论文标题
三维声学散射问题的自适应有限元DTN方法
An adaptive finite element DtN method for the three-dimensional acoustic scattering problem
论文作者
论文摘要
本文涉及在三个维度上通过有限的坚不可摧的障碍物对声学散射的数值解决方案。通过使用Dirichlet到Neumann（DTN）操作员，将障碍物散射问题作为边界值问题提出为边界值问题。使用截短的DTN操作员得出了有限元法的后验误差估计。 A后验误差估计由有限元近似误差和DTN算子的截断误差组成，其中后者显示出相对于截断参数的呈指数衰减。基于A后验误差估计，为障碍物散射问题开发了一种自适应有限元方法。截断参数由DTN操作员的截断误差确定，而局部细化的网格元素通过有限元近似误差标记。提出了数值实验，以证明该方法的有效性。
This paper is concerned with a numerical solution of the acoustic scattering by a bounded impenetrable obstacle in three dimensions. The obstacle scattering problem is formulated as a boundary value problem in a bounded domain by using a Dirichlet-to-Neumann (DtN) operator. An a posteriori error estimate is derived for the finite element method with the truncated DtN operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN operator, where the latter is shown to decay exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element method is developed for the obstacle scattering problem. The truncation parameter is determined by the truncation error of the DtN operator and the mesh elements for local refinement are marked through the finite element approximation error. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.
