A New Parareal Algorithm for Problems with Discontinuous Sources

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.

Recent publications on novel time domain methods

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.

New paper on Waveform Relaxation for Multiscale Problems

jcp 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 →

Book on “Progress in Differential-Algebraic Equations” in production

Logo of Springer's DAE seriesThe 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.”

New Paper in Journal of Mathematics in Industry

Mathematics in IndustryThe 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.

Publication in PAMM on p-refinement in Dynamic Iterations

PAMM coverThe prooceedings of the 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Novi Sad 2013 are online. This includes our paper “An Optimal p-Refinement Strategy for Dynamic Iteration of Ordinary and Differential Algebraic Equations” (Sebastian Schöps, Andreas Bartel, Michael Günther). Continue reading

Paper on BH-Curves accepted by COMPEL

Compel Cover, image taken from http://www.emeraldinsight.com/journals.htm?issn=0332-1649

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.

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Paper on “Winding Functions” accepted

Winding functionsToday, 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.

New article published in SISC

SIAM Journal on Scientific Computing (image taken from www.siam.org

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.

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