Georgia Institute of Technology College of Sciences

Brownian dynamics (BD) is a computational technique for simulating the motions of molecules interacting through hydrodynamic and non-hydrodynamic forces. BD simulations are the main tool used in computational biology for studying diffusion-controlled cellular processes. This talk presents several new numerical linear algebra techniques to accelerate large BD simulations, and related Stokesian dynamics (SD) simulations. These techniques include: 1) a preconditioned Lanczos process for computing Brownian vectors from a distribution with given covariance, 2) low-rank approximations to the hydrodynamic tensor suitable for large-scale problems, and 3) a reformulation of the computations to approximate solutions to multiple time steps simultaneously, allowing the efficient use of data parallel hardware on modern computer architectures.