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
5406.
Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry, 2023 (21) :4574-4577
Mai 2023
Herausgeber: RSC5405.
Ackermann, Julia; Jentzen, Arnulf; Kruse, Thomas; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense
20235404.
[german] Kiesling, Elisabeth; Kremer, Richard; Pereira Vaz, Nuno; Venzlaff, Julian; Bohrmann-Linde, Claudia
Wege aus der Klimakrise – ein BNE-Schülerlaborangebot mit mehrdimensionalem Zugang
MNU Journal, 76 (06/2023) :464 - 471
November 2023
ISSN: 0025-58665403.
Braun, Feodor; Jaschinski, M.; Kirsch, Stefan F.; Schomäcker, Klaus
Synthesis and evaluation of radioiodinated estrogens for diagnosis and therapy of male urogenital tumours
Organic & Biomolecular Chemistry, 21 :3090-3095
März 2023
Herausgeber: RSC
ISSN: 1477-05395402.
Springer, Bastian L.; Holzschneider, K.; Mohr, Fabian; Kirsch, S. F.
Phenanthro[9,10‑d]imidazoles: An Unexpected Synthetic Route
Synthesis, 55 (24) :4224-4230
Oktober 2023
Herausgeber: Thieme
ISSN: 0039-78815401.
Ahmed, Mustafa
Quantifizierung der Genauigkeit der Co-Simulation Scalar Potential Finite Difference Methode bei der Expositionsbestimmung von Menschen durch die vernachlässigte Rückwirkung der körperinduzierten Ströme auf das magnetische Quellfeld
20235400.
Jendoubi, Oussama
Vergleich der magnetischen Streufeldwerte eines induktiven geladenen Taxis zwischen Simulation und Messung im Rahmen des TALAKO-Projekts
20235399.
Bülow, Friedrich; Hahn, Yannik; Meyes, Richard; Meisen, Tobias; others
Transparent and Interpretable State of Health Forecasting of Lithium-Ion Batteries with Deep Learning and Saliency Maps
International Journal of Energy Research, 2023
2023
Herausgeber: Hindawi5398.
Lars, Thun
Investigation of time constraints for quality prediction in arc welding using deep learning
20235397.
Bahja, Ali Rida
Pose Estimation using Deep Learning and Systematic Dataset Generation for Industrial Manufacturing
20235396.
Aad, Georges; others
Search for pair-produced scalar and vector leptoquarks decaying into third-generation quarks and first- or second-generation leptons in pp collisions with the ATLAS detector
JHEP, 2306 :188
20235395.
Aad, Georges; others
Search for pair-produced vector-like top and bottom partners in events with large missing transverse momentum in pp collisions with the ATLAS detector
Eur. Phys. J. C, 83 (8) :719
20235394.
Measurement of $t$-channel production of single top quarks and antiquarks in $pp$ collisions at 13 TeV using the full ATLAS Run 2 dataset
20235393.
5392.
Studies on the improvement of the matching uncertainty definition in top-quark processes simulated with Powheg+Pythia 8
CERN, Geneva
20235391.
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-Holland5390.
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
20235389.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep FDM: Enhanced finite difference methods by deep learning
Franklin Open, 4 :100039
2023
Herausgeber: Elsevier5388.
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: Pergamon5387.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numerische Mathematik, 155 (1-2) :1–34
2023
Herausgeber: Springer New York5386.
Göhring, Timo
Ratio of Electron and Muon Pair Production at High Invariant Mass in Association with a b-jet
20235385.
Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael
Operator splitting for semi-explicit differential-algebraic equations and port-Hamiltonian DAEs
Preprint
20235384.
Beumker, Tim Frederik
Analysis of a combined measurement of $W^\pm \rightarrow \ell^\pm \nu (\ell = e,\mu)$ cross section differential in $\m_T^W$ and $\m_T^W \cross |\eta|$ at high transverse masses at $\sqrt{s} = 13$ TeV with the Atlas detector
20235383.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Genuine Bernstein–Durrmeyer type operators preserving 1 and $x^j$
Annals of Functional Analysis, 15 (1)
Oktober 2023
Herausgeber: Springer Science and Business Media LLC
ISSN: 2008-87525382.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Voronovskaja formula for Aldaz–Kounchev–Render operators: uniform convergence
Analysis and Mathematical Physics, 14 (1)
Dezember 2023
ISSN: 1664-235X
