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
- 2025
5414.
Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Non-convex shape optimization by dissipative Hamiltonian flows
Engineering Optimization, 57 :384--403
20255413.
Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas
Nonlinear Monte Carlo Methods with Polynomial Runtime for Bellman Equations of Discrete Time High-Dimensional Stochastic Optimal Control Problems
Appl. Math. Optim., 91 (1) :26
20255412.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5411.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5410.
Sinani, Mario; Wynn, Andrew; Palacios, Rafael
Physics-Informed Data-Driven Modelling of Nonlinear Aerodynamic Forces of the Pazy Wing
AIAA SciTech Forum, 6-10 January
01 20255409.
Vinod, Vivin; Lyu, Dongyu; Ruth, Marcel; R. Schreiner, Peter; Kleinekathöfer, Ulrich; Zaspel, Peter
Predicting Molecular Energies of Small Organic Molecules With Multi-Fidelity Methods
J. Comp. Chem., 46 (6) :e70056
20255408.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Schrader, Claudia
Produktion eigener VR-Lernsettings im Projekt FoPro-VR. Ein interdisziplinärer Lehransatz für die Lehramtsausbildung
In Mrohs, Lorenz; Franz, Julia; Herrmann, Dominik; Lindner, Konstantin; Staake, Thorsten, Editor, Digitales Lehren und Lernen an der Hochschule. Strategien - Bedingungen - Umsetzung
Seite 191-204
Herausgeber: transcript, Bielefeld
2025
191-204ISBN: 9783839471203
5407.
Vinod, Vivin; Zaspel, Peter
QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules
Sci. Data, 12 (1) :202
2025
Herausgeber: Nature Publishing Group
ISSN: 2052-44635406.
Xue, Chaoyang; Chen, Hui; McGillen, Max R.; Su, Hang; Cheng, Yafang; Kleffmann, Jörg; Li, Guo; Cazaunau, Mathieu; Colomb, Aurélie; Sciare, Jean; DeWitt, Langley; Marchand, Nicolas; Sarda-Esteve, Roland; Petit, Jean-Eudes; Kukui, Alexandre
Role of Heterogeneous Reactions in the Atmospheric Oxidizing Capacity in Island Environments
Environmental Science & Technology, 59 (6) :3153—3164
Februar 2025
ISSN: 0013-936X, 1520-58515405.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Searching Permutations for Constructing Uniformly Distributed Point Sets
PNAS
20255404.
Heintz, Chris; Kersten, Hendrik; Benter, Thorsten; Wissdorf, Walter
Signatures of Charged Droplets from ESI: A Statistical Analysis of Non-summed Mass Spectra Compared to APCI
Journal of the American Society for Mass Spectrometry, 36 (4) :839—849
April 2025
ISSN: 1044-0305, 1879-11235403.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
20255402.
Liu, Qian; Yanchang, Zhang; Zuan, Wang; Wang, Miao; Zhao, Xiaowei
Small-signal stability of sequence-decomposed grid-forming IBRs with DC-link voltage dynamics
Februar 20255401.
Arora, Sahiba; Mui, Jonathan
Smoothing of operator semigroups under relatively bounded perturbations
20255400.
Santos, Daniela Dos; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the Multiobejctive Quasi-Clique Problem
European Journal of Operational Research, 323 :409—424
20255399.
Elghazi, Bouchra; Jacob, Birgit; Zwart, Hans
Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation
Januar 20255398.
Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society5397.
Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings5396.
Günther, Michael
Einführung in die Finanzmathematik5395.
Al{\i}, G; Bartel, A
Electrical RLC networks and diodes5394.
Gjonaj, Erion; Bahls, Christian Rüdiger; Bandlow, Bastian; Bartel, Andreas; Baumanns, Sascha; Belzen, F; Benderskaya, Galina; Benner, Peter; Beurden, MC; Blaszczyk, Andreas; others
Feldmann, Uwe, 143 Feng, Lihong, 515 De Gersem, Herbert, 341 Gim, Sebasti{\'a}n, 45, 333
MATHEMATICS IN INDUSTRY 14 :5875393.
Ehrhardt, Matthias
für Angewandte Analysis und Stochastik5392.
Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations5391.
High order tensor product interpolation in the Combination Technique
preprint, 14 :255390.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388