Applied and Computational Mathematics (ACM)

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





Alcalde, Albert; Fantuzzi, Giovanni; Zuazua, Enrique
Clustering in pure-attention hardmax transformers and its role in sentiment analysis
06 2024


Xu, Zhuo; Tucsnak, Marius
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
06 2024


Ballaschk, Frederic; Bensberg, Kathrin; Crone, Benedikt; Kirsch, S. F.; Menz, Helge
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Herausgeber: RSC


Ishaqat, Aman; Hahmann, Johannes; Lin, Cheng; Zhang, Xiaofeng; He, Chuanjiang; Rath, Wolfgang H.; Habib, Pardes; Sahnoun, Sabri E. M.; Rahimi, Khosrow; Vinokur, Rostislav; Mottaghy, Felix M.; Göstl, Robert; Bartneck, Matthias; Herrmann, Andreas
In Vivo Polymer Mechanochemistry with Polynucleotides
Advanced Materials, 36 :2403752
Mai 2024
ISSN: 1521-4095


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
April 2024


Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 2024


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: 1349-0540


Broschinski, Christian; Majer, Felix; He, Siyang; Kuehne, Alexander J. C.; Göstl, Robert
Mechanochemical Activation of Red-Light-Excited Triplet–Triplet Annihilation Photon Upconversion
ACS Applied Optical Materials
März 2024


Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Spectral analysis of a class of linear hyperbolic partial differential equations
03 2024


Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
Februar 2024
ISSN: 2198-3844


[german] Tausch, Michael W.
Curriculare Innovation - Ein Imperativ für den Chemieunterricht
Band Chemie professionell unterrichten
Herausgeber: T. Palenta
Februar 2024

ISBN: 9783758478413


Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Linear-Quadratic optimal control for boundary controlled networks of waves
02 2024


Celik, I. E.; Mittendorf, Fabia; Gómez-Suárez, Adrián; Kirsch, S. F.
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: 2666-951X


Bensberg, Kathrin; Savvidis, Athanasios; Ballaschk, Frederic; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry - A European Journal, 2024 :e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-6539


[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 2024


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: 1613-6829


[english] Wiebel, Michelle; Bensberg, Kathrin; Wende, Luca; Grandrath, Rebecca; Plitzko, Kathrin; Bohrmann-Linde, Claudia; Kirsch, Stefan F.; Schebb, Nils Helge
Efficient and simple extraction protocol for triterpenic acids from apples
Journal of Chemical Education
Herausgeber: American Chemical Society and Division of Chemical Education, Inc.


Krhac, Kaja; Maschke, Bernhard; van der Schaft, Arjan
Port-Hamiltonian systems with energy and power ports


Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options


Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing


Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital


Calvo-Garrido, MC; Ehrhardt, M; V{\'a}zquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 390


Ehrhardt, M; Günther, M; Bartel, PD Dr A
Mathematische Modellierung in Anwendungen


Ehrhardt, Matthias; Farkas, B{\'a}lint; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas
Operator Splitting and Multirate Schemes


Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

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