We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and it square root are available for the given boundary conditions. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely-used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large scale simulations, an Euler-Maruyama traction scheme and a Trapezoidal Slip scheme, which minimize the number of mobility solves per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in a dense suspensions of confined microrollers, whose height above the wall is set by a combination of thermal noise and active flows. We find the existence of two populations of active particles, slower ones closer to the bottom and faster ones above them, and demonstrate that our method provides quantitative accuracy even with relatively coarse resolutions of the particle geometry.
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