Efficient time-domain simulation

Efficient time-domain simulation methods

Ordinary or differential-algebraic equations are commonly solved in time domain by (implicit) integration methods like the backward Euler method [1]. Those methods subdivide the time axis into small time steps, replace for each step sequentially the derivatives by difference quotients and solve in each time step for all unknowns a nonlinear equation system. This may become very time-consuming or impossible for long time intervals and large systems of equations, in particular if the system stems from a coupled problem that consists of subproblems with different properties. Often each subproblem describes a different physical effect (multiphysics), for example electromagnetic fields and heat distribution. The subproblems are mutually connected by coupling conditions (connecting ‘inputs’ and ‘outputs’). Often, the various phenomena evolve on different time and spatial scales (multiscale).

We are working on parallel-in-time methods, e.g. co-simulation, waveform-relaxation or Parareal methods. They aim at solving problems more efficiently. The ideas are similar to iterative methods for linear equation system.

References

Gander, Martin J. ; Kulchytska-Ruchka, Iryna ; Niyonzima, Innocent ; Schöps, Sebastian :
A New Parareal Algorithm for Problems with Discontinuous Sources.
[Online-Edition: https://doi.org/10.1137/18M1175653]
In: SIAM Journal on Scientific Computing, 41(2) (2) B375-B395. ISSN 1064-8275
[Article] , (2019)

Cortes Garcia, Idoia ; Schöps, Sebastian ; Bortot, Lorenzo ; Maciejewski, Michał ; Prioli, Marco ; Fernandez Navarro, Alejandro Manuel ; Auchmann, Bernhard ; Verweij, Arjan Peter :
Optimized Field/Circuit Coupling for the Simulation of Quenches in Superconducting Magnets.
[Online-Edition: https://doi.org/10.1109/JMMCT.2017.2710128]
In: IEEE Journal on Multiscale and Multiphysics Computational Techniques, 2 (1) S. 97-104. ISSN 2379-8793
[Article] , (2017)

Bartel, Andreas ; Brunk, Markus ; Schöps, Sebastian :
On the Convergence Rate of Dynamic Iteration for Coupled Problems With Multiple Subsystems.
[Online-Edition: http://dx.doi.org/10.1016/j.cam.2013.07.031]
In: Journal of computational and applied mathematics, 262 S. 14-24. ISSN 0377-0427
[Article] , (2014)

Kaufmann, Christoph ; Günther, Michael ; Klagges, Daniel ; Knorrenschild, Michael ; Richwin, Matthias ; Schöps, Sebastian ; ter Maten, E. Jan W. :
Efficient Frequency-Transient Co-Simulation of Coupled Heat-Electromagnetic Problems.
[Online-Edition: http://dx.doi.org/10.1186/2190-5983-4-1]
In: Journal of Mathematics in Industry, 4.1
[Article] , (2014)

Kaufmann, Christoph ; Günther, Michael ; Klagges, Daniel ; Richwin, Matthias ; Schöps, Sebastian ; ter Maten, E. Jan W.
Fontes, Magnus ; Günther, Michael ; Marheineke, Nicole (eds.) :

Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles.
[Online-Edition: http://dx.doi.org/10.1007/978-3-319-05365-3_5]
In: Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry. Springer, Berlin , S. 27-36. ISBN 978-3-319-05364-6
[Book section] , (2014)

Bartel, Andreas ; Brunk, Markus ; Günther, Michael ; Schöps, Sebastian :
Dynamic Iteration For Coupled Problems of Electric Circuits and Distributed Devices.
[Online-Edition: http://dx.doi.org/10.1137/120867111]
In: SIAM Journal on Scientific Computing, 35.2 ISSN 1064-8275
[Article] , (2013)

Schöps, Sebastian ; Bartel, Andreas ; Günther, Michael :
An Optimal p-Refinement Strategy for Dynamic Iteration of Ordinary and Differential Algebraic Equations.
[Online-Edition: http://dx.doi.org/10.1002/pamm.201310262]
In: Proceedings in Applied Mathematics and Mechanics. Wiley , S. 549-552.
[Book section] , (2013)

Schöps, Sebastian ; De Gersem, Herbert ; Bartel, Andreas :
Higher-Order Cosimulation of Field/Circuit Coupled Problems.
[Online-Edition: http://dx.doi.org/10.1109/TMAG.2011.2174039]
In: IEEE Transactions on Magnetics, 48 (2) S. 535-538.
[Article] , (2012)

Schöps, Sebastian ; De Gersem, Herbert ; Bartel, Andreas :
A Cosimulation Framework for Multirate Time Integration of Field/Circuit Coupled Problems.
[Online-Edition: http://dx.doi.org/10.1109/TMAG.2010.2045156]
In: IEEE Transactions on Magnetics, 46 (8) S. 3233-3236.
[Article] , (2010)

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