Iryna Kulchytska-Ruchka

Martin J. Gander, Iryna Kulchytska-Ruchka, Sebastian Schöps

The Parareal algorithm, which is related to multiple shooting, was introduced for solving evolution problems in a time-parallel manner. The algorithm was then extended to solve time-periodic problems. We are interested here in time-periodic systems which are forced with quickly-switching discontinuous inputs. Such situations occur, e.g., in power engineering when electric devices are excited with a pulse-width-modulated signal. In order to solve those problems numerically we consider a recently introduced modified Parareal method with reduced coarse dynamics. Its main idea is to use a low-frequency smooth input for the coarse problem, which can be obtained, e.g., from Fourier analysis. Based on this approach, we present and analyze a new Parareal algorithm for time-periodic problems with highly-oscillatory discontinuous sources. We illustrate the performance of the method via its application to the simulation of an induction machine.

Stephanie Friedhoff, Jens Hahne, Iryna Kulchytska-Ruchka et al.

We consider the usage of parallel-in-time algorithms of the Parareal and multigrid-reduction-in-time (MGRIT) methodologies for the parallel-in-time solution of the eddy current problem. Via application of these methods to a two-dimensional model problem for a coaxial cable model, we show that a significant speedup can be achieved in comparison to sequential time stepping.