title: Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations.
abstract: The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.
authors.affiliation: Beckman Institute, University of Illinois, 405 North Mathews Avenue, Urbana, Illinois 61801, USA.
authors.forename: David J
authors.initials: DJ
authors.lastname: Hardy
authors.affiliation: Department of Computer Science, Purdue University, 305 North University Street, West Lafayette, Indiana 47907, USA.
authors.forename: Matthew A
authors.initials: MA
authors.lastname: Wolff
authors.affiliation: Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, USA.
authors.forename: Jianlin
authors.initials: J
authors.lastname: Xia
authors.affiliation: Beckman Institute, University of Illinois, 405 North Mathews Avenue, Urbana, Illinois 61801, USA.
authors.forename: Klaus
authors.initials: K
authors.lastname: Schulten
authors.affiliation: Department of Computer Science, Purdue University, 305 North University Street, West Lafayette, Indiana 47907, USA.
authors.forename: Robert D
authors.initials: RD
authors.lastname: Skeel
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D056004:Molecular Dynamics Simulation