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

Cooperations

Publications



2022

6124.

[german] Kremer, Richard; Bohrmann-Linde, Claudia; Tausch, Michael W.
Künstliche Photosynthese im Fokus - Photokatalytische Wasserstofferzeugung in der Eintopfzelle
CHEMKON, 29 (6) :646-653
September 2022

6123.

[german] Bohrmann-Linde, Claudia; Gökkus, Yasemin; Humbert, Ludger; Kiesling, Elisabeth; Kremer, Richard; Losch, Daniel; Schmitz, Denise; Zeller, Diana
Analyse, Struktur und Darstellung chemiedidaktischer Elemente aus informatischer Perspektive – Entwicklung eines interdisziplinären Lehrkonzeptes
MNU-Journal, 05.2022 :423-429
September 2022

6122.

Bohrmann-Linde, Claudia; Siehr, Ilona
CHEMIE Einführungsphase Nordrhein-Westfalen
Herausgeber: C.C.Buchner Verlag, Bamberg
August 2022

ISBN: 9783661060019

6121.

[german] Monique, Meier; Zeller, Diana; Stinken-Rösner, Lisa
Interaktive Videoformate für den naturwissenschaftlichen Unterricht. Vom Rezipieren zum Interagieren
Unterricht Biologie, 475 :44-47
07 2022

6120.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Strom aus Bäckerhefe
Nachrichten aus der Chemie, 70 (7-8) :18-21
Juli 2022

6119.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Entwicklung eines lowcost Experiments für den Chemieunterricht am Beispiel der enzymatischen Brennstoffzelle mit Lactase
CHEMKON, 29 (S1) :233-238
Juni 2022

6118.

[german] Zeller, Diana
Medialab – ein dreistufiges Modul zur Entwicklung digitalisierungsbezogener Kompetenzen im Studium des Chemie‐ und Sachunterrichtslehramts
CHEMKON, 29 (S1) :287-292
Juni 2022

6117.

[english] Bohrmann-Linde, Claudia; Zeller, Diana; Meuter, Nico; Tausch, Michael W.
Teaching Photochemistry: Experimental Approaches and Digital Media
ChemPhotoChem, 6 (6) :1-11
Juni 2022

6116.

[german] Kiesling, Elisabeth; Venzlaff, Julian; Bohrmann-Linde, Claudia
BNE im Chemieunterricht – von der Leitlinie BNE NRW zur exemplarischen Unterrichtseinbindung
CHEMKON, 29 (S1) :239-245
Juni 2022

6115.

[german] Zeller, Diana; Meier, Monique
Videos interaktiv erweitern - Forschendes Lernen vielseitig unterstützen
Digital Unterricht Biologie, 4 :10-11
Mai 2022

6114.

[german] Gökkus, Yasemin; Tausch, Michael W.
Explorative Studie zur partizipativen und nutzenorientierten Forschung in der Chemiedidaktik
CHEMKON, 29 (3) :117-124
April 2022

6113.

[german] Banerji, Amitabh; Dörschelln, Jennifer; Schwarz, D.
Organische Leuchtdioden im Chemieunterricht
Chemie in unserer Zeit, 52 (1) :34-41
2022

6112.

Gerlach, Moritz; Glück, Jochen
On characteristics of the range of integral operators
2022

6111.

Petrov, {Pavel S.}; Ehrhardt, Matthias; Trofimov, {M. Yu.}
On the decomposition of the fundamental solution of the {Helmholtz} equation via solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215--228
2022
Herausgeber: IOS Press

6110.

Ballaschk, Frederic; Kirsch, Stefan F.
Oxidations with Iodine(V) Compounds – From Stoichiometric Compounds to Catalysts
In Ishihara, Kazuaki and Muñiz, Kilian, Editor, Iodine Catalysis in Organic Synthesis
Seite 299–334
Herausgeber: Wiley
1 Edition
2022
299–334

6109.

Heldmann, F.; Treibert, S.; Ehrhardt, M.; Klamroth, K.
PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss
IMACM preprint 22/13
2022

6108.

Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
2022

6107.

Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
On intertwining of maxima of sum of translates functions with nonsingular kernels
Trudy Inst. Mat. Mekh. UrO RAN
2022

6106.

Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
2022

6105.

Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
2022

6104.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal Optimization Through Multi-objective Reformulation
math.OC, arXiv:2204.02003
2022
Herausgeber: arXiv

6103.

Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on {GPU}
JMI, 12 (5)
2022

6102.

Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-nume\-rical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
J. Energy Storage, 45 :103746
2022
Herausgeber: Elsevier

6101.

Bartel, Andreas; Günther, Michael
Multirate Schemes -- An Answer of Numerical Analysis to a Demand from Applications
In Michael Günther and Wil Schilders, Editor, Novel Mathematics Inspired by Industrial Challenges
Seite 5--27
Herausgeber: Springer
2022
5--27

6100.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Multi-objective Matroid Optimization with Ordinal Weights
Discrete Applied Mathematics
2022

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