Acta Numerica· 2014Q1· Review
Numerical methods for kinetic equations
- 378citations
- Q1SCImago
- 2014year
Short summary
This review surveys numerical methods for kinetic partial differential equations, highlighting challenges in balancing accuracy and computational complexity for high-dimensional systems.
AI-generated from the title and abstract; the full text is not read.
Key points
- Kinetic equations describe systems with a large number of particles.
- Numerical methods for kinetic equations face challenges due to high dimensionality and physical properties.
- Key numerical techniques include semi-Lagrangian methods, discrete-velocity models, and spectral methods.
- The review discusses advanced concepts like asymptotic-preserving methods and hybrid schemes.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Acta Numerica, 2014 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics