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首页> 外文期刊>Journal of Computational Physics >A multilayer method of fundamental solutions for Stokes flow problems
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A multilayer method of fundamental solutions for Stokes flow problems

机译：斯托克斯流问题的基本解决方案的多层方法

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摘要

The method of fundamental solutions (MFS) is a meshless method for the solution of boundary value problems and has recently been proposed as a simple and efficient method for the solution of Stokes flow problems. The MFS approximates the solution by an expansion of fundamental solutions whose singularities are located outside the flow domain. Typically, the source points (i.e. the singularities of the fundamental solutions) are confined to a smooth source layer embracing the flow domain. This monolayer implementation of the MFS (monolayer MFS) depends strongly on the location of the user-defined source points: On the one hand, increasing the distance of the source points from the boundary tends to increase the convergence rate. On the other hand, this may limit the achievable accuracy. This often results in an unfavorable compromise between the convergence rate and the achievable accuracy of the MFS. The idea behind the present work is that a multilayer implementation of the MFS (multilayer MFS) can improve the robustness of the MFS by efficiently resolving different scales of the solution by source layers at different distances from the boundary. We propose a block greedy-QR algorithm (BGQRa) which exploits this property in a multilevel fashion. The proposed multilayer MFS is much more robust than the monolayer MFS and can compute Stokes flows on general two- and three-dimensional domains. It converges rapidly and yields high levels of accuracy by combining the properties of distant and close source points. The block algorithm alleviates the overhead of multiple source layers and allows the multilayer MFS to outperform the monolayer MFS.
机译：基本解法（MFS）是用于解决边值问题的无网格方法，并且最近已被提出为解决斯托克斯流问题的一种简单有效的方法。 MFS通过扩展奇异点位于流域之外的基本解来近似该解。通常，源点（即基本解的奇异点）仅限于包含流域的平滑源层。 MFS（单层MFS）的这种单层实现在很大程度上取决于用户定义的源点的位置：一方面，增加源点与边界的距离往往会提高收敛速度。另一方面，这可能会限制可达到的精度。这通常会导致MFS的收敛速度和可达到的准确性之间的不利折衷。本工作背后的思想是，MFS的多层实现（多层MFS）可以通过在距边界不同距离处的源层有效地解决解决方案的不同比例，从而提高MFS的鲁棒性。我们提出了一种贪婪的QR块算法（BGQRa），该算法以多级方式利用了此属性。所提出的多层MFS比单层MFS健壮得多，并且可以在一般的二维和三维域上计算Stokes流。通过结合远处和近处的源点的属性，它可以快速收敛并产生高水平的准确性。块算法减轻了多个源层的开销，并允许多层MFS胜过单层MFS。

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