响，计算极具挑战性。所提方法通过Sommerfeld积分表示层状介质的贡献，并将其与适定的粒子散射问题边界积分公式耦合；采用高阶积分方程离散化和散射矩阵处理任意形状粒子，借助多次散射理论高效描述粒子相互作用。为降低大粒子系统的计算成本，进一步通过快速多极方法加速所得多次散射计算，核心公式同时适用于二维和三维情况。针对刚性粒子和自由牵引力粒子的数值实验验证了公式的准确性，并展示了其在直接散射模拟和逆散射应用中的灵活性。
英文摘要
This paper proposes a fast solver for time-harmonic elastic scattering by multiple particles embedded in layered media, with either Dirichlet or Neumann boundary conditions imposed on the particle surfaces. Such problems arise in many important applications, including composite material optimization, nondestructive testing, and subsurface imaging. They are computationally challenging because of strong multiple scattering interactions among the particles and the layered interface. The proposed method represents the layered medium contribution through Sommerfeld integrals and couples this representation with a well-posed boundary integral formulation for the particle scattering problem. High-order integral equation discretization and scattering matrix are used to handle particles of general shape, while multiple scattering theory provides an efficient description of particle interactions. To reduce the cost for large particle systems, the resulting multiple scattering computation is further accelerated by the fast multipole method. The main formulation is developed in both two and three dimensions. Numerical experiments for rigid and traction-free particles validate the accuracy of the formulation, and demonstrate its flexibility in both direct scattering simulations and inverse scattering applications.
