Numerical Analysis Seminar

Wednesday, October 25, 2006

Speaker: Alexander Kurganov, Tulane University
Title: Particle method: advantages, limitations, and future perspectives
Time: 3:00-4:00 pm
Place: Blocker 628

Abstract

This talk is devoted to deterministic particle methods, originally developed for solving linear transport equations. The mathematical idea behind this type of methods is very simple: seek for a solution of the time dependent PDE as a linear combination of Dirac delta-functions whose weights and locations change in time. Their evolution is described by a system of ODEs, which has to be solved numerically.

I will concentrate on several aspects of practical implementation of deterministic particle methods related to the recovery of point values from particle approximations, merging and redistributing particles, and different ways of treating diffusion and dispersion terms.

I will also present a hybrid finite-volume-particle method that allows one to take an advantage of non-dissipative nature of particle methods even in problems that cannot be solved by a "pure" particle method.

Last revised: 10/23/06 By: christov@math