Domain decomposition algorithms for implicit solvation model. Can you be 500 times faster than the fast multipole method?

Benjamin Stamm, University of Pierre et Marie Curie (UPMC - Paris VI)
December 11th, 2013 at 3:30PM–4:30PM in 939 Evans Hall [Map]

Computational chemistry has attracted much attention since this years choice of the Nobel prize winners in chemistry for their contributions to multi-scale models such as the QM/MM method. The large majority of chemically interesting phenomena take place in condensed phase, where the environment (e.g., solvent) can play a crucial role in determining the structure, the properties and the dynamics of the system to be studied. In a practical context, accounting for all solvent molecules in a either Molecular Dynamics (MD) or even Quantum Mechanical (QM) computation is infeasible due to the complexity of the underlying equations. A particular choice of a multi-scale model is to model the solvent environment to be a conducting continuum medium (COSMO-model) and the resulting electrostatic energy contribution to the solvation energy can be computed by solving a Poisson equation in the Van der Waals cavity of the solute molecule.

The mathematical problem is therefore set (and well-posed) and we illustrate how to approximate its solution using Schwarz's domain decomposition method adapted to integral equations. In this manner, the problem can be solved iteratively and the coupling of the local problems is determined by the connectivity of the molecule (in contrast to fast multipole-based boundary element solvers). The resulting numerical scheme is extremely fast and a linear scaling of the computing resources with respect to the number of atoms of the solute molecule can be achieved. In numerical examples we show how this approach outperforms existing methods such as the fast multipole method by several orders of magnitude.