Volume 48, pp. 243-263, 2018.

Convergence analysis of an explicit splitting method for laser plasma interaction simulations

Georg Jansing and Achim Schädle

Abstract

The convergence of a triple splitting method originally proposed by Tückmantel, Pukhov, Liljo, and Hochbruck for the solution of a simple model that describes laser plasma interactions with overdense plasmas is analyzed. For classical explicit integrators it is the large density parameter that imposes a restriction on the time step size to make the integration stable. The triple splitting method contains an exponential integrator in its central component and was specifically designed for systems that describe laser plasma interactions and overcomes this restriction. We rigorously analyze a slightly generalized version of the original method. This analysis enables us to identify modifications of the original scheme such that a second-order convergent scheme is obtained.

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Key words

exponential integrators, highly oscillatory problems, trigonometric integrators, splitting methods

AMS subject classifications

65P10

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