论文标题
三个维度的多个颗粒的快速弹性散射
Fast inverse elastic scattering of multiple particles in three dimensions
论文作者
论文摘要
许多应用需要根据散射信息恢复多个弹性颗粒的几何信息。在本文中，我们考虑了三个维度的多个刚性颗粒的反时谐波弹性散射。我们测量远场信息，并应用时间反转方法来恢复未知的弹性颗粒。根据颗粒之间的大小和距离，考虑了两个机制。首先，基于单个粒子的散射特性给出了用于小且遥远颗粒成像的渐近分析，该分析可用于选择性聚焦。其次，当粒子不小但分离良好时，提出了一种基于多个散射理论和快速多极方法组合的快速算法，以有效地模拟正向多重散射问题并应用于反弹性散射中。数值实验表明该方法可以立即确定多个粒子的位置和形状。
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three dimensions. We measure the far field information and apply the time reversal method to recover the unknown elastic particles. Two regimes are considered depending on the size and distance among particles. First, an asymptotic analysis for the imaging of small and distant particles is given based on the scattering property of a single particle, which can be used for selective focusing. Second, when particles are not small but well-separated, a fast algorithm, based on the combination of multiple scattering theory and fast multipole method, is proposed to efficiently simulate the forward multiple scattering problem and applied in the inverse elastic scattering. Numerical experiments demonstrate the proposed method can determine the locations and shapes of multiple particles instantly.
