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Brownian Dynamics simulations are an important tool for modeling the dynamicsof soft matter. However, accurate and rapid computations of the hydrodynamicinteractions between suspended, microscopic components in a soft material is asignificant computational challenge. Here, we present a new method for BrownianDynamics simulations of suspended colloidal scale particles subject to animportant class of hydrodynamic constraints with practically linear scaling ofthe computational cost with the number of particles modeled. Specifically, weconsider the "stresslet" constraint for which suspended particles resist localdeformation. The presented method is an extension of the recently reportedpositively-split formulation for Ewald summation of the Rotne-Prager-Yamakawa(RPY) mobility tensor to higher order (dipole) terms in the hydrodynamicscattering series [Andrew M. Fiore et al. The Journal of Chemical Physics,146(12):124116, 2017]. The hydrodynamic mobility tensor, which is proportionalto the covariance of particle Brownian displacements, is constructed as anEwald sum in a novel way that guarantees the real-space and wave-space sums areindependently positive-definite for all possible particle configurations. Thisproperty is leveraged to rapidly sample the Brownian displacements from asuperposition of statistically independent processes with the wave-space andreal-space contributions as respective covariances. The cost of computing theBrownian displacements in this way is comparable to the cost of computing thedeterministic displacements. Addition of a stresslet constraint to theover-damped particle equations of motion leads to a stochastic differentialalgebraic equation (SDAE) of index 1, which is integrated in time using amid-point integration scheme that implicitly produces displacements consistentwith the fluctuation-dissipation theorem for the constrained system.

Rapid Sampling of Stochastic Displacements in Brownian Dynamics Simulations with Stresslet Constraints