论文标题
双层结构的弹性波散射的自适应有限元DTN方法
An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures
论文作者
论文摘要
考虑通过双期刚性刚性表面散射时谐波弹性平面波。弹性波运动的位移是由表面上方的开放域中的三维Navier方程建模的。基于以无限级数给出的Dirichlet到Neumann（DTN）操作员，引入了确切的透明边界条件，并将散射问题等效地构成为边界域中的边界值问题。提出了基于后验错误估计的基于自适应有限元DTN方法，以解决DTN操作员被截断为有限术语的离散变分问题。 A后验误差估计值考虑了有限元近似误差和DTN操作员的截断误差，该误差显示出相对于截断参数而呈指数衰减的DTN运算符。提出了数值实验，以说明该方法的有效性。
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.
