论文标题
用于解决矩形腔中Helmholtz问题的非重叠Schwarz方法的传输操作员
Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities
论文作者
论文摘要
在本文中，我们讨论了非重叠的施瓦茨方法的不同传输操作员，该方法适用于求解空腔中的时谐音螺旋式方程（即没有传出波条件的封闭域）。此类问题受到反向传播波的严重影响，后者在为Schwarz方法设计优化的传输操作员时通常被忽略。这项工作探讨了新的运营商考虑到这些后传播浪潮的新操作员，并将其与忽略这些贡献的良好操作员进行了比较。值得注意的是，本文重点介绍了矩形腔的情况，因为可以轻松确定最佳（非本地）传输操作员。尽管如此，也考虑了与这种理想几何形状的偏差。特别地，讨论了具有优化的Schwarz方案的光束线低温恒温器的三维模型中声噪声的计算。这些计算在比较对腔体优化的操作员与针对无界问题优化的操作员进行比较时，在迭代计数中降低了46％。
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.
