Stokes flows are incompressible flows at low Reynolds' number [91], which can be found in many applications such as creeping flows in biological systems and fluid–structure interactions in MEMSs. Stokes flow problems were formulated with BIEs and solved by the BEM for decades with either direct or indirect BIE formulations (see, e.g., Refs. [92, 93]).

For Stokes flow problems using the fast multipole BEM, there are several approaches reported in the literature. Greengard et al. [68] developed a fast multipole formulation for directly solving the biharmonic equations in 2D elasticity with the Stokes flow as a special case. Gomez and Power [37] studied 2D cavity flow governed by Stokes equations by using both direct and indirect BIEs and the FMM in which they used Taylor series expansions of the kernels in real variables directly. Mammoli and Ingber [40] applied the fast multipole BEM to study Stokes flow around cylinders in a bounded 2D domain by using direct and indirect BIEs with the kernels expanded by a Taylor series of the real variables. In the context of modeling a MEMS, Ding and Ye [94] developed a fast BEM by using the precorrected fast Fourier transform (FFT) accelerated technique for computing drag forces with 3D MEMS models with slip BCs. Frangi and co-workers [95–98] conducted extensive research by using the direct BIE formulations and the fast multipole BEM for evaluating damping forces of 3D MEMS structures.