Index Analysis
DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.
Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.
Group members working on that field
- Andreas Bartel
- Michael Günther
Cooperations
- Giuseppe Ali (Academia)
- Sascha Baumanns (Academia)
- Caren Tischendorf (Academia)
Publications
- 2023
4727.
Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon4726.
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
20234725.
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-Holland4724.
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: 0168-92744723.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
20234722.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems--a sensitivity-based approach
arXiv preprint arXiv:2301.02019
20234721.
Thielmann, Oliver
Search for flavour-changing neutral current interactions in the top-quark Higgs boson sector in multi-lepton final states with the ATLAS detector at the LHC at $\sqrt{s} = 13\,\text{TeV}$
Bergische Universität Wuppertal
20234720.
Alameddine, Jean-Marco; others
Simulations of cross media showers with CORSIKA 8
PoS, ICRC2023 :442
20234719.
Asatryan, Hayk; Gaul, Daniela; Gottschalk, Hanno; Klamroth, Kathrin; Stiglmayr, Michael
Ridepooling and public bus services: A comparative case-study
Submitted to Transportation
2023
Herausgeber: arXiv4718.
Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
20234717.
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
Journal of Computational Physics, 488 :112211
2023
Herausgeber: Academic Press4716.
[en] Börger, Kristian; Belt, Alexander; Schultze, Thorsten; Arnold, Lukas
Remote Sensing of the Light-Obscuring Smoke Properties in Real-Scale Fires Using a Photometric Measurement Method
Fire Technology
September 2023
ISSN: 0015-2684, 1572-80994715.
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
arXiv preprint arXiv:2302.01810
Juni 20234714.
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
arXiv preprint arXiv:2302.01810
20234713.
[en] Hehnen, Tristan; Arnold, Lukas
PMMA pyrolysis simulation – from micro- to real-scale
Fire Safety Journal, 141
Dezember 2023
ISSN: 037971124712.
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
20234711.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-{H}amiltonian Systems Modelling in Electrical Engineering
arXiv preprint arXiv:2301.02024
20234710.
Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
20234709.
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
Journal of Computational Physics, 488 :112211
20234708.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian Systems Modelling in Electrical Engineering
arXiv preprint arXiv:2301.02024
20234707.
Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
SIAM J. Matrix Anal. Appl., 44 :1073-1095
20234706.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Positive linear operators preserving certain monomials on [0, ∞)
Dolomites Research Notes on Approximation, 16 :1-9
2023
ISSN: 2035-68034705.
Bahja, Ali Rida
Pose Estimation using Deep Learning and Systematic Dataset Generation for Industrial Manufacturing
20234704.
Göhring, Timo
Ratio of Electron and Muon Pair Production at High Invariant Mass in Association with a b-jet
20234703.
Morejon, Leonel; Condorelli, Antonio; Biteau, Jonathan; Kampert, Karl-Heinz
Propagation of Ultra High-Energy Cosmic Rays in light of the latest EBL constraints
PoS, ICRC2023 :283
2023
