Stokes flow, discussed by G.G. Stokes in 1851, describes many microscopic biological flow phenomena, including cilia-driven transport and flagellar motility; the need to quantify and understand these flows has motivated decades of mathematical and computational research. Regularized stokeslet methods, which have been used and refined over the past 20 years, offer significant advantages in simplicity of implementation, with a recent modification based on nearest-neighbour interpolation providing significant improvements in efficiency and accuracy. Moreover this method can be implemented with the majority of the computation taking place through built-in linear algebra, entailing that state-of-the-art hardware and software developments in the latter, in particular multicore and GPU computing, can be exploited through minimal modifications (‘passive parallelism’) to existing Matlab computer code. Hence, and with widely available GPU hardware, significant improvements in the efficiency of the regularized stokeslet method can be obtained. The approach is demonstrated through computational experiments on three model biological flows: undulatory propulsion of multiple Caenorhabditis elegans, simulation of progression and transport by multiple sperm in a geometrically confined region, and left–right symmetry breaking particle transport in the ventral node of the mouse embryo. In general an order-of-magnitude improvement in efficiency is observed. This development further widens the complexity of biological flow systems that are accessible without the need for extensive code development or specialist facilities. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

中文翻译：

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被动平行正则化的 Stokeslet

斯托克斯流，由 GG Stokes 在 1851 年讨论，描述了许多微观生物流动现象，包括纤毛驱动的运输和鞭毛运动；量化和理解这些流动的需要激发了数十年的数学和计算研究。在过去 20 年中一直使用和改进的正则化 stokeslet 方法在实现简单方面提供了显着的优势，最近基于最近邻插值的修改在效率和准确性方面提供了显着的改进。此外，这种方法可以通过内置线性代数进行大部分计算来实现，这需要后者中最先进的硬件和软件开发，特别是多核和 GPU 计算，可以通过对现有 Matlab 计算机代码进行最少的修改（“被动并行”）来利用。因此，使用广泛可用的 GPU 硬件，可以显着提高正则化 stokeslet 方法的效率。该方法通过对三个模型生物流的计算实验得到证明：多个秀丽隐杆线虫的波动推进、几何受限区域中多个精子的进展和运输模拟，以及小鼠胚胎腹侧节点中的左右对称性破坏粒子运输. 一般来说，观察到效率有一个数量级的提高。这一发展进一步扩大了生物流动系统的复杂性，无需大量代码开发或专业设施即可访问。