Numerical simulation of relativistic laser plasma interaction [Elektronische Ressource] / vorgelegt von Julia Maria Schweitzer

Numerical Simulation ofRelativistic Laser-PlasmaInteractionI n a u g u r a l - D i s s e r t a t i o nzurErlangung des Doktorgrades derMathematisch-Naturwissenschaftlichen Fakult¨atder Heinrich-Heine-Universit¨at Dus¨ seldorfvorgelegt vonJulia Maria Schweitzeraus KrefeldJuni 2008Mathematisches Institutder Heinrich-Heine-Universit¨at Dus¨ seldorfGedruckt mit der Genehmigung derMathematisch-Naturwissenschaftlichen Fakult¨at derHeinrich-Heine-Universit¨at Dusse¨ ldorfReferent: Prof. Dr. Marlis HochbruckKoreferent: Prof. Dr. Karl-Heinz SpatschekTag der mundlic¨ hen Prufung¨ : 03.07.2008Numerical Simulation ofRelativistic Laser-PlasmaInteractionAbstractIn this thesis, we consider the numerical simulation of problems arising in relativistic laser-plasma physics.In a short introduction to the physical problem we derive the model equations, which turnout to be nonlinear wave equations and nonlinear Schr¨odinger equations. In this thesis, weconsider exponential integrators of two different types for the solution of these equations.First we consider Gautschi-type exponential integrators to solve nonlinear wave equations.We present a short overview on the theoretical properties of such methods. Then we detaila one- and two-dimensional implementation for our particular application. To achievean efficient implementation, we employ physical properties of the solution.