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



2024

6990.

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

6989.

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

6988.

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

6987.

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

6986.

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

6985.

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

6984.

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

6983.

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

6982.

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

6981.

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

6980.

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

6979.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6978.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6977.

Petrov, Pavel S; Ehrhardt, Matthias; Kozitskiy, Sergey B
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration :118304
2024
Herausgeber: Elsevier

6976.

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

6975.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

6974.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

6973.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

6972.

Putek, Piotr; PAPLICKI, Piotr; Pulch, Roland; Maten, Jan; Günther, Michael; PA{\L}KA, Ryszard
NONLINEAR MULTIOBJECTIVE TOPOLOGY OPTIMIZATION AND MULTIPHYSICS ANALYSIS OF A PERMANENT-MAGNET EXCITED SYNCHRONOUS MACHINE

6971.

Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs

6970.

Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model

6969.

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

6968.

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

6967.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

6966.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

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