Applied and Computational Mathematics (ACM)

Multirate

Highly integrated electric cicuits show a phenomenon called latency. That is, a processed signal causes activity only in a small subset of the whole circuit (imagine a central processing unit), whereas the other part of the system behaves almost constant over some time - is latent. Such an electric system can be described as coupled system, where the waveforms show different time scales, also refered to as multirate.

More generally, any coupled problem formulation due to coupled physical effects, may cause a multirate problem: image the simulation of car driving on the road, there you need a model for the wheel, the chassis, the dampers, the road,... (cf. co-simulation). Again each system is covered by their own time constant, which might vary over several orders of magnitude comparing different subsystems.

Classical methods cannot exploit this multirate potential, but resolve everything on the finest scale. This causes an over sampling of the latent components. In constrast, Co-simulation or especially dedicated multirate methods are designed to use the inherent step size to resolve the time-domain behaviour of each subystem with the required accuracy. This requires a time-stepping for each.

Group members working in that field

  • Andreas Bartel
  • Michael Günther

Former and ongoing Projects

  • CoMSON
  • ICESTARS
  • 03GUNAVN

Cooperations

Publications



2020

4291.

Doganay, Onur Tanil; Gottschalk, Hanno; Hahn, Camilla; Klamroth, Kathrin; Schultes, Johanna; Stiglmayr, Michael
Gradient based biobjective shape optimization to improve reliability and cost of ceramic components
Optimization and Engineering, 21 (4) :1359-1387
2020

4290.

Xue, Chaoyang; Zhang, Chenglong; Ye, Can; Liu, Pengfei; Catoire, Valéry; Krysztofiak, Gisèle; Chen, Hui; Ren, Yangang; Zhao, Xiaoxi; Wang, Jinhe; Zhang, Fei; Zhang, Chongxu; Zhang, Jingwei; An, Junling; Wang, Tao; Chen, Jianmin; Kleffmann, Jörg; Mellouki, Abdelwahid; Mu, Yujing
HONO Budget and Its Role in Nitrate Formation in the Rural North China Plain
Environmental Science \& Technology, 54 (18) :11048--11057
September 2020
ISSN: 0013-936X, 1520-5851

4289.

Kutzner, Laura; Goloshchapova, Kateryna; Rund, Katharina M.; Jübermann, Martin; Blum, Maximilian; Rothe, Michael; Kirsch, Stefan F.; Schunck, Wolf-Hagen; Kühn, Hartmut; Schebb, Nils Helge
Human lipoxygenase isoforms form complex patterns of double and triple oxygenated compounds from eicosapentaenoic acid
Biochimica et Biophysica Acta (BBA) - Molecular and Cell Biology of Lipids, 1865 (12) :158806
2020
ISSN: 1388-1981

4288.

Burger, Martin; Pinnau, Rene; Totzeck, Claudia; Tse, Oliver; Roth, Andreas
Instantaneous control of interacting particle systems in the mean-field limit
Journal of Computational Physics, 405 :109181
2020

4287.

Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes -- a dynamic-iteration perspective
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor
Page 73--90
Publisher: Springer
2020
73--90

4286.

Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes: a dynamic-iteration perspective
Progress in differential-algebraic equations II, Page 73--90
Springer International Publishing
2020

4285.

Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes: A dynamic-iteration perspective
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor, Progress in Differential-Algebraic Equations IIfromDifferential-Algebraic Equations Forum, Page 73–90
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor
Publisher: Springer Cham
2020

4284.

Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes: A dynamic-iteration perspective
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor, Progress in Differential-Algebraic Equations IIfromDifferential-Algebraic Equations Forum, Page 73–90
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor
Publisher: Springer Cham
2020

4283.

Dietz, Tobias; Klamroth, Kathrin; Kraus, Konstantin; Ruzika, Stefan; Schäfer, Luca E.; Schulze, Britta; Stiglmayr, Michael; Wiecek, Margaret M.
Introducing Multiobjective Complex Systems
European Journal of Operational Research, 280 (2) :581--596
2020
Publisher: Elsevier

4282.

Kaltenbäck, Michael; Skrepek, Nathanael
Joint functional calculus for definitizable self-adjoint operators on {K}rein spaces
Integral Equations Operator Theory, 92 (4) :Paper No. 29, 36
2020

4281.

Kaltenbäck, Michael; Skrepek, Nathanael
Joint functional calculus for definitizable self-adjoint operators on Krein spaces
Integral Equations Operator Theory, 92 (4) :Paper No. 29, 36
2020

4280.

Frommer, Andreas; Jacob, Birgit; Kahl, Karsten; Wyss, Christian; Zwaan, Ian
Krylov type methods exploiting the quadratic numerical range
Electron. Trans. Numer. Anal., 53 :541-561
2020

4279.

Stiglmayr, Michael
Layout problems with reachability constraint
In J. S. Neufeld and U. Buscher and R. Lasch and D. Möst and J. Schönberger , Editor, Operations Research Proceedings 2019
Operations Research 2019
Dresden
In J. S. Neufeld and U. Buscher and R. Lasch and D. Möst and J. Schönberger , Editor
Publisher: Springer, Cham
2020

4278.

Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Linking Baskakov type operators
CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2019, Page 23-38
Publisher: Prof. Marin Drinov Academic Publishing House
2020

4277.

[german] Zeller, Diana; Bohrmann-Linde, Claudia
Mit Früchten zum elektrischen Strom! - Dynamische eBooks am Beispiel des Konzepts ''Alternative Solarzellen mit Titandioxid''
Digital Unterrichten Biologie, 3 :10-11
2020

4276.

Bartel, Andreas; Ehrhardt, Matthias
Modulation of Rayleigh-Benard Convection by Lagrangian Thermal Forcing
APS Division of Fluid Dynamics Meeting Abstracts, Page T01--008
2020

4275.

Ferrari, P.; Serra-Capizzano, S.
Multigrid for $\mathbb{Q}_{k}$ Finite Element Matrices using a (block) Toeplitz symbol approach
Mathematics, 8 (1) :Paper No. 5
2020

4274.

Ferrari, P.; Serra-Capizzano, S.
Multigrid for $\mathbb{Q}_{k}$ Finite Element Matrices using a (block) Toeplitz symbol approach
Mathematics, 8 (1) :Paper No. 5
2020

4273.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
arXiv preprint arXiv:2009.02484
2020

4272.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
Preprint
2020

4271.

Hutzenthaler, Martin; Kruse, Thomas
Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities
SIAM Journal on Numerical Analysis, 58 (2) :929--961
2020
Publisher: SIAM

4270.

Hutzenthaler, Martin; Kruse, Thomas
Multilevel Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities
SIAM Journal on Numerical Analysis, 58 (2) :929–961
2020
Publisher: Society for Industrial and Applied Mathematics

4269.

Kawai, M.; Ida, A.; Matsuba, H.; Nakajima, K.; Bolten, Matthias
Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Page 217-226
Publisher: ACM, New York
2020

4268.

Kawai, M.; Ida, A.; Matsuba, H.; Nakajima, K.; Bolten, M.
Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Page 217-226
Publisher: ACM, New York
2020

4267.

Klamroth, Kathrin; Lang, Bruno; Seyfried, Armin; Stiglmayr, Michael
Network Simulation for Pedestrian Flows with HyDEFS
Collective Dynamics, 5 :1-16
2020