scholarly journals An asymptotic preserving semi-implicit multiderivative solver

2021 ◽  
Vol 160 ◽  
pp. 84-101 ◽  
Author(s):  
Jochen Schütz ◽  
David C. Seal
2018 ◽  
Vol 32 (1) ◽  
pp. 205-215 ◽  
Author(s):  
Bin Zhang ◽  
Hao Chen ◽  
Linying Li ◽  
Xiaoyu Shao

2010 ◽  
Vol 27 (6) ◽  
pp. 1396-1422 ◽  
Author(s):  
Christophe Berthon ◽  
Rodolphe Turpault

2014 ◽  
Vol 36 (2) ◽  
pp. A377-A395 ◽  
Author(s):  
Sebastiano Boscarino ◽  
Philippe G. LeFloch ◽  
Giovanni Russo

Acta Numerica ◽  
2014 ◽  
Vol 23 ◽  
pp. 369-520 ◽  
Author(s):  
G. Dimarco ◽  
L. Pareschi

In this survey we consider the development and mathematical analysis of numerical methods for kinetic partial differential equations. Kinetic equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity. Here we review the basic numerical techniques for dealing with such equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for kinetic equations. This covers the derivation of fast algorithms, the notion of asymptotic-preserving methods and the construction of hybrid schemes.


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