On the development of a Fast Fourier Transform (FFT)-accelerated Stokes flow solver for drag computation on MEMS devices

In this paper we report the development of a technique of computing the fluid drag forces on single and multiple micro-machined devices using a Fast Fourier Transform (FFT)accelerated solver for the integral form of the incompressible Stokes flow equations. The boundary element formulation necessitates the discretization of the surface of the device using a large number of "panels" whose interactions are coupled by multidimensional Stokes kernels. The resulting "n-body" problem generates dense matrices that can be solved in O(n log n) complexity using a pre-corrected FFT approach, where 'n' is the number of panels used in discretizing the surface of the device. However, for single and multi-body problems, steps must be taken to eliminate the null space of the Stokes kernel to obtain a unique solution. Also discussed are techniques of improving the numerical efficiency of the multiresolution computational scheme.