Sciweavers

Share
JCPHY
2016

Numerical methods for high-dimensional probability density function equations

3 years 9 months ago
Numerical methods for high-dimensional probability density function equations
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), systems of stochastic ODEs (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on conditional moments closures and it yields a hierarchy of coupled probability density function equations that resembles the Bogoliubov-BornGreen-Kirkwood-Yvon (BBGKY) hierarchy of kinetic ...
H. Cho, D. Venturi, George E. Karniadakis
Added 06 Apr 2016
Updated 06 Apr 2016
Type Journal
Year 2016
Where JCPHY
Authors H. Cho, D. Venturi, George E. Karniadakis
Comments (0)
books