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
5105.
Haussmann, Norman; Stroka, Steven; Schmuelling, Benedikt; Clemens, Markus
GPU-accelerated body-internal electric field exposure simulation using low-frequency magnetic field sampling points
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 42 (5) :982-992
01 2023
Herausgeber: Emerald Publishing Limited
ISSN: 0332-16495104.
Stroka, S.; Haussmann, N.; Zang, M.; Schmuelling, B.; Clemens, M.
GPU-Based Near Real-Time Estimation of the Human Body Penetrating Low-Frequency Magnetic Fields Using Free-Space Field Measurements
IEEE Transactions on Magnetics, 59 (5) :1-4
20235103.
[german] Gökkus, Yasemin; Kremer, Richard; Zeller, Diana; Bohrmann-Linde, Claudia
H5P angereicherte Videos für den Chemieunterricht und die Lehrkräfteausbildung
In Bohrmann-Linde, C.; Gökkuş, Y.; Kremer, R.; Zeller, D., Editor, Band Netzwerk Digitalisierter Chemieunterricht. Sammelband NeDiChe-Treff 2021
Seite 9-18
Herausgeber: Chemiedidaktik. Bergische Universität Wuppertal
2023
9-185102.
Kienitz, Jörg
Hedging in the age of statistical learning
Wilmott, 2023 (126) :94–102
2023
Herausgeber: Wilmott Magazine5101.
Morejon, Leonel; Kampert, Karl-Heinz
Implementing hadronic interactions in CRPropa to study bursting sources of UHECRs
PoS, ICRC2023 :285
20235100.
5099.
Jacob, Birgit; Zwart, Hans
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain: An Introduction
20235098.
Schweitzer, Marcel
Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Linear Algebra Appl., 656 :247-276
20235097.
Schweitzer, Marcel
Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Linear Algebra Appl., 656 :247-276
2023
Herausgeber: Elsevier5096.
Kiendler-Scharr, Astrid; Becker, Karl-Heinz; Doussin, Jean-François; Fuchs, Hendrik; Seakins, Paul; Wenger, John; Wiesen, Peter
Introduction to Atmospheric Simulation Chambers and Their Applications
In Doussin, Jean-François and Fuchs, Hendrik and Kiendler-Scharr, Astrid and Seakins, Paul and Wenger, John, Editor, A Practical Guide to Atmospheric Simulation Chambers
Seite 1—72
Herausgeber: Springer International Publishing, Cham
2023
1—72ISBN: 978-3-031-22276-4 978-3-031-22277-1
5095.
[en] Lauer, Patrick; Arnold, Lukas; Brännström, Fabian
Inverse modelling of pyrolization kinetics with ensemble learning methods
Fire Safety Journal
Januar 2023
ISSN: 037971125094.
Lars, Thun
Investigation of time constraints for quality prediction in arc welding using deep learning
20235093.
Abdul Halim, Adila; others
Investigations of a Novel Energy Estimator using Deep Learning for the Surface Detector of the Pierre Auger Observatory
PoS, ICRC2023 :275
20235092.
Albi, Giacomo; Ferrarese, Federica; Totzeck, Claudia
Kinetic based optimization enhanced by genetic dynamics
20235091.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Kompetenzförderung durch Erklärvideos in einem Selbstlernbuch zum Einstieg in die Organische Chemie
MNU-Journal, 01.2023 :48-54
2023
ISSN: 0025-58665090.
[german] Zeller, Diana; Bohrmann-Linde, Claudia
Kritischer Umgang mit Videos im naturwissenschaftlichen Unterricht (KriViNat)
In Wilke, T.; Rubner, I., Editor, Band DiCE-Tagung 2023 - Digitalisation in Chemistry Education
Herausgeber: Friedrich-Schiller-Universität Jena, Institut für Anorganische und Analytische Chemie, Jena
20235089.
Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
SIAM J. Sci. Comput. :S223-S253
20235088.
Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
SIAM J. Matrix Anal. Appl., 44 (2) :693-717
20235087.
Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
SIAM J. Matrix Anal. Appl., 44 (2) :693-717
20235086.
[german] Tausch, Michael W.
Licht und Farbe – ein Muss für den Chemieunterricht
CHEMKON, 30
20235085.
Gesell, Hendrik; Janoske, Uwe
Magnetohydrodynamic Analysis of Load Shifting in Hall-Héroult Cells
Journal of Sustainable Metallurgy :1--9
2023
Herausgeber: Springer International Publishing Cham5084.
Matyokubov, Kh Sh; Ehrhardt, Matthias
Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
Physics Letters, Section A, 479 :128928
2023
Herausgeber: North-Holland5083.
Matyokubov, Kh Sh; Ehrhardt, Matthias
Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
Physics Letters, Section A, 479 :128928
2023
Herausgeber: North-Holland5082.
Ehrhardt, Matthias
Mathematical Analysis and a Nonstandard Scheme for a Model of the Immune Response against COVID-19
20235081.
Measurement of $t$-channel production of single top quarks and antiquarks in $pp$ collisions at 13 TeV using the full ATLAS Run 2 dataset
2023