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
4630.
Bauß, Julius; Parragh, Sophie N.; Stiglmayr, Michael
Adaptive Improvements of Multi-objective Branch and Bound
20234629.
Metzmacher, Andreas; Burgmann, Sebastian; Janoske, Uwe
$\mu$PIV measurements of the phase-averaged velocity distribution within wavy films
Experiments in Fluids, 64 (4) :81
2023
Herausgeber: Springer Berlin Heidelberg Berlin/Heidelberg4628.
Pereselkov, Sergey; Kuz’kin, Venedikt; Ehrhardt, Matthias; Tkachenko, Sergey; Rybyanets, Pavel; Ladykin, Nikolay
3D Modeling of sound field hologram of moving source in presence of internal waves causing horizontal refraction.
Preprint IMACM
20234627.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A characteristic boundary condition for multispeed lattice Boltzmann methods
Communications in Computational Physics, 33 (1) :101–117
2023
Herausgeber: Global Science Press4626.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A combined method for stability analysis of linear time invariant control systems based on Hermite-Fujiwara matrix and Cholesky decomposition
The Canadian Journal of Chemical Engineering, 101 (12) :7043–7052
2023
Herausgeber: John Wiley & Sons4625.
Zargaran, Amin; Dolshanskiy, Wladislaw; Stepanyuk, Alexey; Pauer, Werner; Janoske, Uwe
A hybrid approach based on Lagrangian particles and immersed-boundary method to characterize rotor--stator mixing systems for high viscous mixtures
Chemical Engineering Journal, 473 :145062
2023
Herausgeber: Elsevier4624.
Fatoorehchi, Hooman; Zarghami, Reza; 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
20234623.
Fatoorehchi, Hooman; Zarghami, Reza; 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
20234622.
Fatoorehchi, Hooman; Zarghami, Reza; 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
Preprint IMACM
20234621.
Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
SIAM J. Matrix Anal. Appl., 44 (3) :1073-1095
20234620.
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
20234619.
Edeko, Nikolai; Jamneshan, Asgar; Kreidler, Henrik
A Peter-Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions
20234618.
Kordon, Florian; Stiglmayr, Michael; Maier, Andreas; Vicario, Celia Mart{\'{\i}}n; Pertlwieser, Tobias; Kunze, Holger
A principled representation of elongated structures using heatmaps
Scientific Reports, 13 (15253)
September 20234617.
Könen, David; Stiglmayr, Michael
An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems
20234616.
Halim, A. Abdul; others
Constraining the sources of ultra-high-energy cosmic rays across and above the ankle with the spectrum and composition data measured at the Pierre Auger Observatory
JCAP, 05 :024
20234615.
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
20234614.
Frommer, Andreas; Schweitzer, Marcel
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
20234613.
[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
20234612.
[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: 037971124611.
Dehne, Tobias
Assessment of horizontal flame spread with solid pyrolysis modelling in the Fire Dynamics Simulator
Bergische Universität Wuppertal
20234610.
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 Gruyter4609.
Hastir, Anthony; Hosfeld, René; Schwenninger, Felix L.; Wierzba, Alexander A.
BIBO stability for funnel control: semilinear internal dynamics with unbounded input and output operators
20234608.
Gorski, Jochen; Klamroth, Kathrin; Sudhoff, Julia
Biobjective optimization problems on matroids with binary costs
Optimization, 72 (7) :1931-1960
2023
Herausgeber: Taylor & Francis4607.
[german] Grandrath, Rebecca
CapCut – intuitive und vollständige Videobearbeitung
:1-2
2023
Herausgeber: Friedrich-Schiller-Universität Jena, Institut für Anorganische und Analytische Chemie4606.
Hosfeld, René; Jacob, Birgit; Schwenninger, Felix L.
Characterization of Orlicz admissibility
Semigroup Forum, 106 :633–661
2023