Dynamic Iteration Schemes

Dynamic iteration via source coupling
Standard time-integration methods solve transient problems all at once. This may become very inefficient or impossible for large systems of equations. Imaging that such large systems often stem from a coupled problem formulation, where different physical phenomena interact and need to be coupled in order to produce a precise mathematical model.
E.g. highly integrated electric circuits (as in memory chips or CPUs) produce heat, which effects in turn their behavior as electrical system; thus one needs to couple electric and thermal subproblem descriptions. On the one hand, this creates multiple time scales due to different physical phenomena, which demands an efficient treatment, see multirate. On the other hand, in a professional environment one usually has dedicated solvers for the subproblems, which need to be used, and an overall problem formulation is not feasible for any of the involved tools.
For those partitioned problems a dynamic iteration method becomes beneficial or even the sole way-out: it keeps the subproblems separate, solves subproblems sequentially (or in parallel) and iterates until convergence (fixed-point interation). Thus the subproblem's structure can be exploited in the respective integration.
To guarantee or to speed up convergence the time interval of interest is split into a series of windows. Then the time-integration of the windows is applied sequentially and in each window the subproblems are solved iteratively by your favoured method.
Group members working on that field
- Andreas Bartel
- Michael Günther
Former and ongoing Projects
Cooperation
- Herbert De Gersem, Katholieke Universiteit Leuven
Publications
- 2024
5275.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Diekmann, Charlotte; Schrader, Claudia
Virtual Reality für den Chemieunterricht
Nachrichten aus der Chemie, 72 (6) :15-22
20245274.
Acu, Ana-Maria; Heilmann, Margareta; Raş, Ioan; Steopoaie, Ancuta Emilia
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov operators
Applicable Analysis and Discrete Mathematics :1-16
20245273.
Sprachsensibler Chemieunterricht digital umgesetzt - Ein Seminarexkurs im Rahmen des Praxissemesters
20245272.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences5271.
Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael; Marheineke, Nicole
Splitting Techniques for DAEs with port-Hamiltonian Applications
Preprint
20245270.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian systems’ modelling in electrical engineering
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor, Scientific Computing in Electrical Engineering: SCEE 2022, Amsterdam, The Netherlands, July 2022ausMathematics in Industry, Seite 133–143
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor
Herausgeber: Springer Cham
20245269.
Jacob, Birgit; Glück, Jochen; Meyer, Annika; Wyss, Christian; Zwart, Hans
Stability via closure relations with applications to dissipative and port-Hamiltonian systems
J. Evol. Equ., 24 :Paper No. 62
20245268.
Bartel, A.; Clemens, M.; Günther, M.; Jacob, Birgit; Reis, T.
Port-Hamiltonian Systems Modelling in Electrical Engineering
Band 43
Herausgeber: Springer, Cham.
van Beurden, M., Budko, N.V., Ciuprina, G., Schilders, W., Bansal, H., Barbulescu, R. Edition
20245267.
Fasi, Massimiliano; Gaudreault, Stéphane; Lund, Kathryn; Schweitzer, Marcel
Challenges in computing matrix functions
20245266.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and xj
Mathematical Methods in the Applied Sciences, 47 (18) :13718-13733
20245265.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators
20245264.
Bauß, Julius; Stiglmayr, Michael
Augmenting Biobjective Branch & Bound with Scalarization-Based Information
Mathematical Methods of Operations Research
20245263.
Vinod, Vivin; Zaspel, Peter
Benchmarking Data Efficiency in Δ-ML and Multifidelity Models for Quantum Chemistry.
20245262.
Kiesling, Elisabeth; Venzlaff, Julian; Bohrmann-Linde, Claudia
BNE-Fortbildungsreihe für Lehrkräfte und Studierende in der Didaktik der Chemie
Herausgeber: Gemeinsamer Studienausschuss (GSA) in der School of Education an der Bergischen Universität Wuppertal
Newsletter Lehrer*innenbildung an der Bergischen Universität Wuppertal
Juli 20245261.
Klass, Friedemann; Bartel, Andreas; Gabbana, PD Alessandro
Boundary conditions for multi-speed lattice Boltzmann methods
20245260.
Bailo, Rafael; Barbaro, Alethea; Gomes, Susana N.; Riedl, Konstantin; Roith, Tim; Totzeck, Claudia; Vaes, Urbain
CBX: Python and Julia Packages for Consensus-Based Interacting Particle Methods
Journal of Open Source Software, 9 (98) :6611
2024
Herausgeber: The Open Journal5259.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195–208
2024
Herausgeber: Pergamon5258.
Bauß, Julius; Stiglmayr, Michael
Adapting Branching and Queuing for Multi-objective Branch and Bound
Operations Research Proceedings 2023
Herausgeber: Springer
20245257.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195-208
Juli 2024
ISSN: 0898-12215256.
Yoda, R.; Bolten, M.; Nakajima, K.; Fujii, A.
Coarse-grid operator optimization in multigrid reduction in time for time-dependent Stokes and Oseen problems
Jpn. J. Ind. Appl. Math.
20245255.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Commutativity and spectral properties for a general class of Szasz-Mirakjan-Durrmeyer operators
Advances in Operator Theory, 10 (1) :14
20245254.
Vorberg, Lukas; Jacob, Birgit; Wyss, Christian
Computing the Quadratic Numerical Range
Journal of Computational and Applied Mathematics :116049
20245253.
Klamroth, Kathrin; Stiglmayr, Michael; Totzeck, Claudia
Consensus-Based Optimization for Multi-Objective Problems: A Multi-Swarm Approach
Journal of Global Optimization
20245252.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London5251.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London