Parallel-in-time simulation of an electrical machine using MGRIT
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PINT 2019
Parallel-in-time simulation of an electrical machine using MGRIT Matthias Bolten1 · Stephanie Friedhoff1 · Jens Hahne1 · Sebastian Schöps2 Received: 6 December 2019 / Accepted: 15 July 2020 © The Author(s) 2020
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. Keywords Parallel-in-time · Multigrid-reduction-in-time (MGRIT) · Spatial coarsening · Electrical machine
1 Introduction Induction motors are electrical machines in which the magnetic field in the rotor is obtained by an asynchronous motion with respect to the field in the stator, e.g. [1]. In the design process of such machines, motion and electromagnetic fields are numerically determined by space and time discretization of Maxwell’s equations. The spatial discretization, typically by finite elements, may lead to large Communicated by Daniel Ruprecht.
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Jens Hahne [email protected] Matthias Bolten [email protected] Stephanie Friedhoff [email protected] Sebastian Schöps [email protected]
1
Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42097 Wuppertal, Germany
2
Centre for Computational Engineering, Technische Universität Darmstadt, 64293 Darmstadt, Germany
models, e.g., due to resolving the so-called skin effect [2], but this is often mitigated by considering only two-dimensional models. More computational burden comes from the fact that large time intervals must be considered for simulating the start-up phase, i. e., until the machine reaches its steady state. Moreover, machines are commonly excited by pulse-width modulated (PWM) excitation
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