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
- Herbert De Gersem, Katholieke Universiteit Leuven
Publications
- 2024
5250.
Vinod, Vivin; Zaspel, Peter
Assessing Non-Nested Configurations of Multifidelity Machine Learning for Quantum-Chemical Properties
Machine Learning: Science and Technology, 5 (4) :045005
20245249.
B. Jacob, C. Totzeck
Port-Hamiltonian Structure of Interacting Particle Systems and Its Mean-Field Limit
SIAM Multiscale Modelling & Simulation, 22
20245248.
Günther, M.; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Math. Control Signals Syst.
20245247.
Schaefers, Kevin; Peardon, Michael
A modified Cayley transform for SU(3)
20245246.
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, 577 :118304
2024
Herausgeber: Academic Press5245.
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, 577 :118304
2024
Herausgeber: Academic Press5244.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics, 101 (9-10) :1094–1112
2024
Herausgeber: Taylor & Francis5243.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics, 101 (9-10) :1094–1112
2024
Herausgeber: Taylor & Francis5242.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics
20245241.
Schäfers, Kevin; Peardon, Michael; Günther, Michael
A modified Cayley transform for SU (3)
Preprint
20245240.
Schäfers, Kevin; Peardon, Michael; Günther, Michael
A modified Cayley transform for SU (3)
Preprint
20245239.
Ehrhardt, Matthias
A nonstandard finite difference scheme for a time-fractional model of Zika virus transmission
Mathematical Biosciences and Engineering, 21 (1) :924–962
2024
Herausgeber: AIMS Press5238.
Gaul, Daniela; Klamroth, Kathrin; Pfeiffer, Christian; Stiglmayr, Michael; Schulz, Arne
A Tight Formulation for the Dial-a-Ride Problem
European Journal of Operational Research
September 2024
Herausgeber: Elsevier BV
ISSN: 0377-22175237.
Ehrhardt, Matthias
A nonstandard finite difference scheme for a time-fractional model of Zika virus transmission
Mathematical Biosciences and Engineering, 21 (1) :924–962
2024
Herausgeber: AIMS Press5236.
5235.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A numerical study of the impact of variance boundary conditions for the Heston model
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Springer
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Herausgeber: Bergische Universität Wuppertal
20245234.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A numerical study of the impact of variance boundary conditions for the Heston model
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Springer
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Herausgeber: Bergische Universität Wuppertal
20245233.
Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
A Port-Hamiltonian System Perspective on Electromagneto-Quasistatic Field Formulations of Darwin-Type
Preprint
20245232.
Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
A Port-Hamiltonian System Perspective on Electromagneto-Quasistatic Field Formulations of Darwin-Type
Preprint
20245231.
Hoang, Manh Tuan; Ehrhardt, Matthias
A second-order nonstandard finite difference method for a general Rosenzweig-MacArthur predator--prey model
Journal of Computational and Applied Mathematics :115752
2024
Herausgeber: Elsevier5230.
Dächert, Kerstin; Fleuren, Tino; Klamroth, Kathrin
A simple, efficient and versatile objective space algorithm for multiobjective integer programming
Mathematical Methods of Operations Research
20245229.
Kapllani, Lorenc; Teng, Long
{A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations}
20245228.
M., Günther; Jacob, B.; Totzeck, C.
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Math. Control Signals Syst., 36 :957–977
20245227.
Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes
Preprint
20245226.
Allmendinger, Richard; Fonseca, Carlos M.; Sayin, Serpil; Wiecek, Margaret M.; Stiglmayr, Michael
Multiobjective Optimization on a Budget (Dagstuhl Seminar 23361)
2024
Herausgeber: Schloss Dagstuhl – Leibniz-Zentrum für Informatik