  Brownian Dynamics simulations are an important tool for modeling the dynamics
of soft matter. However, accurate and rapid computations of the hydrodynamic
interactions between suspended, microscopic components in a soft material is a
significant computational challenge. Here, we present a new method for Brownian
Dynamics simulations of suspended colloidal scale particles subject to an
important class of hydrodynamic constraints with practically linear scaling of
the computational cost with the number of particles modeled. Specifically, we
consider the "stresslet" constraint for which suspended particles resist local
deformation. The presented method is an extension of the recently reported
positively-split formulation for Ewald summation of the Rotne-Prager-Yamakawa
(RPY) mobility tensor to higher order (dipole) terms in the hydrodynamic
scattering series [Andrew M. Fiore et al. The Journal of Chemical Physics,
146(12):124116, 2017]. The hydrodynamic mobility tensor, which is proportional
to the covariance of particle Brownian displacements, is constructed as an
Ewald sum in a novel way that guarantees the real-space and wave-space sums are
independently positive-definite for all possible particle configurations. This
property is leveraged to rapidly sample the Brownian displacements from a
superposition of statistically independent processes with the wave-space and
real-space contributions as respective covariances. The cost of computing the
Brownian displacements in this way is comparable to the cost of computing the
deterministic displacements. Addition of a stresslet constraint to the
over-damped particle equations of motion leads to a stochastic differential
algebraic equation (SDAE) of index 1, which is integrated in time using a
mid-point integration scheme that implicitly produces displacements consistent
with the fluctuation-dissipation theorem for the constrained system.
