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Boundary integral methods are advantageous when simulating viscous flowaround rigid particles, due to the reduction in number of unknowns andstraightforward handling of the geometry. In this work we present a fast andaccurate framework for simulating spheroids in periodic Stokes flow, which isbased on the completed double layer boundary integral formulation. Theframework implements a new method known as quadrature by expansion (QBX), whichuses surrogate local expansions of the layer potential to evaluate it to veryhigh accuracy both on and off the particle surfaces. This quadrature method isaccelerated through a newly developed precomputation scheme. The long rangeinteractions are computed using the spectral Ewald (SE) fast summation method,which after integration with QBX allows the resulting system to be solved in Mlog M time, where M is the number of particles. This framework is suitable forsimulations of large particle systems, and can be used for studying e.g. porousmedia models.

A fast integral equation method for solid particles in viscous flow using quadrature by expansion