# Parareal for a magnetoquasistatic model (Iryna Kulchytska-Ruchka, Technische Universität Darmstadt)

09.10.2018 14:00

Various applications in electrical engineering (e.g., electric motors) are often modeled by the so-called magnetoquasistatic approximation of the Maxwell’s equations, also known as the eddy current model. It leads to an initial-boundary value problem for the system of partial differential(-algebraic) equations. Depending on the complexity of the system and its discretization, the numerical solution of such a problem might be computationally expensive and therefore very time-consuming. This causes the necessity to develop efficient solution approaches, e.g., by means of decomposition in the time domain and parallelization. In particular, the Parareal algorithm is able to solve evolution problems in parallel via a joint application of the fine and the coarse propagators.

The focus of this talk is on systems, which involve quickly-switching discontinuous excitations. Such situations occur, e.g., in power engineering when electric devices are supplied with a pulse-width-modulated signal. To deal with such systems we propose a new Parareal method, whose main idea is to solve the coarse problem using a low-frequency smooth input. The choice of the coarse input with reduced dynamics can be based, e.g., on the Fourier analysis of the given source function. We illustrate convergence of the developed approach via numerical tests for a model problem in one dimension. Performance of the algorithm for practical demands in electrical engineering is shown via its application to the simulation of an induction machine.

### Lieu

Room 623, Séminaire d'analyse numérique

### Organisé par

Section de mathématiques### Intervenant-e-s

Iryna Kulchytska-Ruchka, Technische Universität Darmstadtentrée libre