We recently proposed a new Parareal algorithm for problems with discontinuous sources which are common in electrical engineering, e.g., when an electric device is supplied with a pulse-width-modulated signal. Our algorithm uses a smooth input for the coarse problem with reduced dynamics. In the new arXiv preprint 1803.05503
preprint an error estimates is derived that shows how the input reduction influences the overall convergence rate of the algorithm. The theoretical results are supported by numerical experiments, including an eddy current simulation of an induction machine.
Three papers from us on novel methods for time domain simulation of electromagnetic phenomenas have been published last week:
- ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations in: Radio Science. doi: 10.1002/2017RS006357.
- Solving nonlinear circuits with pulsed excitation by multirate partial differential equations in IEEE Transactions on Magnetics. doi: 10.1109/TMAG.2017.2759701.
- Parallel-in-time Simulation of Eddy Current Problems using Parareal in IEEE Transactions on Magnetics. doi: 10.1109/TMAG.2017.2763090.
Preprints can be found at arXiv
Our paper on Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems (Innocent Niyonzima, Christophe Geuzaine, Sebastian Schöps) has been accepted by JCP
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton–Raphson scheme. The resolution of many mesoscale problems per Gauss point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauss point. Continue reading →
The book “Progress in Differential-Algebraic Equations. Deskriptor 2013” (ISBN 978-3-662-44925-7) is now in production and will be available later this year, see Springer’s website
“This book contains the proceedings of the 8th Workshop on Coupled Descriptor Systems held March 2013 in the Castle of Eringerfeld, Geseke in the neighborhood of Paderborn, Germany. It examines the wide range of current research topics in descriptor systems, including mathematical modeling, index analysis, wellposedness of problems, stiffness and different time-scales, cosimulation and splitting methods and convergence analysis. In addition, the book also presents applications from the automotive and circuit industries that show that descriptor systems provide challenging problems from the point of view of both theory and practice.
The book contains nine papers and is organized into three parts: control, simulation, and model order reduction. It will serve as an ideal resource for applied mathematicians and engineers, in particular those from mechanics and electromagnetics, who work with coupled differential equations.”
The paper “Efficient frequency-transient co-simulation of coupled heat-electromagnetic problems” together with Christof Kaufmann, Michael Günther, Daniel Klagges, Michael Knorrenschild, Matthias Richwiny and Jan ter Maten has been accepted for publication and will appear soon in the Journal of Mathematics in Industry
, a peer-reviewed open access journal published under the brand SpringerOpen.
The paper “Extended Brauer Model for Ferromagnetic Materials: Analysis & Computation” (a joint work with Timo Hülsmann, Andreas Bartel and Herbert De Gersem) has been accepted for publication in COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering. It was also recently presented at SCEE 2012.
Today, a new paper on “Winding Functions in Transient Magnetoquasistatic Field-Circuit Coupled Simulations” (together with Herbert De Gersem
and Thomas Weiland
) was accepted by COMPEL
. The article reviews the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and (modified) loop analyses using the abstract concept of “winding functions”. Furthermore the coupling is interpreted in the spirit of Tonti diagrams.
Andreas Bartel, Markus Brunk, Michael Günther, and I have published a new article in the current issue 35(2) of SIAM’s Journal of Scientific Computing (Section: Computational Methods in Science and Engineering). The paper discusses dynamic iteration for coupled problems of electric circuits and distributed devices.
Probably, everybody working in academia is aware of the current Elsevier boycott. The discussion was started by Timothy Gowers on his blog. Recently, he published a summary of the results of the campaign.
However there are only few alternatives, for example “prepaid” journals as Springer’s Open Access series, e.g., Journal of Mathematics in Industry. The market might change soon: a true open access journal “Episciences.org project” was founded. It is based on arxiv and is reported to start publishing in the first half of 2013.