Abstract

In this paper the Stokes system in an unbounded domain is solved by the artificial boundary method. The novelty lies in an operator form of the exact Dirichlet-to-Neumann (DtN) mapping. With the help of the Chebyshev rational approximation of the square root function, we derive a highly accurate approximate DtN mapping, which can be numerically implemented without resorting to the eigen-decomposition in terms of the vectorial spherical harmonics. In addition, we develop an efficient block preconditioner for the augmented truncated saddle point problem. Numerical experiments demonstrate the effectiveness of the proposed method.

中文翻译：

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三维斯托克斯系统外问题的精确人工边界条件的有效实现

摘要

本文采用人工边界法求解无界域中的斯托克斯系统。新颖之处在于精确的 Dirichlet-to-Neumann (DtN) 映射的算子形式。在平方根函数的切比雪夫有理逼近的帮助下，我们推导出了一个高精度的近似 DtN 映射，它可以在不借助向量球谐函数的特征分解的情况下进行数值实现。此外，我们为增强的截断鞍点问题开发了一种有效的块预条件器。数值实验证明了所提出方法的有效性。