An extension of the Generalized Geometry Ewald-like Method (GGEM) (J.P. Hernandez-Ortiz et al., Physical Review Letters, 98, 140602, 2007), to include higher moments of the hydrodynamic force, and lubrication interactions, is presented. GGEM is an O(N) method to calculate hydrodynamic interactions between N particles. The hydrodynamic forces are split into a near-field and far-field part similar to the Accelerated Stokesian Dynamics (ASD) method (A. Sierou and J.F. Brady, Journal of Fluid Mechanics, 448, 115, 2001). The far-field contribution is split into a local part, calculated analytically, and a global part, which is calculated by numerically solving Stokes equations on a mesh. This replaces the FFT based sum in the ASD method. The resulting method is O(N) as opposed to O(NlogN) in the ASD method. In confined systems, the new method has the added advantage that the confining walls do not have to be discretized into particles in order to capture the hydrodynamic effect of the walls.

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