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
- 2021
4591.
Doganay, Onur Tanil
Biobjective shape optimization algorithms enhanced by derivative information
Dissertation
Dissertation
Bergische Universität Wuppertal
20214590.
Illmann, Niklas; Patroescu-Klotz, Iulia; Wiesen, Peter
Biomass burning plume chemistry: OH-radical-initiated oxidation of 3-penten-2-one and its main oxidation product 2-hydroxypropanal
Atmospheric Chemistry and Physics, 21 (24) :18557--18572
Dezember 2021
ISSN: 1680-73244589.
Venzlaff, Julian; Kiesling, Elisabeth; Bohrmann-Linde, Claudia
BNE und Chemieunterricht - BNE als roter Faden durch die Schulchemie und Beispiel einer Lerneinheit zur Klimawirksamkeit von Kohlenstoffdioxid
CHEMKON
20214588.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models
Finance and Stochastics, 25 (4) :757--810
2021
Herausgeber: Springer Berlin Heidelberg4587.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models
Finance and Stochastics, 25 (4) :757–810
2021
Herausgeber: Springer Verlag4586.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models
Finance and Stochastics, 25 (4) :757--810
2021
Herausgeber: Springer Berlin Heidelberg4585.
Bohrmann-Linde, Claudia; Siehr, Ilona
Chemie Baden-Württemberg Chemie Gesamtband 11-12
Herausgeber: C.C.Buchner Verlag, Bamberg
2021ISBN: 978-3-661-06011-8
4584.
Harbrecht, Helumt; Jakeman, John D; Zaspel, Peter
Cholesky-Based Experimental Design for Gaussian Process and Kernel-Based Emulation and Calibration
CiCP, 29 (4) :1152-1185
20214583.
Gaul, Daniela; Schmidt, Daniel R.
Chvátal-Gomory cuts for the Steiner tree problem
Discrete Applied Mathematics, 291 :188-200
2021
ISSN: 0166-218X4582.
Schimp, Michael; others
Combined Search for UHE Neutrinos from Binary Black Hole Mergers with the Pierre Auger Observatory
PoS, ICRC2021 :968
20214581.
Kandolf, Peter; Koskela, Antti; Relton, Samuel D.; Schweitzer, Marcel
Computing low-rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods
Numer. Linear Algebra Appl., 28 (6) :e2401, 31
2021
ISSN: 1070-53254580.
Kandolf, Peter; Koskela, Antti; Relton, Samuel D.; Schweitzer, Marcel
Computing low-rank approximations of the Frechet derivative of a matrix function using Krylov subspace methods
Numer. Linear Algebra Appl., 28 (6) :e2401, 31
2021
ISSN: 1070-53254579.
Kandolf, Peter; Koskela, Antti; Relton, Samuel D.; Schweitzer, Marcel
Computing low-rank approximations of the Frechet derivative of a matrix function using Krylov subspace methods
Numer. Linear Algebra Appl., 28 (6) :e2401, 31
2021
ISSN: 1070-53254578.
Gottowik, Marvin; Schl\"uter, Felix; Huege, Tim; Rautenberg, Julian
CoREAS simulations of inclined air showers predict refractive displacement of the radio-emission footprint
PoS, ICRC2021 :277
20214577.
Jacob, Birgit; Schwenninger, Felix; Vorberg, Lukas
Correction to: Remarks on input-to-state stability of collocated systems with saturated feedback
Math. Control Signals Systems, 33 :195
20214576.
Bannenberg, MWFM; Ciccazzo, Angelo; Günther, Michael
Coupling of model order reduction and multirate techniques for coupled dynamical systems
Applied Mathematics Letters, 112 :106780
2021
Herausgeber: Pergamon4575.
Bannenberg, MWFM; Ciccazzo, Angelo; Günther, Michael
Coupling of model order reduction and multirate techniques for coupled dynamical systems
Applied Mathematics Letters, 112 :106780
2021
Herausgeber: Elsevier4574.
Bannenberg, MWFM; Ciccazzo, Angelo; Günther, Michael
Coupling of model order reduction and multirate techniques for coupled dynamical systems
Applied Mathematics Letters, 112 :106780
2021
Herausgeber: Elsevier4573.
Alves Batista, Rafael; others
CRPropa 3.2: a framework for high-energy astroparticle propagation
PoS, ICRC2021 :978
20214572.
Aab, Alexander; others
Deep-learning based reconstruction of the shower maximum $X_{max}$ using the water-Cherenkov detectors of the Pierre Auger Observatory
JINST, 16 (07) :P07019
20214571.
Klosterköther, Anja; Kurtenbach, Ralf; Wiesen, Peter; Kleffmann, Jörg
Determination of the emission indices for NO, NO\(_{2}\), HONO, HCHO, CO, and particles emitted from candles
Indoor Air, 31 (1) :116--127
Januar 2021
ISSN: 0905-6947, 1600-06684570.
[german] Grandrath, Rebecca; Zeller, Diana; Bohrmann-Linde, Claudia
Digitale Lehr- und Lerntools für den Chemieunterricht mithilfe von Powerpoint. Teil 2.
Chemie & Schule, 36 (1) :13-16
Januar 20214569.
Rendon Enriquez, Ibeth N.; Körber, Florian; Palma-Cando, Alex; Scherf, Ullrich; Tausch, Michael W.
Dünne Polymerfilme durch oxydative oder reduktive Elektropolymerisation für eine Anwendung in elektrochromen Fenstern und als Dünnschichtsensoren
Chemie in unserer Zeit
20214568.
Günther, Michael; Bartel, Andreas; Jacob, Birgit; Reis, Timo
Dynamic iteration schemes and port-Hamiltonian formulation in coupled DAE circuit simulation
International Journal of Circuit Theory and Applications, 49 (2) :430--452
20214567.
Günther, Michael; Bartel, Andreas; Jacob, Birgit; Reis, Timo
Dynamic iteration schemes and port-Hamiltonian formulation in coupled differential-algebraic equation circuit simulation
International Journal of Circuit Theory and Applications, 49 (2) :430–452
2021
Herausgeber: John Wiley & Sons
