SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Multilevel Summation for Dispersion: A Linear-Time Algorithm for $r^{-6}$ Potentials

D. Tameling, P. Springer, P. Bientinesi and A.E. Ismail

Abstract
The multilevel summation method (MLS) was introduced to evaluate long-range interactions in molecular dynamics (MD) simulations. Based on a multilevel matrix summation, [3] MLS was initially developed for Coulomb potentials [1, 2]; with this work, we extend MLS to dispersion interactions. While formally short-ranged, for an accurate calculation of forces and energies in cases such as interfacial systems, dispersion potentials require long-range methods. Since long-range solvers tend to dominate the time needed to perform MD calculations, increasing their performance is of vital importance. Compared to other long-range solvers, such as mesh-based Ewald and fast multipole methods, MLS is particularly attractive for its ability to handle all forms of boundary conditions and for its linear performance. We discuss how the implementation of MLS for dispersion potentials differs from the Coulomb case, and present results establishing the accuracy and efficiency of the method.

Bibliography
[1] R.D. Skeel, I. Tezcan and D.J. Hardy, Multiple grid methods for classical molecular dynamics, J. Comput. Chem., 23 (2002), pp. 673-684.
[2] D.J. Hardy, Multilevel summation for the fast evaluation of forces for the simulation of biomolecules, Ph.D. thesis, University of Illinois at Urbana-Champaign (2006).
[3] A. Brandt and A. A. Lubrecht, Multilevel matrix multiplication and fast solution of integral equations, J. Comput. Phys., 90 (1990), pp. 348-370.

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