Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Acoust Soc Am. 2011 Apr;129(4):1783-93. doi: 10.1121/1.3531931.
The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate.
声波和电磁波与周期结构的相互作用在广泛的科学和技术问题中起着重要作用。本贡献集中于稳健和高阶数值模拟模型，用于模拟地球内部产生的压力波与靠近表面的沉积层相互作用。本文描述了一种用于不规则形状周期分层介质散射回波数值模拟的边界微扰方法。该方法仅需要对层界面进行离散化（因此未知量的数量比有限差分和有限元模拟小一个数量级），同时不仅避免了特殊求积规则的需要，也避免了边界积分/元方法所特有的密集线性系统。该方法是 Bruno 和 Reitich 的“场展开法”在两层电介质结构上的推广。通过同时简单地考虑整个结构，而不是分别在各个层中求解，可以按与界面数量成比例的时间恢复全场。与原始的场展开方法一样，这种方法非常高效且谱精度高。
