Magnetic field simulations using explicit time integration with higher order schemes
ISSN: 0332-1649
Article publication date: 24 November 2021
Issue publication date: 10 May 2022
Abstract
Purpose
A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the resulting system of differential algebraic equations is reformulated into a system of ordinary differential equations (ODE). The ODE system is integrated in time by using explicit time integration schemes. The purpose of this paper is to investigate explicit time integration for eddy current problems with respect to the performance of the first-order explicit Euler scheme and the Runge-Kutta-Chebyshev (RKC) method of higher order.
Design/methodology/approach
The ODE system is integrated in time using the explicit Euler scheme, which is conditionally stable by a maximum time step size. To overcome this limit, an explicit multistage RKC time integration method of higher order is used to enlarge the maximum stable time step size. Both time integration methods are compared regarding the overall computational effort.
Findings
The numerical simulations show that a finer spatial discretization forces smaller time step sizes. In comparison to the explicit Euler time integration scheme, the multistage RKC method provides larger stable time step sizes to diminish the overall computation time.
Originality/value
The explicit time integration of the Schur complement vector potential formulation of eddy current problems is accelerated by a multistage RKC method.
Keywords
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant CL143/11-2 and SCHO1562/1-2. The work of S. Schöps was supported by the Exellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering, Technical University of Darmstadt.
Citation
Kähne, B., Clemens, M. and Schöps, S. (2022), "Magnetic field simulations using explicit time integration with higher order schemes", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 41 No. 3, pp. 915-924. https://doi.org/10.1108/COMPEL-03-2021-0090
Publisher
:Emerald Publishing Limited
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