Seminarreihe "structure preserving numerical methods for hyperbolic equations" im Oberseminar Mathematische Strömungsmechanik: Qin Li
Low rank structure in the forward and inverse kinetic theory
|Datum:||16.04.2021, 15:00 - 16:00 Uhr|
This talk is part of the seminar series "structure preserving numerical methods for hyperbolic equations", click here for more details
Kinetic theory is a body of theory from statistical mechanics. It is useful in describing the dynamics of a large number of particles, but its high dimensional structure makes the computation infeasible. In multi-scale regimes, however, kinetic equations can be compressed: The Boltzmann equation is asymptotically equivalent to the Euler equations, and the radiative transfer equation is asymptotically equivalent to the diffusion equation. In linear algebra, this phenomenon is equivalent to a system being of low rank. I will discuss how the low rank structure forms, and how it affects the computation. In the forward regime, inserting the low-rank structure greatly advances the computation, but in the inverse regime, the system being of low rank typically makes the problems significantly harder.nd large space scale simulations to approach the macroscopic scales. A highly accurate deduced equation of state for the Euler equations establishes a one-to-one correspondence of the molecular dynamics and the continuum solutions.
via Zoom video conference (request the Zoom link from firstname.lastname@example.org)