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
5037.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
20235036.
Bolten, Matthias; Ekström, S.-E.; Furci, I.; Serra-Capizzano, S.
A note on the spectral analysis of matrix sequences via GLT momentary symbols: from all-at-once solution of parabolic problems to distributed fractional order matrices
Electron. Trans. Numer. Anal., 58 :136--163
20235035.
Edeko, Nikolai; Jamneshan, Asgar; Kreidler, Henrik
A Peter-Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions
20235034.
Bauß, Julius; Parragh, Sophie N.; Stiglmayr, Michael
Adaptive Improvements of Multi-objective Branch and Bound
20235033.
Carrillo, Jose Antonio; Totzeck, Claudia; Vaes, Urbain
Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints
, Modeling and Simulation for Collective Dynamics,Lecture Notes Series, Institute for Mathematical Sciences, NUS Band 40
20235032.
Könen, David; Stiglmayr, Michael
An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems
20235031.
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
20235030.
Frommer, Andreas; Schweitzer, Marcel
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
20235029.
[german] Zeller, Diana
App des Monats: Monatliche Steckbriefe für einen abwechslungsreichen Einsatz digitaler Medien im Chemieunterricht
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
20235028.
[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: 037971125027.
Dehne, Tobias
Assessment of horizontal flame spread with solid pyrolysis modelling in the Fire Dynamics Simulator
Bergische Universität Wuppertal
20235026.
Schäfers, Torben; Teng, Long
Asymmetry in stochastic volatility models with threshold and time-dependent correlation
Studies in Nonlinear Dynamics & Econometrics, 27 (2) :131–146
2023
Herausgeber: De Gruyter5025.
Hastir, Anthony; Hosfeld, René; Schwenninger, Felix L.; Wierzba, Alexander A.
BIBO stability for funnel control: semilinear internal dynamics with unbounded input and output operators
20235024.
Gorski, Jochen; Klamroth, Kathrin; Sudhoff, Julia
Biobjective optimization problems on matroids with binary costs
Optimization, 72 (7) :1931-1960
2023
Herausgeber: Taylor & Francis5023.
[german] Grandrath, Rebecca
CapCut – intuitive und vollständige Videobearbeitung
:1-2
2023
Herausgeber: Friedrich-Schiller-Universität Jena, Institut für Anorganische und Analytische Chemie5022.
Hosfeld, René; Jacob, Birgit; Schwenninger, Felix L.
Characterization of Orlicz admissibility
Semigroup Forum, 106 :633–661
20235021.
Bohrmann-Linde, Claudia; Siehr, Ilona
Chemie Qualifikationsphase Nordrhein-Westfalen
Herausgeber: C.C.Buchner Verlag, Bamberg
2023ISBN: 978-3-661-06002-6
5020.
Albrecht, Johannes; others
Comparison and efficiency of GPU accelerated optical light propagation in CORSIKA\textasciitilde{}8
PoS, ICRC2023 :417
20235019.
Ehrhardt, Matthias
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
März 2023
Herausgeber: Academic Press5018.
Petrov, Pavel; Matskovskiy, Andrey; Zakharenko, Alena; Zavorokhin, German; Dosso, Stan
Generalized Pekeris-Buldyrev waveguide and its properties
submitted to J. Acoust. Soc. Am.
Juni 20235017.
Heldmann, Fabian; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
arXiv preprint arXiv:2302.01810
Juni 20235016.
Bartel, A.; Günther, M.; Jacob, Birgit; Reis, T.
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numer. Math., 155 (1-2) :1-34
20235015.
Vinod, Vivin; Maity, Sayan; Zaspel, Peter; Kleinekathöfer, Ulrich
Multifidelity Machine Learning for Molecular Excitation Energies
J. Chem. Theory Comput., 19 (21) :7658-7670
20235014.
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
Preprint
20235013.
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
Preprint
2023
