Coupled DAE Problems

A circuit (DAE model) coupled to a magnetostatic field device (PDE model)
Coupled Problems of differential-algebraic equations (DAEs) arise typically from either multiphysical modeling (e.g. in circuit simulation with heating) or from refined modeling, where crucial parts of the original problem are replaced by a better, but computational more expensive model (e.g. circuits refined by field models). Furthermore splitting methods may turn a monolithic DAE problem into coupled subproblems, e.g. because of different time scales (multirate). In any case the DAEs arise from network approaches or space-discretization of PDAEs (Partial Differential Algebraic Equations).
Often the coupled equations have quite different properties, i.e., symmetries, definiteness or time scales. Thus the coupled system must be analyzed (e.g. the index) and tailored methods have to be developed (e.g. dynamic iteration).
Details
Publications
- 2024
5225.
Vinod, Vivin; Zaspel, Peter
Investigating Data Hierarchies in Multifidelity Machine Learning for Excitation Energies
20245224.
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
20245223.
Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Linear-Quadratic optimal control for boundary controlled networks of waves
20245222.
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
December 20245221.
Costa, G Morais Rodrigues; Ehrhardt, Matthias
Mathematical analysis and a nonstandard scheme for a model of the immune response against COVID-19
Volume 793
Page 251–270
Publisher: AMS Contemporary Mathematics
2024
251–2705220.
Costa, G Morais Rodrigues; Ehrhardt, Matthias
Mathematical analysis and a nonstandard scheme for a model of the immune response against COVID-19
Volume 793
Page 251–270
Publisher: AMS Contemporary Mathematics
2024
251–2705219.
Bolten, Matthias; Kilmer, Misha E.; MacLachlan, Scott
Multigrid preconditioning for regularized least-squares problems
SIAM J. Sci. Comput., 46 (5) :s271—s295
2024
ISSN: 1064-82755218.
Schultes, Johanna
Multiobjective optimization of shapes using scalarization techniques
Dissertation
Dissertation
Bergische Universität Wuppertal
20245217.
Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Non-convex shape optimization by dissipative {H}amiltonian flows
Engineering Optimization
20245216.
Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes
Preprint
20245215.
Bolten, M.; Doganay, O. T.; Gottschalk, H.; Klamroth, K.
Non-convex shape optimization by dissipative Hamiltonian flows
Eng. Optim. :1—20
20245214.
Bauß, Julius
On improvements of multi-objective branch and bound
Dissertation
Dissertation
Bergische Universität Wuppertal
20245213.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
On some Cauchy problems and positive linear operators
Mediterranean Journal of Mathematics, accepted
20245212.
Lorenz, Jan; Zwerschke, Tom; Schaefers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
20245211.
Kruse, Thomas; Strack, Philipp
Optimal dynamic control of an epidemic
Operations Research, 72 (3) :1031–1048
2024
Publisher: INFORMS5210.
Kruse, Thomas; Strack, Philipp
Optimal dynamic control of an epidemic
Operations Research, 72 (3) :1031–1048
2024
Publisher: INFORMS5209.
Vinod, Vivin; Kleinekathöfer, Ulrich; Zaspel, Peter
Optimized multifidelity machine learning for quantum chemistry
Mach. Learn.: Sci. Technol., 5 (1) :015054
20245208.
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
20245207.
Jamil, Hamza
Intrusive and non-intrusive uncertainty quantification methodologies for pyrolysis modeling
Fire Safety Journal, 143 :104060
2024
ISSN: 0379-71125206.
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
20245205.
Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
20245204.
Santos, Daniela Scherer; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Ensuring connectedness for the Maximum Quasi-clique and Densest $k$-subgraph problems
20245203.
Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes.
20245202.
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
Publisher: AIMS Press5201.
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