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
- 2024
5284.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences5283.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences5282.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences5281.
Rohde, Martin; Burgmann, Sebastian; Janoske, Uwe
The impact of a two-dimensional vibration excitation on the critical incident flow velocity of a sessile droplet
International Journal of Multiphase Flow, 171 :104663
2024
Herausgeber: Pergamon5280.
Reiter, Kendra; Schmidt, Marie; Stiglmayr, Michael
The Line-Based Dial-a-Ride Problem
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)Band123ausOpen Access Series in Informatics (OASIcs), Seite 14:1—14:20
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs)
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor
Herausgeber: Schloss Dagstuhl — Leibniz-Zentrum für Informatik, Dagstuhl, Germany
20245279.
Khosrawi-Rad, Bijan; Grogorick, Linda; Strohmann, Timo; Robra-Bissantz, Susanne
Toward a Method for Design Science Research Meta-Studies to Improve the Reusability of Design Principles
International Conference on Design Science Research in Information Systems and Technology (DESRIST)
Trollhättan, Schweden
20245278.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Preprint IMACM
2024
Herausgeber: Bergische Universität Wuppertal5277.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Diekmann, Charlotte; Schrader, Claudia
Virtual Reality für den Chemieunterricht
Nachrichten aus der Chemie, 72 (6) :15-22
20245276.
Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Steopoaie, Ancuta Emilia
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov operators
Applicable Analysis and Discrete Mathematics :1-16
2024- 2023
5275.
Haussmann, N.; Stroka, S.; Mazaheri, S.; Clemens, M.
Using Point Clouds for Material Properties Smoothing in Low-Frequency Numerical Dosimetry Simulations
21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024)
Jeju, South Korea
Dezember 20235274.
Kähne, B.; Clemens, M.
A GPU Accelerated Semi-Implicit Method for Large-Scale Nonlinear Eddy-Current Problems Using Adaptive Time Step Control
21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024)
Jeju, South Korea
Dezember 20235273.
[en] Börger, Kristian; Ellingham, Jennifer; Belt, Alexander; Schultze, Thorsten; Bieder, Stefan; Weckman, Elizabeth; Arnold, Lukas
Assessing performance of LEDSA and Radiance method for measuring extinction coefficients in real-scale fire environments
Fire Safety Journal, 141
Dezember 2023
ISSN: 037971125272.
[en] Hehnen, Tristan; Arnold, Lukas
PMMA pyrolysis simulation – from micro- to real-scale
Fire Safety Journal, 141
Dezember 2023
ISSN: 037971125271.
Gernandt, Hannes; Hinsen, Dorothea; Cherifi, Karim
The difference between port-Hamiltonian, passive and positive real descriptor systems
Mathematics of Control, Signals, and Systems
Dezember 20235270.
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: 1664-235X5269.
Stroka, S.; Kasolis, F.; Haussmann, N.; Clemens, M.
Efficient Low-Frequency Human Exposure Assessment with the Maximum Entropy Snapshot Sampling
21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024)
Jeju, Korea
November 20235268.
Xuan, Mingjun; Fan, Jilin; Khiêm, Vu Ngoc; Zou, Miancheng; Brenske, Kai-Oliver; Mourran, Ahmed; Vinokur, Rostislav; Zheng, Lifei; Itskov, Mikhail; Göstl, Robert; Herrmann, Andreas
Polymer Mechanochemistry in Microbubbles
Advanced Materials, 35 (47) :2305130
November 2023
ISSN: 1521-40955267.
Stroka, S.; Haussmann, N.; Clemens, M.
Efficient Assessment of High-Resolution Low-Frequency Magnetic Field Exposure Scenarios Using Reduced Order Models
15th Scientific Computing in Electrical Engineering (SCEE 2024)
Darmstadt, Germany
November 20235266.
Alameddine, Jean-Marco; Albrecht, Johannes; Dembinski, Hans; Gutjahr, Pascal; Kampert, Karl-Heinz; Rhode, Wolfgang; Sackel, Maximilian; Sandrock, Alexander; Soedingrekso, Jan
Improvements in charged lepton and photon propagation for the software PROPOSAL
November 20235265.
[german] Grandrath, Rebecca
Videoschnitt für Einsteiger:innen
Unterricht Biologie - Das Schülerarbeitsheft, 51 :32-36
November 20235264.
[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: 0025-58665263.
He, Siyang; Schog, Simon; Chen, Ying; Ji, Yuxin; Panitz, Sinan; Richtering, Walter; Göstl, Robert
Photoinduced Mechanical Cloaking of Diarylethene-Crosslinked Microgels
Advanced Materials, 35 (41) :2305845
Oktober 2023
ISSN: 1521-40955262.
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: 0039-78815261.
Abdul Halim, A.; others
Demonstrating Agreement between Radio and Fluorescence Measurements of the Depth of Maximum of Extensive Air Showers at the Pierre Auger Observatory
Oktober 20235260.
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: 2008-8752