Abstract
Motivated by the task to design quench protection systems for superconducting magnets in particle accelerators we address a coupled field/circuit simulation based on a magneto-quasistatic field modeling. We investigate how a waveform relaxation of Gauß-Seidel type performs for a coupled simulation when circuit solving packages are used that describe the circuit by the modified nodal analysis. We present sufficient convergence criteria for the coupled simulation of FEM discretised field models and circuit models formed by a differential-algebraic equation (DAE) system of index 2. In particular, we demonstrate by a simple benchmark system the drastic influence of the circuit topology on the convergence behavior of the coupled simulation.
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References
L. Bortot et al., STEAM: a hierarchical co-simulation framework for superconducting accelerator magnet circuits. IEEE Trans. Appl. Super. 28(3) (2018). 4900706
I. Cortes Garcia et al., Optimized field/circuit coupling for the simulation of quenches in superconducting magnets. IEEE J. Multiscale Multiphys. Comput. Tech. 2(1), 97–104 (2017)
I. Cortes Garcia, H. De Gersem, S. Schöps, A structural analysis of field/circuit coupled problems based on a generalised circuit element. Numer. Algorithm. 83(1), 373–394 (2020)
C.R.I. Emson, C.W. Trowbridge, Transient 3d eddy currents using modified magnetic vector potentials and magnetic scalar potentials. IEEE Trans. Magn. 24(1), 86–89 (1988)
D. Estévez Schwarz, C. Tischendorf, Structural analysis of electric circuits and consequences for MNA. Int. J. Circ. Theor. Appl. 28(2), 131–162 (2000)
C.-W. Ho, A.E. Ruehli, P.A. Brennan, The modified nodal approach to network analysis. IEEE Trans. Circ. Syst. 22(6), 504–509 (1975)
E. Lelarasmee, A.E. Ruehli, A.L. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 1(3), 131–145 (1982)
M. Matthes, Numerical Analysis of Nonlinear Partial Differential-Algebraic Equations: A Coupled and an Abstract Systems Approach. Dissertation, Universität zu Köln, 2012
D. Meeker, Finite Element Method Magnetics, version 4.2 (25feb2018 build) edition, 2018
P. Monk, Finite Element Methods for Maxwell’s Equations (Oxford University Press, Oxford, 2003)
J. Pade, Analysis and waveform relaxation for a differential-algebraic electrical circuit model. Dissertation, Humboldt University of Berlin, 2021
J. Pade, C. Tischendorf, Waveform relaxation: a convergence criterion for differential-algebraic equations. Numer. Algorithm. 81, 1327–1342 (2019)
C. Pechstein, Multigrid-Newton-methods for nonlinear-magnetostatic problems. Master’s thesis, Universität Linz, 2004
S.J. Salon, Finite Element Analysis of Electrical Machines (Kluwer, Boston, 1995)
S. Schöps, Multiscale Modeling and Multirate Time-Integration of Field/Circuit Coupled Problems (VDI Verlag. Fortschritt-Berichte VDI, Reihe, 2011)
S Schöps, H. De Gersem, A. Bartel, A cosimulation framework for multirate time-integration of field/circuit coupled problems. IEEE Trans. Magn. 46(8), 3233–3236 (2010)
Acknowledgements
This work is supported by the ‘Excellence Initiative’ of the German Federal and State Governments, the Graduate School of CE at TU Darmstadt and DFG grant SCHO1562/1-2. Further, we acknowledge financial support under BMWi grant 0324019E and by DFG under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, ID 390685689).
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Garcia, I.C., Pade, J., Schöps, S., Tischendorf, C. (2021). Waveform Relaxation for Low Frequency Coupled Field/Circuit Differential-Algebraic Models of Index 2. In: van Beurden, M., Budko, N., Schilders, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-84238-3_20
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