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Iterative Methods in Time Domain

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Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

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Abstract

The simulation of large, coupled, multiphysical problems typically poses considerable challenges. Their multiphysical character frequently involves the coupling of systems of equations with different mathematical properties, time rates and sizes, whose coupled solution has to be numerically approximated together with one method. Furthermore, especially when considering space-discretised models, each subsystems can become very large and computationally costly to solve. In this chapter two time domain simulation algorithms are presented that can be applied to field-circuit coupled systems. This includes co-simulation techniques (in particular the waveform relaxation method) that can be used to exploit the different mathematical properties of the systems. Also, to further speed up the computation time, the parallel-in-time method Parareal is presented and adapted to the case of differential-algebraic equations.

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Notes

  1. 1.

    The choice of coupling the magnetic and thermal systems monolithically is not mandatory. However, in the LHC quench protection circuit examples simulated within STEAM both systems are implemented within the same software (COMSOL) and thus solving them together is the intuitive option.

  2. 2.

    InitDAE is a package for Python that is able to numerically compute the system’s index and consistent initial conditions https://www.mathematik.hu-berlin.de/~lamour/software/python/InitDAE/html/index.html.

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Authors and Affiliations

  1. Computational Electromagnetics, Institute for Accelerator Science and Electromagnetic Fields, Technische Universität Darmstadt, Darmstadt, Hessen, Germany

    Idoia Cortes Garcia

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Cortes Garcia, I. (2021). Iterative Methods in Time Domain. In: Mathematical Analysis and Simulation of Field Models in Accelerator Circuits. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-63273-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-63273-1_5

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