Parallel in Ort und Zeit
Partielle oder differential-algebraische Gleichungen werden üblicherweise im Zeitbereich durch Integrationsverfahren wie die implizite Euler-Methode gelöst. Diese Verfahren unterteilen die Zeitachse in kleine Zeitschritte, ersetzen sequentiell für jeden Schritt die Ableitungen durch Differenzquotienten und lösen in jedem Zeitschritt für alle Unbekannten ein nichtlineares Gleichungssystem. Das kann für lange Zeiträume und große Gleichungssysteme sehr zeitaufwendig oder unmöglich werden, insbesondere wenn das System durch ein gekoppeltes Problem gegeben ist, das aus Teilproblemen mit unterschiedlichen Eigenschaften besteht. Oftmals beschreibt jedes Teilproblem einen anderen physikalischen Effekt (Multiphysik), zum Beispiel elektromagnetische Felder und Wärmeausbreitung. Die Teilprobleme werden durch Koppelungsbedingungen (Verbindung von „Eingängen“ und „Ausgängen“) miteinander verbunden. Häufig entwickeln sich die verschiedenen Phänomene auf unterschiedlichen Zeit- und Raumskalen (multiskalen Effekt). Diese gegebene Zerlegung kann man ausnutzen um die Simulation (in Ort und Zeit) zu parallelisieren und so zu erheblich zu beschleunigen.
Wir arbeiten an Parallel-in-Time-Methoden, z.B. Co-Simulation, Waveform-Relaxation [2] oder Parareal-Methoden. Diese Verfahren zielen darauf ab, Probleme schneller zu lösen. Die Ideen sind ähnlich zu iterative Methoden für lineare Gleichungssysteme.
Pels, Andreas ; Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2021):
Parallel-in-Time Simulation of Power Converters Using Multirate PDEs.
In: Scientific Computing in Electrical Engineering SCEE 2020, Mathematics in Industry. Springer. ARXIV: 2006.06544, forthcoming. [In Proceedings]
Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2021):
Towards a Parallel-in-Time Calculation of Time-Periodic Solutions with Unknown Period.
In: Scientific Computing in Electrical Engineering SCEE 2020, Mathematics in Industry. Springer. ARXIV: 2004.01612, forthcoming. [In Proceedings]
Kulchytska-Ruchka, Iryna ; Schöps, Sebastian ; Hinze, Michael ; Friedhoff, Stephanie ; Ulbrich, Stefan ; Rain, Oliver. PASIROM: Parallel Simulation and Robust Optimization of Electro-Mechanical Energy Converters. In German Success Stories on Mathematics in Industry, volume 35 of Mathematics in Industry. Springer, 2021, inprint. [In Collection]
Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2021):
Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a Multi-Harmonic Coarse Grid Correction.
In: SIAM Journal on Scientific Computing, 43, (1), pp. C61–C88, ISSN: 1064-8275, DOI: 10.1137/20M1314756, ARXIV: 1908.05245. [Article]
Cortes Garcia, Idoia ; Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2021):
Parareal for Higher Index Differential Algebraic Equations.
Cornell University, ARXIV: 2107.07755. [Preprint].
Cortes Garcia, Idoia ; Pade, Jonas ; Schöps, Sebastian ; Tischendorf, Caren (2021):
Waveform relaxation for low frequency coupled field/circuit differential-algebraic models of index 2.
In: Scientific Computing in Electrical Engineering SCEE 2020, Mathematics in Industry. Springer. ARXIV: 2005.13272, forthcoming. [In Proceedings]
Gander, Martin J. ; Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2020):
A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs.
In: Domain Decomposition Methods in Science and Engineering XXV, volume 138 of Lecture Notes in Computational Science and Engineering. Springer. ISBN: 978-3-030-56749-1, DOI: 10.1007/978-3-030-56750-7_27, ARXIV: 1810.12372. [In Proceedings]
Cortes Garcia, Idoia ; Kulchytska-Ruchka, Iryna ; Clemens, Markus ; Schöps, Sebastian (2020):
Parallel-in-Time Solution of Eddy Current Problems Using Implicit and Explicit Time-stepping Methods.
In: IEEE 19th Biennial Conference on Electromagnetic Field Computation (CEFC 2020). DOI: 10.1109/CEFC46938.2020.9451465, ARXIV: 2012.07603. [In Proceedings]
Cortes Garcia, Idoia ; Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2020):
Efficient Simulation of Field/Circuit Coupled Systems with Parallelised Waveform Relaxation.
In: IEEE Transactions on Magnetics, 56, (2), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2952695, ARXIV: 1909.08895. [Article]
Bolten, Matthias ; Friedhoff, Stephanie ; Hahne, Jens ; Schöps, Sebastian (2020):
Parallel-in-Time Simulation of an Electrical Machine using MGRIT.
In: Computing and Visualization in Science, ISSN: 1432-9360, DOI: 10.1007/s00791-020-00333-2, ARXIV: 1912.03106. [Article]
Bast, Denys ; Kulchytska-Ruchka, Iryna ; Schöps, Sebastian ; Rain, Oliver (2020):
Accelerated Steady-State Torque Computation for Induction Machines using Parallel-In-Time Algorithms.
In: IEEE Transactions on Magnetics, 56, (2), pp. 1–9, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2945510, ARXIV: 1902.08277. [Article]
Kulchytska-Ruchka, Iryna ; De Gersem, Herbert ; Schöps, Sebastian (2019):
An efficient steady-state analysis of the eddy current problem using a parallel-in-time algorithm.
In: The Tenth International Conference on Computational Electromagnetics (CEM 2019). ISBN: 978-1-83953-066-1, DOI: 10.1049/cp.2019.0113, ARXIV: 1905.13076. [In Proceedings]
Gander, Martin J. ; Kulchytska-Ruchka, Iryna ; Niyonzima, Innocent ; Schöps, Sebastian (2019):
A New Parareal Algorithm for Problems with Discontinuous Sources.
