Parallel and explicit methods for the simulation of eddy current problems

• Applicants: Professor Dr. Markus Clemens; Professor Dr. Sebastian Schöps
• Subject Area: Electrical Energy Systems, Power Management, Power Electronics, Electrical Machines and Drives ; Mathematics
• Term: from 2013 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 235014286

• Final Report Year: 2022

Final Report Abstract

The project addressed methods for the accelerated simulation of eddy current problems using (semi-) explicit and parallel time integration methods. The challenge was to reduce the computational effort due to the time oversampling of explicit methods, which can only operate stably with small time step sizes. Selective update schemes for nonlinear material characteristics and the exterior space were developed, which already compensate for the main disadvantages due to oversampling. The explicit methods must additionally repeatedly solve the same system of equations with varying right-hand sides. For this purpose, Proper Orthogonal Decomposition as well as Subspace Projection Extrapolation techniques were proposed, which could significantly reduce the number of iterations of iterative equation system solvers. The explicit Runge-Kutta-Chebyshev time integration method, whose stability region grows quadratically with the number of intermediate Runge-Kutta steps, has proven to be a well suitable explicit time integrator. This method combination already beats conventional implementations based on implicit methods. However, the newly developed parareal variants increase this advantage by at least one more order of magnitude.

Publications

• Transient Simulation of Non-linear Electro-Quasistatic Field Problems Accelerated by Multiple GPUs. In: IEEE Transactions on Magnetics 52.3 (2016). Article #9401204
  C. Richter, S. Schöps, J. S. Dutiné, R. Schreiber und M. Clemens
  
• Investigation of the Time Integration Methods on the Parareal Method for Field Computation of Eddy Currents Problems. In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). Hrsg. von O. A. Mohammed. Digest. 2016. ISBN: 978-1-5090-1032-5
  I. Niyonzima, M. Clemens und S. Schöps
  
• Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current Problems. In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). Hrsg. von O. A. Mohammed. Digest. 2016. ISBN: 978-1-5090-1032-5
  J. S. Dutine, M. Clemens und S. Schöps
  
• Explicit time integration of eddy current problems using a selective matrix update strategy. In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 36.5 (2017). Hrsg. von J. K. Sykulski und D. Lowther, S. 1364–1371
  J. S. Dutiné, M. Clemens und S. Schöps
  
• Explicit Time Integration Techniques for Electro- and Magneto-Quasistatic Field Simulations. In: Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA) 2017. Hrsg. von R. D. Graglia. IEEE, 2017
  J. S. Dutiné, C. Richter, C. Jörgens, S. Schöps und M. Clemens
  
• Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current Problems. In: IEEE Transactions on Magnetics 53.6 (2017), S. 1–4
  J. S. Dutiné, M. Clemens und S. Schöps
  
• Explicit Time Integration of Transient Eddy Current Problems. In: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 31.2 (2018)
  J. S. Dutiné, M. Clemens, S. Schöps und G. Wimmer
  
• Parallel-in-time Simulation of Eddy Current Problems using Parareal. In: IEEE Transactions on Magnetics 54.3 (2018), S. 1–4
  S. Schöps, I. Niyonzima und M. Clemens
  
• Survey on semi-explicit time integration of eddy current problems. In: Scientific Computing in Electrical Engineering SCEE 2016. Hrsg. von U. Langer, W. Amrhein und W. Zulehner. Bd. 28. Mathematics in Industry. Berlin: Springer, 2018. ISBN : 978-3-319-75537-3
  J. S. Dutiné, M. Clemens und S. Schöps
  
• Efficient Simulation of Field/Circuit Coupled Systems with Parallelised Waveform Relaxation. In: IEEE Transactions on Magnetics 56.2 (2020), S. 1–4
  I. Cortes Garcia, I. Kulchytska-Ruchka und S. Schöps
  
• Parallel and Explicit Time Integration of Transient Nonlinear Magneto- and Electroquasistatic Fields. Dissertation. Wuppertal: Bergische Universitat Wuppertal, 2020
  J. S. Dutiné
  
• Parallel-in-Time Solution of Eddy Current Problems Using Implicit and Explicit Time-stepping Methods. In: IEEE 19th Biennial Conference on Electromagnetic Field Computation (CEFC 2020). 2020
  I. Cortes Garcia, I. Kulchytska-Ruchka, M. Clemens und S. Schöps
  
• Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a Multi-Harmonic Coarse Grid Correction. In: SIAM Journal on Scientific Computing 43.1 (2021), S. C61–C88
  I. Kulchytska-Ruchka und S. Schöps
  
• Magnetic field simulations using explicit time integration with higher order schemes. In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (2021)
  B. Kähne, M. Clemens und S. Schöps
  
• Parareal for Index Two Differential Algebraic Equations. In: Numerical Algorithms (2022)
  I. Cortes Garcia, I. Kulchytska-Ruchka und S. Schöps