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

Cooperation

Publications



2025

5446.

Xu, Zhuo
Input-to-state type Stability for Simplified Fluid-Particle Interaction System
Mai 2025

5445.

Asya, Berçin V.; Wang, Sitao; Euchler, Eric; Khiêm, Vu Ngoc; Göstl, Robert
Optical Force Probes for Spatially Resolved Imaging of Polymer Damage and Failure
Aggregate, 6 (4) :e70014
April 2025
ISSN: 2692-4560

5444.

Hahmann, Johannes; Schüpp, Boris N.; Ishaqat, Aman; Selvakumar, Arjuna; Göstl, Robert; Gräter, Frauke; Herrmann, Andreas
Sequence-specific, mechanophore-free mechanochemistry of DNA
Chem, 11 (4) :102376
April 2025
ISSN: 2451-9294, 2451-9308

5443.

Ocqueteau, Vicente; Tucsnak, Marius
On an Initial Value Problem Describing the Small Oscillations of a Floating Cylinder
April 2025

5442.


Solid-Supported Iodine(V) Reagents in Organic Synthesis
Chemistry - A European Journal, 2025 :e202500670
03 2025
Herausgeber: Wiley
ISSN: 1521-3765

5441.

[German] Grandrath, Rebecca; Wiebel, Michelle; Bensberg, Kathrin; Schebb, Nils Helge; Bohrmann-Linde, Claudia
Aus der Schale in die Schule
Nachrichten aus der Chemie, 73 (3) :10-12
März 2025

5440.

Storch, Sonja; Campagna, Davide; Aydonat, Simay; Göstl, Robert
Mechanochemical generation of nitrogen-centred radicals for the formation of tertiary amines in polymers
RSC Mechanochemistry, 2 (2) :240-245
März 2025

5439.


Aus der Schale in die Schule
Nachrichten aus der Chemie, 2025 :10-12
02 2025
Herausgeber: Wiley
ISSN: 1868-0054

5438.

Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A Space Mapping approach for the calibration of financial models with the application to the Heston model
2025

5437.

Frommer, Andreas; Rinelli, Michele; Schweitzer, Marcel
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
Math. Comp., 94 :801-823
2025

5436.

Hoffe, Leon; Ulutas, Berna; Klamroth, Kathrin; Bracke, Stefan
Assessing the effectiveness and efficiency of selected solution approaches for two-dimensional stock cutting problems (Part III): Hybrid Approach For Printed Circuit Boards
AUTOMATION 2025: Conference on Automation — Innovations and Future Perspectives
2025

5435.

Kiesling, Elisabeth; Bohrmann-Linde, Claudia
Carbon Capture and Storage - Nachweis von adsorbiertem Kohlenstoffdioxid
Naturwissenschaften im Unterricht Chemie, 1/25 :Versuchskarteikarte
Februar 2025

5434.

Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Constructing Optimal Star Discrepancy Sets
accepted in Proceedings of the AMS
2025

5433.

Kunze, Markus; Mui, Jonathan; Ploss, David
Elliptic operators with non-local Wentzell-Robin boundary conditions
2025

5432.

Song, Yongcun; Wang, Ziqi; Zuazua, Enrique
FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning
Neural Network, 181
Januar 2025

5431.

Kienitz, J; Moodliyar, L
Gaussian views explained
Wilmott, 2025 (135) :72–77
2025
Herausgeber: Wilmott Magazine

5430.

Xu, Zhuo; Tucsnak, Marius
Global Exponential Stabilization for a Simplified Fluid-Particle Interaction System
Januar 2025

5429.

Bartel, Andreas; Schaller, Manuel
Goal-oriented time adaptivity for port-Hamiltonian systems
Journal of Computational and Applied Mathematics, 461 :116450
2025
ISSN: 0377-0427

5428.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
Computer Physics Communications, 309 :109478
2025
ISSN: 0010-4655

5427.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
Computer Physics Communications, 309 :109478
2025
ISSN: 0010-4655

5426.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators and their application to lattice QCD simulations
PoS, LATTICE2024 :025
2025

5425.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators and their application to lattice QCD simulations
PoS, LATTICE2024 :025
2025

5424.

Krhac, Kaja; Schuller, Frederic P.; Stramigioli, Stefano
Hybrid Schrödinger-Liouville and projective dynamics
2025

5423.

Shaju, K.; Laepple, T.; Hirsch, N.; Zaspel, P.
Ice borehole thermometry: Sensor placement using greedy optimal sampling
EGUsphere, 2025 :1—25
2025

5422.

Vinod, Vivin; Zaspel, Peter
Investigating Data Hierarchies in Multifidelity Machine Learning for Excitation Energies
J. Chem. Theory Comput., 21 (6) :3077-3091
2025