标题： 一种用于双周期结构弹性波散射的自适应有限元DtN方法 显示英文标题

标题： An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures

摘要： 考虑时间谐波弹性平面波被双周期刚性表面散射的问题。 弹性波运动的位移由表面上方一个开区域中的三维Navier方程进行建模。 基于Dirichlet-to-Neumann（DtN）算子，该算子表示为一个无限级数，引入了一个精确的透明边界条件，并将散射问题等价地转化为一个有界域中的边界值问题。 提出了一种基于后验误差估计的自适应有限元DtN方法，以求解离散变分问题，其中DtN算子被截断为有限项。 后验误差估计考虑了有限元近似误差和DtN算子的截断误差，该误差被证明随着截断参数呈指数级衰减。 数值实验用于说明所提出方法的有效性。 显示英文摘要

摘要： Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the Dirichlet-to-Neumann (DtN) operator, which is given as an infinite series, an exact transparent boundary condition is introduced and the scattering problem is formulated equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed to solve the discrete variational problem where the DtN operator is truncated into a finite number of terms. The a posteriori error estimate takes account of the finite element approximation error and the truncation error of the DtN operator which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to illustrate the effectiveness of the proposed method.