Modellordnungsreduktionstechniken für elektro-quasistatische Simulationsverfahren in der elektrischen Energieübertragungstechnik
Mathematik
Zusammenfassung der Projektergebnisse
During the project, a novel framework for model reduction of nonlinear transient EQS problems, based on snapshot reduced basis methods, has been developed. In particular, a variety of tools from time-series analysis, information theory, and machine learning have been adjusted to fit the problems of interest, and have been exploited in order to establish (a) stopping criteria for snapshot sampling (global sampling) and (b) sampling rules that reduce the size of the initial set of snapshots (local sampling). Item (a) is of great importance for the reduced basis methods community, since there was no known algorithm for interrupting the sampling process, and ad hoc methods were often used. Item (b) enabled a range of methods that do not rely on the singular value decomposition, and hence, resulted in computationally less demanding methods for generating reduced bases, as well as a state-of-the-art perspective to reduced basis model reduction. Further, node sampling methods that are based on entropy and statistical divergences have been developed and tested as viable replacements of the discrete empirical interpolation method, which relies on suboptimal greedy sampling of interpolation nodes. This preliminary work has been justified by numerical experiments, while refined variations of it need to be tested in the future. In addition to model reduction, the developed methods have been employed in order to improve the speed of convergence of the underlying nonlinear and linear iterative algorithms, by estimating starting values that are in the vicinity of the actual solutions, at low computational cost. Whenever possible, the performance of the developed algorithms has benefited by parallel CPU and GPU implementations, while space and time parallelization methods have been also covered, in parts.
Projektbezogene Publikationen (Auswahl)
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Explicit Time Integration Techniques for Electro- and Magneto-Quasistatic Field Simulations, International Conference on Electromagnetics in Advanced Applications & IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (ICEAA IEEE-APS 2017), Verona, Italy, 11.-15.09.2017
J. Dutiné, C. Richter, S. Schöps, M. Clemens
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GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields, IEEE Transactions on Magnetics, vol. 53, no. 6, June 2017
C. Richter, S. Schöps, M. Clemens
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Entropy Snapshot Filtering for QR-based Model Reduction of Transient Nonlinear Electro-Quasistatic Simulations, 22nd Conference on the Computation of Electromagnetic Fields (COMPUMAG 2019), Paris, France, 15.-19.07.2019
F. Kasolis, M. Clemens
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Model Order Reducibility of Nonlinear Electro-Quasistatic Problems, COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, ISSN 0332-1649, July 2019
F. Kasolis, M. Clemens
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Parallel-in-Time Simulation of Nonlinear Transient Electro-Quasistatic Field Problems, 22nd Conference on the Computation of Electromagnetic Fields (COMPUMAG 2019), Paris, France, 15.-19.07.2019
M. Henkel, F. Kasolis, M. Clemens
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Recurrence Analysis for Model Order Reduction of Nonlinear Transient Electro-Quasistatic Field Problems, 21st Edition of the International Conference on Electromagnetics in Advanced Applications and 9th edition of the IEEE- APS Topical Conference on Antennas and Propagation in Wireless Communications (ICEAA- IEEE APWC 2019), Granada, Spain, 9.-13.09.2019
F. Kasolis, D. Zhang, M. Clemens
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Start Value Estimation Using Gaussian Process Regression for Transient Electro-Quasistatic Fields Simulations, 22nd Conference on the Computation of Electromagnetic Fields (COMPUMAG 2019), Paris, France, 15.-19.07.2019
D. Zhang, C. Richter, F. Kasolis, M. Clemens
