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

5103.

Jendoubi, Oussama
Vergleich der magnetischen Streufeldwerte eines induktiven geladenen Taxis zwischen Simulation und Messung im Rahmen des TALAKO-Projekts
2023

5102.

Alameddine, Jean-Marco; others
The particle-shower simulation code CORSIKA 8
PoS, ICRC2023 :310
2023

5101.

Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
2023

5100.

Clemens, Markus; Günther, Michael
Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework
2023 International Conference on Electromagnetics in Advanced Applications (ICEAA), Seite 1–1
Herausgeber: IEEE
2023

5099.

Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
2023

5098.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland

5097.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland

5096.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland

5095.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta–Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics
2023
ISSN: 0168-9274

5094.

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

5093.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems--a sensitivity-based approach
arXiv preprint arXiv:2301.02019
2023

5092.


Studies on the improvement of the matching uncertainty definition in top-quark processes simulated with Powheg+Pythia 8
CERN, Geneva
2023

5091.

Bolten, Matthias; Donatelli, M.; Ferrari, P.; Furci, I.
Symbol based convergence analysis in block multigrid methods with applications for Stokes problems
Appl. Numer. Math., 193 :109-130
2023

5090.

Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
2023

5089.

Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60 :35
2023

5088.

Günther, Michael; Sandu, Adrian; Schäfers, Kevin; Zanna, Antonella
Symplectic GARK methods for partitioned Hamiltonian systems
2023

5087.

Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
2023

5086.

Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
2023

5085.

Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
2023

5084.


Synthesis and evaluation of radioiodinated estrogens for diagnosis and therapy of male urogenital tumours
Organic & Biomolecular Chemistry, 2023 (21) :3090-3095
2023
Herausgeber: RSC
ISSN: 1477-0539

5083.

Bolten, Matthias; Friedhoff, S.; Hahne, J.
Task graph-based performance analysis of parallel-in-time methods
Parallel Comput., 118 :103050
2023

5082.

Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
2023

5081.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Seserman, Andra
Poisson approximation to the binomial distribution: extensions to the convergence of positive operators
Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117
2023

5080.

Ehrhardt, Matthias
Use of interference patterns to control sound field focusing in shallow water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI

5079.

Jäschke, Jens; Skrepek, Nathanael; Ehrhardt, Matthias
Mixed-dimensional geometric coupling of port-Hamiltonian systems
Applied Mathematics Letters, 137 :108508
2023
Herausgeber: Pergamon