Colloquium: Dr. Robert Skeel
March 6 @ 2:00 pm - 3:30 pmFree
Fast N-Body Calculations with Periodic Boundary Conditions
Dr. Robert Skeel
Arizona State University
Adjunct Faculty, School of Mathematical and Statistical Sciences
“Fast methods for calculating 2-body interactions have application in particle simulations, partial differential equations, and spatial statistics. Periodic boundary conditions are commonly employed for molecular science and cosmology. However, there is a modeling problem due to the “conditional” convergence in the case of Coulomb and gravitational forces. And, indeed, more than one interpretation is proposed in the literature. Presented is an answer suggested by the finite speed with which forces act. For the fast calculation of such forces, the most celebrated method is the fast multipole method and its tree-code predecessor. However, molecular simulations typically employ mesh-based approximations and the fast Fourier transform. Both types of methods have significant drawbacks, which in most respects are overcome by a more obscure method called multilevel summation. Presented here are the key elements that contribute to the high performance of multilevel summation: separation of length scales, source-destination separable approximations, and the use of B-splines. Also, a case is made for the suitability of multilevel summation for GPU implementation and large-scale parallelism. Results of a comparsion with particle-mesh Ewald are given.”
Light refreshments will be served @ 1:30 pm in EMS E424A.