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  • Title: Parallel O(N) Stokes' solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries.
    Author: Zhao X, Li J, Jiang X, Karpeev D, Heinonen O, Smith B, Hernandez-Ortiz JP, de Pablo JJ.
    Journal: J Chem Phys; 2017 Jun 28; 146(24):244114. PubMed ID: 28668032.
    Abstract:
    An efficient parallel Stokes' solver has been developed for complete description of hydrodynamic interactions between Brownian particles in bulk and confined geometries. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green's function formalism. A scalable parallel computational approach is presented, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the general geometry Ewald-like method. Our approach employs a highly efficient iterative finite-element Stokes' solver for the accurate treatment of long-range hydrodynamic interactions in arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallel Stokes' solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem leads to an O(N) parallel algorithm. We illustrate the new algorithm in the context of the dynamics of confined polymer solutions under equilibrium and non-equilibrium conditions. The method is then extended to treat suspended finite size particles of arbitrary shape in any geometry using an immersed boundary approach.
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