Using incomplete Cholesky factorization to increase the time step in molecular dynamics simulations

Abstract

Incomplete Cholesky (IC) factorization is widely used as a preconditioner for accelerating the convergence of the conjugate gradient iterative method. The IC factorization has been used in continuum mechanics and other applications that require solutions of elliptic partial differential equations. In this study, we propose an efficient use of the IC factorization to increase the time step and accelerate molecular dynamics simulations. Previously, we proposed the semi-implicit Hessian correction (SimHec) scheme (Washio et al., 2021) for overdamped Langevin dynamics of polymer simulations. SimHec constructs an approximation of the Hessian matrix by superposing the corrected elemental Hessian matrices associated with the interactions within a limited bandwidth along the polymer chain. The resulting narrow-bandwidth system is efficiently solved by an overlapped skyline solver in parallel. In this study, we integrate the non-local interactions in the polymer chain into the corrected Hessian matrix, and approximate the components of the Hessian matrix outside the narrow bandwidth using the IC factorization. This strategy allows us to use time steps that are 150–1000 times larger than those used in the explicit scheme without a severe increase in the computational load.