Survey on Semi-explicit Time Integration of Eddy Current Problems
The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary differential equation system by applying a generalized Schur complement. Applying the explicit Euler time integration scheme to this system results in a small maximum stable time step size. Fast computations are required in every time step to yield an acceptable overall simulation time. Several acceleration methods are presented.
This work was supported by the German Research Foundation DFG (grant numbers CL143/11-1, SCHO1562/1-1). The third author is supported by the Excellence Initiative of the German Federal and State Governments and The Graduate School of Computational Engineering at TU Darmstadt.
- 2.Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd rev. edn. Springer, Berlin (1996)Google Scholar
- 6.Dutiné, J., Clemens, M., Schöps, S., Wimmer, G.: Explicit time integration of transient eddy current problems. Int J Numer Model. e2227 (2017) https://doi.org/10.1002/jnm.2227
- 12.Chatterjee, A.: An introduction to the proper orthogonal decomposition. Curr. Sci. 78(7), 808–817 (2000)Google Scholar