In: SIAM Journal on Scientific Computing, 41, (2), pp. B375–B395, ISSN: 1064-8275, DOI: 10.1137/18M1175653, ARXIV: 1803.05503. [Article]
Friedhoff, Stephanie ; Hahne, Jens ; Kulchytska-Ruchka, Iryna ; Schöps, Sebastian (2019):
Exploring Parallel-in-Time Approaches for Eddy Current Problems.
In: Progress in Industrial Mathematics at ECMI 2018, volume 30 of The European Consortium for Mathematics in Industry, 373–379. Springer. ISBN: 9783030275495, DOI: 10.1007/978-3-030-27550-1_47, ARXIV: 1810.13263. [In Proceedings]
Schöps, Sebastian ; Niyonzima, Innocent ; Clemens, Markus (2018):
Parallel-in-time Simulation of Eddy Current Problems using Parareal.
In: IEEE Transactions on Magnetics, 54, (3), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2017.2763090, ARXIV: 1706.05750. [Article]
Dutiné, Jennifer Susanne ; Clemens, Markus ; Schöps, Sebastian (2018):
Survey on semi-explicit time integration of eddy current problems.
In: Scientific Computing in Electrical Engineering SCEE 2016, volume 28 of Mathematics in Industry. Springer. ISBN: 978-3-319-75537-3, DOI: 10.1007/978-3-319-75538-0_13. [In Proceedings]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus (2017):
GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields.
In: IEEE Transactions on Magnetics, 53, (6), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2017.2662234, ARXIV: 1612.09447. [Article]
Merkel, Melina ; Niyonzima, Innocent ; Schöps, Sebastian (2017):
ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations.
In: Radio Science, 52, (12), pp. 1558–1569, ISSN: 0048-6604, DOI: 10.1002/2017RS006357, ARXIV: 1705.08019. [Article]
Dutiné, Jennifer Susanne ; Clemens, Markus ; Schöps, Sebastian (2017):
Explicit time integration of eddy current problems using a selective matrix update strategy.
In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 36, (5), pp. 1364–1371, ISSN: 0332-1649, DOI: 10.1108/COMPEL-02-2017-0100. [Article]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus (2016):
GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields.
In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). ISBN: 978-1-5090-1032-5, DOI: 10.1109/CEFC.2016.7816199, URL: http://cefc2016.org, Digest. [In Proceedings]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus (2016):
Multi-GPU Acceleration of Algebraic Multigrid Preconditioners.
In: Scientific Computing in Electrical Engineering SCEE 2014, number 23 in Mathematics in Industry, 83–90. Springer. ISBN: 978-3-319-30399-4, DOI: 10.1007/978-3-319-30399-4_9. [In Proceedings]
Richter, Christian ; Schöps, Sebastian ; Dutiné, Jennifer Susanne ; Schreiber, Robert ; Clemens, Markus (2016):
Transient Simulation of Nonlinear Electro-Quasistatic Field Problems Accelerated by Multiple GPUs.
In: IEEE Transactions on Magnetics, ISSN: 0018-9464, DOI: 10.1109/TMAG.2015.2466602, Article #9401204. [Article]
Niyonzima, Innocent ; Clemens, Markus ; Schöps, Sebastian (2016):
Investigation of the Time Integration Methods on the Parareal Method for Field Computation of Eddy Currents Problems.
In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). ISBN: 978-1-5090-1032-5, DOI: 10.1109/CEFC.2016.7816372, URL: http://cefc2016.org, Digest. [In Proceedings]
Merkel, Melina ; Niyonzima, Innocent ; Schöps, Sebastian (2016):
An Application of ParaExp to Electromagnetic Waves.
In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), 121–124. IEEE. ISBN: 978-1-5090-2503-9, DOI: 10.1109/URSI-EMTS.2016.7571330, ARXIV: 1607.00368. [In Proceedings]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus (2015):
Multi-GPU Acceleration of Algebraic Multigrid Preconditioners for Elliptic Field Problems.
In: IEEE Transactions on Magnetics, 51, (3), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2014.2357332. [Article]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus. Sykulski, Jan (editor) (2014):
GPU-Accelerated Mixed Precision Algebraic Multigrid Preconditioners for Discrete Elliptic Field Problems.
In: 9th IET International Conference on Computation in Electromagnetics (CEM 2014). IET. DOI: 10.1049/cp.2014.0185. [In Proceedings]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus (2014):
GPU-Acceleration of Algebraic Multigrid Preconditioners for Discrete Elliptic Field Problems.
In: IEEE Transactions on Magnetics, 50, (2), pp. 461–464, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2283099. [Article]
Bartel, Andreas ; Hülsmann, Timo ; Kühn, Jan ; Pulch, Roland ; Schöps, Sebastian (2014):
Influence of Measurement Errors on Transformer Inrush Currents Using Different Material Models.
In: IEEE Transactions on Magnetics, 50, (2), pp. 485–488, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2284072. [Article]
Scholz, Eike ; Ye, Hanyu ; Schöps, Sebastian ; Clemens, Markus (2013):
A Parallel FEM Matrix Assembly for Electro-Quasistatic Problems on GPGPU Systems.
In: IEEE Transactions on Magnetics, 49, (5), pp. 1801–1804, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2239624. [Article]
Richter, Christian ; Schöps, Sebastian ; Clemens, Markus (2013):
GPU Acceleration of Finite Difference Schemes Used in Coupled Electromagnetic/Thermal Field Simulations.
In: IEEE Transactions on Magnetics, 49, (5), pp. 1649–1652, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2238662. [Article]
