高精度声散射：等几何分析与局部高阶远场展开ABC
Highly accurate acoustic scattering: Isogeometric Analysis coupled with local high order Farfield Expansion ABC
摘要：
本文研究了高阶局部吸收边界条件（ABC）与一般曲线有限元法（FEM）的独特组合及其在时谐声波等几何分析（IGA）中的实现。ABC雇用最近设计的Villamizar，Acosta和Dastrup [J。333（2017）331]。它们是从精确的远场展开表示的传出波在外部的区域所包围的人工边界。因此，由于人工边界上的ABC的误差可以方便地减少，这样的主要误差来自于在计算域的内部使用的体积离散方法。反过来，通过适当地实现{ \it p-}和{ \it h}-细化，可以使内部的误差与人工边界处的误差一样小。我们应用这种新的方法，圆柱形，球形和任意形状的散射体，包括原型潜艇。我们的数值结果表现出谱近似和高阶收敛速度。此外，他们表明，所提出的方法可以减少污染和人工边界的错误可以忽略不计的水平，即使在非常低和高频率的制度，而粗离散密度的IGA。因此，我们开发了一个高精度的计算平台，以数值求解二维和三维的时谐声波散射。
英文摘要：
This work is concerned with a unique combination of high order local absorbing boundary conditions (ABC) with a general curvilinear Finite Element Method (FEM) and its implementation in Isogeometric Analysis (IGA) for time-harmonic acoustic waves. The ABC employed were recently devised by Villamizar, Acosta and Dastrup [J. Comput. Phys. 333 (2017) 331] . They are derived from exact Farfield Expansions representations of the outgoing waves in the exterior of the regions enclosed by the artificial boundary. As a consequence, the error due to the ABC on the artificial boundary can be reduced conveniently such that the dominant error comes from the volume discretization method used in the interior of the computational domain. Reciprocally, the error in the interior can be made as small as the error at the artificial boundary by appropriate implementation of {\it p-} and {\it h}- refinement. We apply this novel method to cylindrical, spherical and arbitrary shape scatterers including a prototype submarine. Our numerical results exhibits spectral-like approximation and high order convergence rate. Additionally, they show that the proposed method can reduce both the pollution and artificial boundary errors to negligible levels even in very low- and high- frequency regimes with rather coarse discretization densities in the IGA. As a result, we have developed a highly accurate computational platform to numerically solve time-harmonic acoustic wave scattering in two- and three-dimensions.
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