Asymptotic-Preserving schemes. Modeling, simulation and mathematical analysis of magnetically confined plasmas
Received: 26 September 2012
Accepted: 5 December 2012
Mathematics Subject Classification (2010): 34E05, 34K25, 34K26, 34K28, 76M45, 82D10, 82D37.
Keywords: Singularly-Perturbed problems, Ill-conditionned problems, Asymptotic-Preserving schemes, Numerics, Asymptotic Analysis.
Abstract: These lecture notes summarize a succession of works dealing with the construction as well as the mathematical and numerical study of Asymptotic-Preserving schemes in the kinetic and fluid framework. Asymptotic-Preserving schemes are highly efficient numerical schemes, conceived to treat singularly perturbed problems, which are characterized by the occurrence of a stiff term. Standard schemes are generally inefficient, or even prone to break down when the small perturbation parameter tends to zero, leading thus to the need of new (multiscale) numerical techniques suitable for this kind of problems. Singularly perturbed problems arise in several domains of application, we shall focus in these notes on magnetically confined plasma physics.