Applied Math Seminar: Low rankness in forward and inverse kinetic theory

Seminar | March 21 | 11 a.m.-12 p.m. | 891 Evans Hall

 Qin Li, University of Wisconsin–Madison

 Department of Mathematics

Multi-scale kinetic equations can be compressed: in certain regimes, the Boltzmann equation is asymptotically equivalent to the Euler equations, and the radiative transfer equation is asymptotically equivalent to the diffusion equation. A lot of detailed information is lost when a system passes to the limit. In linear algebra, it is equivalent to a system being of low rank. I will discuss such transition and how it affects the computation: mainly, in the forward regime, inserting low-rankness could greatly advances the computation, while in the inverse regime, the system being of low rank typically makes the problems significantly harder.