Katharina Schratz

Asymptotic preserving schemes for the Klein---Gordon equation in the non-relativistic limit regime

We consider the Klein–Gordon equation in the non-relativistic limit regime, i.e. the speed of light

Trigonometric integrators for quasilinear wave equations

c

Trigonometric time integrators for the Zakharov system

c tending to infinity. We construct an asymptotic expansion for the solution with respect to the small parameter depending on the inverse of the square of the speed of light. As the first terms of this asymptotic can easily be simulated our approach allows us to construct numerical algorithms that are robust with respect to the large parameter

A GRASS GIS Implementation of the Savage-Hutter Avalanche Model and Its Application to the 1987 Val Pola Event

c

Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime

c producing high oscillations in the exact solution.

Stability of Exponential Operator Splitting Methods for Noncontractive Semigroups

We introduce efficient and robust exponential-type integrators for Klein-Gordon equations which resolve the solution in the relativistic regime as well as in the highly-oscillatory non-relativistic regime without any step-size restriction, and under the same regularity assumptions on the initial data required for the integration of the corresponding limit system. In contrast to previous works we do not employ any asymptotic/multiscale expansion of the solution. This allows us derive uniform convergent schemes under far weaker regularity assumptions on the exact solution. In particular, the newly derived exponential-type integrators of first-, respectively, second-order converge in the non-relativistic limit to the classical Lie, respectively, Strang splitting in the nonlinear Schrodinger limit.