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SUMMARY:Dynamical low-rank approximation for computational plasma physics
DTSTART:20221129T161500
DTEND:20221129T171500
DTSTAMP:20260408T020624Z
UID:3fdee899139cd00f33724b6833434c3c84a690ffb2d1902fc5327547
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Lukas Einkemmer\, University of Innsbruck  \nComputatio
 nal Mathematics Seminar \n\nAbstract: Solving high-dimensional kinetic equ
 ations (such as the Vlasov equation\, gyrokinetic equations\, or the Boltz
 mann equations) numerically is extremely challenging. Methods that discret
 ize phase space suffer from the exponential growth of the number of degree
 s of freedom\, the so-called curse of dimensionality\, while Monte Carlo m
 ethods converge slowly and suffer from numerical noise. In addition\, stan
 dard complexity reduction techniques (such as sparse grids) usually perfor
 m rather poorly due to the lack of smoothness for such problems.\nDynamica
 l low-rank techniques approximate the dynamics by a set of lower-dimension
 al functions. For those low-rank factors\, partial differential equations 
 are derived that can then be solved numerically.\nFinding a good separatio
 n between the variables is often driven by physical insight. For example\,
  for kinetic  Alfvén waves we separate the directions parallel and perp
 endicular to the magnetic field lines in order to obtain an efficient appr
 oximation. Due to this flexibility and their capacity to handle non-smooth
  solutions\, dynamical low-rank approximations have been shown to work wel
 l for a range of kinetic equations. In this talk\, we also discuss some re
 cent advances in dynamical low-rank techniques that lead to structure-pres
 erving algorithms and introduce our software framework (Ensign\; see http
 s://github.com/leinkemmer/Ensign) that facilitates the implementation of s
 uch methods on multi-core CPU and GPU based systems.
LOCATION:MA A3 31 https://plan.epfl.ch/?room==MA%20A3%2031
STATUS:CONFIRMED
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