SIAM Southeastern Atlantic Section Conference

September 18-19, 2021

Mini-symposium (MS)

MS18: Advances in Memory Efficient Numerical Algorithms for Kinetic Problems

Organizers: Stefan Schnake, Oak Ridge National Laboratory

Abstract: Current research in popular fields such as plasma physics, semiconductors, radiation transport, and general kinetic theory often requires discretization of phase spaces with up to six dimensions. These problems suffer from the so-called curse of dimensionality which makes storage and computational requirements impractical for full resolution numerical approximations. In order to make numerical simulations tractable on modern supercomputers, research has aimed to reduce the memory footprint of such approximations. More mature techniques such as Particle in Cell (PIC) and Monte-Carlo methods reduce memory requirements but can fail to capture physical phenomenon without a large sample size. This
mini-symposium features more recent techniques that focus on reducing memory requirements of more traditional Eulerian methods. Some techniques employ algorithms to reduce the raw number of degrees of freedom while minimally affecting accuracy; other techniques such as Reduced Order Modeling (ROM) and Dynamic Low-Rank approximation (DLRA) model low-rank features of the problem.


Sunday, September 19, 10:30 AM – 12:30 PM

Room: Libry 4033

10:30 – 11:00 Dmitry Anistratov, North Carolina State University, Implicit methods with reduced memory for time-dependent radiation transport problems

11:00 – 11:30 Zheng Sun, University of Alabama, Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport

11:30 – 12:00 Minwoo Shin, University of Notre Dame, A Hybrid decomposition method for the BGK equation

12:00 – 12:30 Stefan Schnake, Oak Ridge National Laboratory, Residual based rank adaptive algorithms for dynamic low-rank approximation