[01605] Recent advances in computational methods for kinetic and hyperbolic equations
Session Time & Room : 5B (Aug.25, 10:40-12:20) @E702
Type : Proposal of Minisymposium
Abstract : In recent years, there have been significant advances in computational algorithms for kinetic and hyperbolic equations. New methods have been designed that can achieve efficient simulations while preserving key structures of the underlying solutions. This minisymposium will bring experts in this area to present some key advances, including numerical methods and model reduction for wave equations and kinetic equations. Novel schemes and their properties will be discussed with applications in electromagnetic waves, plasma simulations and applications in gas dynamics and nuclear engineering.
[03143] A Natural Model Reduction Framework for Kinetic Equations
Format : Talk at Waseda University
Author(s) :
Ruo Li (Peking University)
Abstract : To investigate a kinetic equation with prescribed low dimensional input data set, the solutions provided by the equation has to be confined in a low dimensional manifold. We propose in this article a natural framework for the model reduction of the kinetic equation with such the setup that an approximate solution manifold with finite dimension is available. The method results in a symmetric hyperbolic system automatically with natural assumptions. As the applications of the framework, we present some interesting cases, some of which gives brand-new models with elegant features. A few essential factors, including conservative quantities and entropy increasing, can be discussed in terms of the properties of the approximate the solution manifold.
