Dokument: Numerical Simulation of Relativistic Laser-Plasma Interaction

Titel:Numerical Simulation of Relativistic Laser-Plasma Interaction
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URN (NBN):urn:nbn:de:hbz:061-20080710-114955-7
Dokumententyp:Wissenschaftliche Abschlussarbeiten » Dissertation
Autor: Schweitzer, Julia Maria [Autor]
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Dateien vom 08.07.2008 / geändert 08.07.2008
Beitragende:Prof. Dr. Hochbruck, Marlis [Betreuer/Doktorvater]
Prof. Dr. Spatschek, Karl-Heinz [Gutachter]
Stichwörter:exponential integrator, Gautschi-type method, Rosenbrock-type method
Dewey Dezimal-Klassifikation:500 Naturwissenschaften und Mathematik » 510 Mathematik
Beschreibung:In this thesis, we consider the numerical simulation of problems arising in relativistic laser-plasma physics.

In an introduction to the physical problem we derive the model equations and then consider exponential integrators of two different types for the solution.

First we consider Gautschi-type exponential integrators to solve nonlinear wave equations. After a short overview on the theoretical properties of such methods, we detail a one- and two-dimensional implementation for our particular application. To achieve an efficient implementation, we employ physical properties of the solution. In the one-dimensional case, we perform extensive comparisons to a standard method and demonstrate the superior performance of the exponential integrator for this problem. For the two-dimensional case, we consider different geometries and present a parallelized scheme. The means of parallelization are tailored to the problem and the different modifications of the integrator in use. We give some comparisons to a standard method, too. Moreover, we present a physical application, where our code was used to optimize the setup of a plasma lens to focus the laser pulse.

In the second part of this thesis, we propose and analyze exponential Rosenbrock-type integrators for the solution of stiff or oscillatory first
order systems of differential equations such as the Schrödinger equation. For these methods, we present a thorough convergence and stability analysis in a semigroup framework and study the influence of perturbations on the method. Moreover, we detail a variable step size implementation employing Krylov subspace techniques to evaluate the matrix functions times some vectors. We present an extensive comparison to other methods used for such problems and
demonstrate, that our implementation is competitive. Finally, we solve the nonlinear Schrödinger equation arising in the laser-plasma context with the exponential Rosenbrock-type integrator.
Fachbereich / Einrichtung:Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Angewandte Mathematik
Dokument erstellt am:08.07.2008
Dateien geändert am:08.07.2008
Promotionsantrag am:12.06.2008
Datum der Promotion:03.07.2008
Status: Gast