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
5325.
Fan, Jilin; Xuan, Mingjun; Zhang, Kuan; Vinokur, Rostislav; Zheng, Lifei; Göstl, Robert; Herrmann, Andreas
Accelerated Mechanophore Activation and Drug Release in Network Core-Structured Star Polymers Using High-Intensity Focused Ultrasound
Small Science, 4 (8) :2400082
August 20245324.
Song, Yongcun; Wang, Ziqi; Zuazua, Enrique
Approximate and Weighted Data Reconstruction Attack in Federated Learning
08 20245323.
Fan, Jilin; Zhang, Kuan; Xuan, Mingjun; Gao, Xiang; Vinokur, Rostislav; Göstl, Robert; Zheng, Lifei; Herrmann, Andreas
High-Intensity Focused Ultrasound-Induced Disulfide Mechanophore Activation in Polymeric Nanostructures for Molecule Release
CCS Chemistry, 6 (8) :1895-1907
August 20245322.
A Formal Synthesis of (+)-Hannokinol Using a Chiral Horner–Wittig Reagent
Molecules, 29 :3710
07 2024
Herausgeber: MDPI
ISSN: 1420-30495321.
Alcalde, Albert; Fantuzzi, Giovanni; Zuazua, Enrique
Clustering in pure-attention hardmax transformers and its role in sentiment analysis
06 20245320.
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Herausgeber: RSC5319.
Aydonat, Simay; Hergesell, Adrian H.; Seitzinger, Claire L.; Lennarz, Regina; Chang, George; Sievers, Carsten; Meisner, Jan; Vollmer, Ina; Göstl, Robert
Leveraging mechanochemistry for sustainable polymer degradation
Polymer Journal, 56 (4) :249-268
April 2024
ISSN: 1349-05405318.
Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 20245317.
Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
Februar 2024
ISSN: 2198-38445316.
[german] Tausch, Michael W.
Curriculare Innovation - Ein Imperativ für den Chemieunterricht
Band Chemie professionell unterrichten
Herausgeber: T. Palenta
Februar 2024ISBN: 9783758478413
5315.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 9
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X5314.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry - A European Journal, 2024 :e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-65395313.
[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 20245312.
Izak-Nau, Emilia; Niggemann, Louisa P.; Göstl, Robert
Brownian Relaxation Shakes and Breaks Magnetic Iron Oxide-Polymer Nanocomposites to Release Cargo
Small, 20 (4) :2304527
Januar 2024
ISSN: 1613-68295311.
[english] Wiebel, Michelle; Bensberg, Kathrin; Wende, Luca; Grandrath, Rebecca; Plitzko, Kathrin; Bohrmann-Linde, Claudia; Schebb, Nils Helge
Efficient and simple extraction protocol for triterpenic acids from apples
Journal of Chemical Education
April 2024
Herausgeber: American Chemical Society and Division of Chemical Education, Inc.5310.
Oleanolic Acid-Derived High-Glass-Transition-Temperature Methacrylic Polymers
Sustainable Chemistry & Engineering
Dezember 2024
Herausgeber: ACS
ISSN: 2168-04855309.
Krhac, Kaja; Maschke, Bernhard; van der Schaft, Arjan
Port-Hamiltonian systems with energy and power ports
IFAC-PapersOnLine, 58(6) :280-285
Mai 20245308.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov subspace methods: Matrix Sylvester equations
Math. Comp.
20245307.
Liu, Qian
Small-signal synchronization stability of sequence-decomposed grid-forming IBRs
Dezember 20245306.
Santos, Daniela Scherer; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the multiobjective quasi-clique problem
20245305.
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 Sciences5304.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research, 336 (1) :637–659
2024
Herausgeber: Springer Netherlands5303.
[english] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Simple biofuel cells: the superpower of baker’s yeast
Science in School - The European journal for science teachers, 66
Februar 20245302.
Andersen, Kim Allan; Boomsma, Trine Krogh; Efkes, Britta; Forget, Nicolas
Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization
Management Science
20245301.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research, 336 (1) :637–659
2024
Herausgeber: Springer Netherlands