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



2023

6833.

Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry
05 2023

6832.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Dem Apfel ans Leder
Nachrichten aus der Chemie, 71 :12-14
März 2023

6831.

Fatoorehchi, Hooman; Zarghami, Reza; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
2023

6830.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6829.

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

6828.

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

6827.

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

6826.

Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics

6825.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6824.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6823.

Günther, Michael; Kossaczk{\`y}, Igor
Lab Exercises for Numerical Analysis and Simulation I: ODEs

6822.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csom{\'o}s, Petra; Farag{\'o}, Istv{\'a}n; Fekete, Imre; others
Invited Papers

6821.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388

6820.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388

6819.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6818.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6817.

Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations

6816.

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

6815.

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 :587

6814.

Al{\i}, G; Bartel, A; Günther, M
Electrical RLC networks and diodes

6813.

Günther, Michael
Einführung in die Finanzmathematik

6812.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

6811.

Tripiccione, Betreuer Raffaele; Ehrhardt, Matthias; Alexandrou, Constantia; Toschi, Federico; Simma, Hubert; Schifano, Co-Betreuer Sebastiano Fabio
Daniele Simeoni 1836010

6810.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society

6809.

Ehrhardt, Matthias
Computerunterstützte Mathematik Zeiten

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