标题： 一种自适应有限元DtN方法在周期结构的声弹性相互作用问题中的应用 显示英文标题

标题： An Adaptive Finite Element DtN Method for the Acoustic-Elastic Interaction Problem in Periodic Structures

摘要： 考虑一个时谐声波平面波入射到具有无界周期性表面的弹性体上的问题。 假设表面以上的介质充满均匀的可压缩无粘性空气/流体，其质量密度恒定；而弹性体被假定为各向同性和线性的。 通过同时引入声波和弹性波的Dirichlet-to-Neumann（DtN）算子，该模型被表述为周期结构中的声弹性相互作用问题。 基于对偶性论证，推导了与截断有限元逼近相关的后验误差估计。 后验误差估计由有限元逼近误差和两种不同DtN算子的截断误差组成，其中后者关于截断参数呈指数衰减。 基于该后验误差，提出了求解周期结构中声弹性相互作用问题的自适应有限元算法。 数值实验展示了所提出算法的有效性。 显示英文摘要

摘要： Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid of constant mass density, while the elastic body is assumed to be isotropic and linear. By introducing the Dirichlet-to-Neumann (DtN) operators for acoustic and elastic waves simultaneously, the model is formulated as an acoustic-elastic interaction problem in periodic structures. Based on a duality argument, an a posteriori error estimate is derived for the associated truncated finite element approximation. The a posteriori error estimate consists of the finite element approximation error and the truncation error of two different DtN operators, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error, an adaptive finite element algorithm is proposed for solving the acoustic-elastic interaction problem in periodic structures. Numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm.