Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Asymptotic-preserving dynamical low-rank approximation for bridging kinetic and fluid regimes
Solving the full Boltzmann or Vlasov equations numerically is often computationally prohibitive. Due to the high-dimensional phase space, the number of degrees of freedom scales as the sixth power in the number of unknowns in each dimension. This is often referred to as the curse of dimensionality. A promising approach to avoid this are so-called dynamical low-rank approximations. The main idea of this approach is that the numerical solution is written as a low-rank approximation, where basis functions that either depend on space or on velocity/angle are propagated forward in time, thus overcoming the curse of dimensionality.
We will discuss recent advances of dynamical low-rank methods for collision kinetic equations and their analysis. In particular, we will address the following questions: a) when is the solution of a kinetic equation low-rank b) can we devise numerical methods that (similar to the PDE case) provably converge to the relevant fluid dynamics as the Knudson number goes to zero) and c) how often do we need to evaluate the (high-dimensional) Boltzmann collision operator.
No Notes/Supplements Uploaded