numerical analysis operator splitting method initial value problems iterative solver method stability analysis beam propagation methods transport equation Operator Splitting Method for Coupled Problems: Transport and Maxwell Equations Juergen Geiser Geiser Juergen Felix Knüttel Knüttel Felix Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 24 pp.

Operator Splitting Method for Coupled Problems: Transport and Maxwell Equations

Juergen Geiser , Felix Knüttel

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 24 pp.

MSC 2000

35K15 Initial value problems for second-order, parabolic equations
35K57 Reaction-diffusion equations

Abstract
In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge-Kutta methods instead of the Yee's algorithm. Further we balance the solver method between the Maxwell and Transport equation.

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