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.

由于其易于实施，对复杂的移动几何结构进行自然处理以及去除要集成的奇异函数，因此正则化Stokeslet方法被广泛用于微观生物流体动力学中。由于线性系统大小与解析快速变化的正则Stokeslet内核所需的数值分辨率的耦合，因此该方法的标准实现方式会承受较高的计算成本。在这里，我们展示了使用正则化参数的粗略值进行的Richardson外推法如何理想地降低正交误差，从而在不降低精度的情况下显着降低了存储和解决方案成本。斯托克斯流中阻力和迁移率问题的数值实验支持了该分析，确认了准确性和/或效率提高了几个数量级。