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Efficient time integration of the Maxwell-Klein-Gordon equation in the nonrelativistic limit regime

Krämer, Patrick; Schratz, Katharina

Abstract: The Maxwell-Klein-Gordon equation describes the interaction of a charged particle with an electromagnetic field. Solving this equation in the non-relativistic limit regime, i.e. the speed of light c formally tending to infinity, is numerically very delicate as the solution becomes highly-oscillatory in time. In order to resolve the oscillations, standard numerical time integration schemes require severe time step restrictions depending on the large parameter c2. The idea to overcome this numerical challenge is to filter out the high frequencies explicitly by asymptotically expanding the exact solution with respect to the small parameter c-2. This allows us to reduce the highly-oscillatory problem to its corresponding non-oscillatory Schrodinger-Poisson limit system. On the basis of this expansion we are then able to construct effcient numerical time integration schemes, which do NOT suffer from any c-dependent time step restriction.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000056578
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-565786
KITopen ID: 1000056578
Verlag KIT, Karlsruhe
Umfang 18 S.
Serie CRC 1173 ; 2016/19
Schlagworte Maxwell-Klein-Gordon, time integration, highly-oscillatory, wave equation, non-relativistic limit
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