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
- 2025
5484.
Hilbig, André; Schmitz, Denise
Informatikdidaktische Sicht auf Barrierefreiheit als Unterrichts- und Forschungsgegenstand
INFOS 2025 – 21. GI-Fachtagung Informatik und Schule
Stoos, Schweiz
20255483.
Vinod, Vivin; Zaspel, Peter
Investigating Data Hierarchies in Multifidelity Machine Learning for Excitation Energies
J. Chem. Theory Comput., 21 (6) :3077-3091
20255482.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Kernels for composition of positive linear operators
20255481.
[german] Grandrath, Rebecca; Orhan, Nalan; Bohrmann-Linde, Claudia
Konzeption einer Projektwoche zu den Themen Food Waste und Food Loss für die gymnasiale Oberstufe
In Andreas Keil, Annika Hanau und Julian Dietze (Hg.): BNE in der Lehrkräftebildung. Erkenntnisse aus Forschung und Praxis., Editor
Seite 315-325
Herausgeber: Waxmann
2025
315-3255480.
Khosrawi-Rad, Bijan; Keller, Paul; Grogorick, Linda; Benner, Dennis; Janson, Andreas; Robra-Bissantz, Susanne
Let's Play with AI! A 2x2 Experiment on Collaborative vs. Competitive Game Elements for Pedagogical Conversational Agents
Pre-ICIS SIG Services Workshop on Synergizing Service Ecosystems with AI
Bangkok, Thailand
20255479.
Vinod, Vivin; Zaspel, Peter
LFaB: Low-fidelity as Bias for Active Learning in the chemical configuration space
20255478.
Schmitz, Denise
LinkedIn-Posts zur Jahrestagung
Nachhaltige IT und Alternativen zu Big Tech, 49
2025
Herausgeber: Gesellschaft für Informatik e.V.5477.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Motivieren mit (Teil-)Aufgaben zur Erklärvideoproduktion im Chemieunterricht
In Johannes Huwer, Timm Wilke, Amitabh Banerji, Editor, Band Progress in Digitalisation in Chemistry Education 2024. Digitales Lehren und Lernen an Hochschule und Schule im Fach Chemie
Seite 37-42
Herausgeber: Waxmann-Verlag, Münster New York
2025
37-42ISBN: 978-3-8188-0042-0
5476.
Finster, Rebecca; Grogorick, Linda; Robra-Bissantz, Susanne
Navigation im Cyberraum: Die NIS2-Umsetzung in der öffentlichen Verwaltung - mit KOMPASS und SEXTANT
Fachtagung Rechts- und Verwaltungsinformatik (RVI)
Hamburg
20255475.
Schweitzer, Marcel
Near instance optimality of the Lanczos method for Stieltjes and related matrix functions
SIAM J. Matrix Anal. Appl., 46 :1846-1865
20255474.
Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Non-convex shape optimization by dissipative Hamiltonian flows
Engineering Optimization, 57 :384--403
20255473.
Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas
Nonlinear Monte Carlo Methods with Polynomial Runtime for Bellman Equations of Discrete Time High-Dimensional Stochastic Optimal Control Problems
Appl. Math. Optim., 91 (1) :26
20255472.
Arlinghaus, Clarissa Sabrina; Schmitz, Denise
NRW vernetzt sich – Neue Regionalgruppe Frauen und Informatik gestartet
Nachhaltige IT und Alternativen zu Big Tech, 49
2025
Herausgeber: Gesellschaft für Informatik e.V.5471.
Figueira, José Rui; Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff Santos, Julia
On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization
Operations Research Letters :107302
20255470.
Löhken, Lara; Stiglmayr, Michael
On the multiobjective cable-trench problem
Journal of Combinatorial Optimization, 49 (55)
20255469.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5468.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5467.
Sinani, Mario; Wynn, Andrew; Palacios, Rafael
Physics-Informed Data-Driven Modelling of Nonlinear Aerodynamic Forces of the Pazy Wing
AIAA SciTech Forum, 6-10 January
Januar 20255466.
Vinod, Vivin; Lyu, Dongyu; Ruth, Marcel; R. Schreiner, Peter; Kleinekathöfer, Ulrich; Zaspel, Peter
Predicting Molecular Energies of Small Organic Molecules With Multi-Fidelity Methods
J. Comp. Chem., 46 (6) :e70056
20255465.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Schrader, Claudia
Produktion eigener VR-Lernsettings im Projekt FoPro-VR. Ein interdisziplinärer Lehransatz für die Lehramtsausbildung
In Mrohs, Lorenz; Franz, Julia; Herrmann, Dominik; Lindner, Konstantin; Staake, Thorsten, Editor, Digitales Lehren und Lernen an der Hochschule. Strategien - Bedingungen - Umsetzung
Seite 191-204
Herausgeber: transcript, Bielefeld
2025
191-204ISBN: 9783839471203
5464.
Khosrawi-Rad, Bijan; Keller, Paul; Benner, Dennis; Grogorick, Linda; Borchers, Arne; Janson, Andreas; Leimeister, Jan Marco; Robra-Bissantz, Susanne
Promoting Students’ Motivation in Language Education with Gamified Pedagogical Conversational Agents
Computers & Education, 238 :1–24
20255463.
Vinod, Vivin; Zaspel, Peter
QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules
Sci. Data, 12 (1) :202
2025
Herausgeber: Nature Publishing Group
ISSN: 2052-44635462.
Patel, Vivak; Maldonado, D Adrian; Melnichenko, Maksim; Pritchard, Nathaniel; Rao, Vishwas; Rebrova, Elizaveta; Sankararaman, Sriram; Schweitzer, Marcel
Scientific Applications Leveraging Randomized Linear Algebra
20255461.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Searching Permutations for Constructing Uniformly Distributed Point Sets
Proceedings of the National Academy of Sciences, 122 (14) :e2424464122
20255460.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
2025