(419b) Fast Stokesian Dynamics Simulations with Applications to Brownian Motion and Arbitrarily Shaped Particles

In this talk, I will present recent work developing Stokesian Dynamics simulations with O(N) computational complexity. Stokesian Dynamics models the hydrodynamic interaction among suspended particles at low Reynolds number by superimposing two dissipative forces on the particles: one many bodied force which is derived from a far-field description of the particulate hydrodynamics, and one pair-wise force derived typically from lubrication approximations for the hydrodynamics of two nearly touching particles. We show how to reformulate the Stokesian Dynamics problem as a classic saddle-point problem for which a natural Schur complement preconditioner emerges. This pre-conditioner ensures that solution of linear systems of equations for the forces and velocities on the particles are linear in the number of particles N. In one application, this formulation enables us to adapt the positively split Ewald method to generate samples of the noise in Stokesian Dynamics simulations of suspensions of Brownian particles with O(N) computational complexity. In another application, we illustrate how the immersed boundary method can be applied in a straightforward fashion to extend all of these calculations to dispersions of particles with arbitrary shape.