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

5225.

Vinod, Vivin; Zaspel, Peter
Investigating Data Hierarchies in Multifidelity Machine Learning for Excitation Energies
2024

5224.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
SIAM J. Sci. Comput., 46 (2) :S223-S253
2024

5223.

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

5222.

Xu, Zhuo; Tucsnak, Marius
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
Mathematical Control and Related Fields, 14(4) :1477-1500
Dezember 2024

5221.

Costa, G Morais Rodrigues; Ehrhardt, Matthias
Mathematical analysis and a nonstandard scheme for a model of the immune response against COVID-19
Band 793
Seite 251–270
Herausgeber: AMS Contemporary Mathematics
2024
251–270

5220.

Costa, G Morais Rodrigues; Ehrhardt, Matthias
Mathematical analysis and a nonstandard scheme for a model of the immune response against COVID-19
Band 793
Seite 251–270
Herausgeber: AMS Contemporary Mathematics
2024
251–270

5219.

Bolten, Matthias; Kilmer, Misha E.; MacLachlan, Scott
Multigrid preconditioning for regularized least-squares problems
SIAM J. Sci. Comput., 46 (5) :s271—s295
2024
ISSN: 1064-8275

5218.

Schultes, Johanna
Multiobjective optimization of shapes using scalarization techniques
Dissertation
Dissertation
Bergische Universität Wuppertal
2024

5217.

Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Non-convex shape optimization by dissipative {H}amiltonian flows
Engineering Optimization
2024

5216.

Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes
Preprint
2024

5215.

Bolten, M.; Doganay, O. T.; Gottschalk, H.; Klamroth, K.
Non-convex shape optimization by dissipative Hamiltonian flows
Eng. Optim. :1—20
2024

5214.

Bauß, Julius
On improvements of multi-objective branch and bound
Dissertation
Dissertation
Bergische Universität Wuppertal
2024

5213.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
On some Cauchy problems and positive linear operators
Mediterranean Journal of Mathematics, accepted
2024

5212.

Lorenz, Jan; Zwerschke, Tom; Schaefers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
2024

5211.

Kruse, Thomas; Strack, Philipp
Optimal dynamic control of an epidemic
Operations Research, 72 (3) :1031–1048
2024
Herausgeber: INFORMS

5210.

Kruse, Thomas; Strack, Philipp
Optimal dynamic control of an epidemic
Operations Research, 72 (3) :1031–1048
2024
Herausgeber: INFORMS

5209.

Vinod, Vivin; Kleinekathöfer, Ulrich; Zaspel, Peter
Optimized multifidelity machine learning for quantum chemistry
Mach. Learn.: Sci. Technol., 5 (1) :015054
2024

5208.

Frommer, Andreas; Ramirez-Hidalgo, Gustavo; Schweitzer, Marcel; Tsolakis, Manuel
Polynomial preconditioning for the action of the matrix square root and inverse square root
Electron. Trans. Numer. Anal., 60 :381-404
2024

5207.

Jamil, Hamza
Intrusive and non-intrusive uncertainty quantification methodologies for pyrolysis modeling
Fire Safety Journal, 143 :104060
2024
ISSN: 0379-7112

5206.

Hosfeld, René; Jacob, Birgit; Schwenninger, Felix; Tucsnak, Marius
Input-to-state stability for bilinear feedback systems
SIAM Journal on Control and Optimization, 62 (3) :1369-1389
2024

5205.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
2024

5204.

Santos, Daniela Scherer; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Ensuring connectedness for the Maximum Quasi-clique and Densest $k$-subgraph problems
2024

5203.

Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes.
2024

5202.

Kapllani, Lorenc; Teng, Long
Deep learning algorithms for solving high-dimensional nonlinear backward stochastic differential equations
Discrete and continuous dynamical systems - B, 29 (4) :1695–1729
2024
Herausgeber: AIMS Press

5201.

Ackermann, Julia; Jentzen, Arnulf; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
arXiv:2406.10876 :64 pages
2024