  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 twenty 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 C. 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.
