Gallagher M T, Smith D J
Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Birmingham, UK.
School of Mathematics, University of Birmingham, Birmingham, UK.
R Soc Open Sci. 2021 May 26;8(5):210108. doi: 10.1098/rsos.210108.
The method of regularized stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly varying regularized stokeslet kernel. Here, we show how Richardson extrapolation with coarse values of the regularization parameter is ideally suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.
正则化斯托克斯元法因其易于实现、能自然处理复杂移动几何形状以及可去除奇异函数以便进行积分，而在微观尺度生物流体动力学中得到广泛应用。该方法的标准实现方式存在较高计算成本，这是因为线性系统规模与解析快速变化的正则化斯托克斯元核所需的数值分辨率相互耦合。在此，我们展示了使用正则化参数的粗值进行理查森外推法如何非常适合减少求积误差，从而在不损失精度的情况下显著降低存储和求解成本。关于斯托克斯流中阻力和迁移率问题的数值实验支持了这一分析，证实了在精度和/或效率方面有几个数量级的提升。
