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Abstract: A two-dimensional fluid laser–plasma integrator for stratified plasma–vacuum systems is presented. Inside a plasma, a laser pulse can be longitudinally compressed from ten or more wave-lengths to one or two cycles. However, for physically realistic simulations, transversal effects have to be included, because transversal instabilities can destroy the pulse and transversal compression in the plasma as well as focusing in vacuum allows much higher intensities to be reached. In contrast to the one-dimensional case, where a two-step implementation of the Gautschi-type exponential integrator with constant step-size turned out to be sufficient, it is essential to enable changes of the time step-size for the two-dimensional case. The use of a one-step version of the Gautschi-type integrator, being accurate of second order independent of the highest frequencies arising in the system, is proposed. In vacuum this allows to take arbitrarily large time-steps. To optimize runtime and memory requirements within the plasma, a splitting of the Laplacian is suggested. This splitting allows to evaluate the matrix functions arising in the Gautschi-type method by one-dimensional Fourier transforms. It is also demonstrated how the different variants of the scheme can be parallelized. Numerical experiments illustrate the superior performance and accuracy of the integrator compared to the standard leap-frog method. Finally, we discuss the simulation of a layered plasma–vacuum structure using the new method. [Copyright &y& Elsevier]

Abstract: Nonlinear wave motion in dispersive media is solved numerically. The model applies to laser propagation in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi-type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wave-equations. In order to reduce the number of spatial grid points, a physically motivated quasi-envelope approach (QEA) is introduced. The new method turns out to reduce the computational time significantly compared to the standard leap-frog scheme. [Copyright &y& Elsevier]