Symplectic multi-time step parareal algorithms applied to molecular dynamics

Christophe Audouze (1) , Marc Massot (1) , Sebastian Volz (1)

1 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion

In this paper we propose a new parareal algorithm for parallelizing in time molecular dynamics problems. The original structure of this algorithm allows one to consider multi-time stepping, namely two levels of temporal discretization, providing a larger range for the fine and coarse solvers definition. We also prove the symplecticity of this method, which is an expected behavior of the molecular dynamics integrators. The relevance of this algorithm is numerically demonstrated by applying it to three-dimensional atomic lattices on parallel computer architectures. For lattices of more than 20000 atoms we get attractive speed-up with proper choice for the coarse solver definition and for the number of processors.

Mots clés: temporal parallelization; parareal algorithm; ODE integration; multi-time stepping; symplectic integration; molecular dynamics

Domaines: Modélisation et simulation; Analyse numérique [math.NA]

Christophe Audouze, Marc Massot, Sebastian Volz. Symplectic multi-time step parareal algorithms applied to molecular dynamics. 2009. ⟨hal-00358459⟩