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



scheduled 2023

6180.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer
scheduled 2023

6179.

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

6178.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6177.

Teng, Long; Ehrhardt, Matthias; G\"unther, Michael
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific
scheduled 2023

6176.

{Duffy, D.; Kienitz, J.}
Monte Carlo Frameworks - Building Customisable and High-performance C++ Applications
Herausgeber: {John Wiley \& Sons, Chichester}

6175.

{Kienitz, J.}
Stochastic Processes in Finance I
{Wilmott Magazine}

6174.

{Kienitz, J.}
Stochastic Processes in Finance II
{Wilmott Magazine}, {6}

6173.

{Kienitz, J.}
Stochastic Processes in Finance III
{Wilmott Magazine}
{2009}

6172.

{Beyer, P.; Kienitz, J.}
{Pricing {F}orward {S}tart {O}ption in {M}odels based on {L}évy {P}rocesses}
{The Icfai University Journal of Derivatives Markets}, {6(2)} :{7--23}
{2009}

6171.

{Kienitz, J.}
{The {CGMY} model}
{The Encyclopedia of Quantitative Finance (ed. Cont), Wiley}
{2009}

6170.

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

6169.

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

6168.

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

6167.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer
2023

6166.

Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
2023

6165.

Bauß, Julius; Stiglmayr, Michael
Augmenting Biobjective Branch \& Bound with Scalarization-Based Information
Submitted to Mathematical Methods of Operations Research
2023
Herausgeber: arXiv

6164.

Carrillo, Jose Antonio; Totzeck, Claudia; Vaes, Urbain
Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints
, Modeling and Simulation for Collective Dynamics,Lecture Notes Series, Institute for Mathematical Sciences, NUS Band 40
2023

6163.

[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Kompetenzförderung durch Erklärvideos in einem Selbstlernbuch zum Einstieg in die Organische Chemie
MNU-Journal, 01.2023 :48-54
2023
ISSN: 0025-5866

6162.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6161.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Mit Lactase und Lactose zum elektrischen Strom - enzymatische Brennstoffzellen auf Filterpapierbasis für den Chemieunterricht.
CHEMKON, 30 (1) :37-41
Januar 2023

6160.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
2023

6159.

[english] Rendon-Enriquez, Ibeth; Palma-Cando, Alex; Körber, Florian; Niebisch, Felix; Forster, Michael; Tausch, Michael W.; Scherf, Ullrich
Thin Polymer Films by Oxidative or Reductive Electropolymerization and Their Application in Electrochromic Windows and Thin-Film Sensors
molecules, 28 (2) :883
Januar 2023

6158.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6157.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6156.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

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