IMPLEMENTING THE CELL MULTIPOLE METHOD FOR DIPOLAR AND CHARGED DIPOLAR SYSTEMS

Recently, substantial progress has been made in reducing the cost of c omputing Coulomb sums in fields such as astrophysics and molecular dyn amics (MD). This has culminated in the fast multipole method (FMM), an d its Cartesian counterpart, the cell multipole method (CMM). In MD si mulations, these methods provide efficient and accurate algorithms for computing the energy and forces of charge-charge interactions. Howeve r, dipolar interactions are as important and as challenging to compute . In this paper we implement the cell multipole method (CMM) for dipol ar domains. This CMM implementation is an accurate and efficient appro ach for computing interactions in million-particle dipolar systems. In addition, we use CMM to treat systems of permanent dipoles and induce d dipoles, permanent charges and permanent dipoles, and permanent char ges and induced dipoles. We derive and discuss expressions for accurat e and efficient computation of all interactions in these systems. The approach is also applicable to polarizable charged dipolar systems. Fi nally, we apply one-level CMM and hierarchical CMM to arbitrary dipola r systems and discuss accuracy and speed. The hierarchical implementat ion of CMM is shown to scale linearly with the number of dipoles.