In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising optimized transmission operators for the Schwarz method. This work explores new operators taking into account those back-propagating waves and compares them with well-established operators neglecting these contributions. Notably, this paper focuses on the case of rectangular cavities, as the optimal (non-local) transmission operator can be easily determined. Nonetheless, deviations from this ideal geometry are considered as well. In particular, computations of the acoustic noise in a three-dimensional model of the helium vessel of a beamline cryostat with optimized Schwarz schemes are discussed. Those computations show a reduction of 46% in the iteration count, when comparing an operator optimized for cavities with those optimized for unbounded problems.
翻译：在本文中，我们讨论不同的传输算子，适用于非重叠Schwarz方法，用于求解闭合域（即不具有发散波条件）中的时谐Helmholtz方程。这些问题受到反向传播波的严重影响，而在设计Schwarz方法的优化传输算子时常常被忽略。本文探讨了考虑到这些反向传播波的新算子，并与忽略这些贡献的成熟算子进行了比较。值得注意的是，本文重点研究矩形空腔的情况，因为最佳（非局部）传输算子可以很容易地确定。尽管如此，我们也考虑了与理想几何形状的偏差。特别是，我们讨论了使用优化的Schwarz方案计算带束线低温容器的三维模型中的声噪声。这些计算显示，与针对无边界问题优化的算子相比，优化空腔算子的迭代次数减少了46％。
相关内容
微信扫码咨询专知VIP会员