Fast and spectrally accurate summation of 2-periodic Stokes potentials

Abstract

We derive a Ewald decomposition for the Stokeslet in planar periodicity and a novel PME-type O(N log N) method for the fast evaluation of the resulting sums. The decomposition is the natural 2P counterpart to the classical 3P decomposition by Hasimoto, and is given in an explicit form not found in the literature. Truncation error estimates are provided to aid in selecting parameters. The fast, PME-type, method appears to be the first fast method for computing Stokeslet Ewald sums in planar periodicity, and has three attractive properties: it is spectrally accurate; it uses the minimal amount of memory that a gridded Ewald method can use; and provides clarity regarding numerical errors and how to choose parameters. Analytical and numerical results are give to support this. We explore the practicalities of the proposed method, and survey the computational issues involved in applying it to 2-periodic boundary integral Stokes problems.

References in corpus (3)

• Electrostatics in Periodic Slab Geometries I
• Nature-inspired microfluidic propulsion using magnetic actuation
• Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems

Cited by in corpus (6)

• Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
• Large Scale Brownian Dynamics of Confined Suspensions of Rigid Particles
• An accurate integral equation method for simulating multi-phase Stokes flow
• Flexibly imposing periodicity in kernel independent FMM: A Multipole-To-Local operator approach
• Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall
• A unified integral equation scheme for doubly-periodic Laplace and Stokes boundary value problems in two dimensions