Cartesian Treecode Algorithms for Electrostatic Interactions in Molecular Dynamics Simulations.

Abstract

This thesis is concerned with algorithms for evaluating the Coulomb potential en- ergy and forces due to interacting charged particles in molecular dynamics (MD) sim- ulations. We consider Cartesian treecode algorithms which replace particle-particle interactions by particle-cluster interactions which are then evaluated using multipole approximations. Three related projects are carried out.

First, the particle-cluster Cartesian Treecode Ewald (CTE) method for periodic systems is validated for an MD simulation of liquid methyl chloride. We show that the CTE method reproduces the structural and dynamical bulk liquid properties obtained with the Particle-Mesh Ewald method. The cpu time for the current im- plementation of the CTE method is within an order of magnitude of the cpu time for the PME method.

Second, a leaf-cluster treecode method is developed and tested. In free space the algorithm is almost 2 times as fast and in periodic systems it is almost 1.5 times as fast as the particle-cluster algorithm, with comparable accuracy.

Finally, two parallel versions of the particle-cluster CTE method are implemented in the DL POLY software package. One version based on the replicated data strategy is developed for DL POLY 2 and found to scale well for up to 64 processors. A second version based on the domain decomposition method is developed for DL POLY 3 and preliminary results are presented.