Physics Colloquium: Dr. Lyudmyla Barannyk, Department of Mathematics, University of Idaho
Monday, February 6 2012 at 4:00 PM
Location: EP 209
Physics Colloquium with Dr. Lyudmyla Barannyk, department of mathematics, University of Idaho, titled, "Fast Algorithms for Mesoscale Evolution of Large Particle Systems," will occur Feb. 6 at 4 p.m. in EP 209.
Abstract: We develop efficient algorithms for simulating dynamics of space-time averages of large systems of ordinary differential equations (ODEs). Averaging produces partial differential equations (PDEs) that are exact but cannot be simulated without solving the underlying ODEs. We approximate these exact PDEs by new closed form constitutive equations that can be evaluated without solving the underlying ODEs. The main idea is to rewrite the nonlinear averages as linear convolutions that relate micro- and mesoscale dynamical functions. The convolutions can be approximately inverted using regularization methods developed for solving ill-posed problems. We test the method numerically on Fermi-Pasta-Ulam chains with two different potentials: the classical Lennard-Jones, and the purely repulsive potential used in granular materials modeling. The results show very good agreement between exact quantities and their closed form approximations. This is joint work with Alexander Panchenko, Washington State University.