Abstract We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are needed, such that parallelization in time becomes highly relevant for reducing the simulation time. The MGRIT algorithm is an iterative method that allows calculating multiple time steps simultaneously by using a time-grid hierarchy. It is particularly well suited for introducing time parallelism in the simulation of electrical machines using existing application codes, as MGRIT is a non-intrusive approach that essentially uses the same time integrator as a traditional time-stepping algorithm. However, the key difficulty when using time-stepping routines of existing application codes for the MGRIT algorithm is that the cost of the time integrator on coarse time grids must be less expensive than on the fine grid to allow for speedup over sequential time stepping on the fine grid. To overcome this difficulty, we consider reducing the costs of the coarse-level problems by adding spatial coarsening. We investigate effects of spatial coarsening on MGRIT convergence when applied to two numerical models of an induction machine, one with linear material laws and a full nonlinear model. Parallel results demonstrate significant speedup in the simulation time compared to sequential time stepping, even for moderate numbers of processors.

Matthias Bolten

Stephanie Friedhoff

Jens Hahne

Sebastian Schöps

Computing and Visualization in Science

Devoted to computational sciences, this journal publishes pioneering methods and applications that bring about the solution of complex problems, or even make such solutions possible at all. Since visualization has become an important scientific tool, especially in the analysis of complex situations, it is treated in close connection with the other areas covered by the journal.

The journal "Computing and Visualization in Science" is dedicated to computational sciences, publishing pioneering methods and applications that solve complex problems or make such solutions possible. As visualization has become an essential scientific tool, particularly in analyzing complex situations, it is closely integrated with other areas covered by the journal.

《Computing and Visualization in Science》期刊致力于计算科学，发表开创性的方法和应用，以解决复杂问题，甚至使这些解决方案成为可能。随着可视化成为一种重要的科学工具，尤其是在复杂情况的分析中，期刊将其与其他领域紧密结合。

Parallel-in-time simulation of an electrical machine using MGRIT

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