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
- 2019
4016.
Ehrhardt, Matthias
Transparent nonlinear networks
Physical Review E, 100 (3) :032204
2019
Herausgeber: American Physical Society4015.
Ehrhardt, Matthias
Transparent nonlinear networks
Physical Review E, 100 (3) :032204
2019
Herausgeber: American Physical Society4014.
Ehrhardt, Matthias
Transparent quantum graphs
Physics Letters A, 383 (20) :2382–2388
2019
Herausgeber: North-Holland4013.
Ehrhardt, Matthias
Transparent quantum graphs
Physics Letters A, 383 (20) :2382--2388
2019
Herausgeber: North-Holland4012.
Ehrhardt, Matthias
Transparent quantum graphs
Physics Letters A, 383 (20) :2382–2388
2019
Herausgeber: North-Holland4011.
Pulch, Roland; Putek, Piotr; Maten, E. Jan W.; Schoenmaker, Wim
Uncertainty quantification: Introduction and implementations
In ter Maten, E. Jan W. and Brachtendorf, Hans-Georg and Pulch, Roland and Schoenmaker, Wim and De Gersem, Herbert, Editor aus Mathematics in Industry
Seite 197–221
Herausgeber: Springer Cham
2019
197–2214010.
Netzel, Katrin
Untersuchung von Lignin aus Papierabwässern mittels Py-GCxGC/TOF-MS und Ofenpyrolyse
20194009.
Karg, Patrick
Untersuchung zu Imid-Amid-Gleichgewichten bei Hydroxycarbonsäure-Amiden
20194008.
Rapp, Ulrike
Untersuchung zur Quantifizierung von Mikroplastik mittels offline-Py-GCxGC-MS
20194007.
Otte, Adrian
Untersuchungen von Holzproben aus unterschiedlichen Holzschichten
20194006.
Goss, Jonas
Untersuchungen von Totholz nicht-heimischer Arten in Arnsberg sowie Totholz von Mammutbäumen in Kaldenkirchen
20194005.
Schlösser, Leonie Gwindy
Untersuchungen zur Gewässersanierung
20194004.
[german] Kremer, Richard; Tausch, Michael W.
Unterwegs zur künstlichen Photosynthese - Photokatalytische Reduktionen in Modellexperimenten
Chemie und Schule, 34 (3) :15-29
20194003.
Eichfelder, Gabriele; Klamroth, Kathrin; Niebling, Julia
Using a {B}&{B} algorithm from multiobjective optimization to solve constrained optimization problems
AIP Conference Proceedings 2070
Herausgeber: AIP Publishing
20194002.
Bolten, M.; Hahn, C.
Using composite finite elements for shape optimization with a stochastic objective functional
In I. Farag{\'o} and F. Izs{\'a}k and P. L. Simon, Editor, Progress in Industrial Mathematics at ECMI 2018Band30ausMathematics in Industry, Seite 515--520
In I. Farag{\'o} and F. Izs{\'a}k and P. L. Simon, Editor
Herausgeber: Springer, Cham
20194001.
Bolten, Matthias; Hahn, C.
Using composite finite elements for shape optimization with a stochastic objective functional
In I. Farago and F. Izsak and P. L. Simon, Editor, Progress in Industrial Mathematics at ECMI 2018Band30ausMathematics in Industry, Seite 515-520
In I. Farago and F. Izsak and P. L. Simon, Editor
Herausgeber: Springer, Cham
20194000.
Bolten, M.; Hahn, C.
Using composite finite elements for shape optimization with a stochastic objective functional
In I. Farago and F. Izsak and P. L. Simon, Editor, Progress in Industrial Mathematics at ECMI 2018Band30ausMathematics in Industry, Seite 515-520
In I. Farago and F. Izsak and P. L. Simon, Editor
Herausgeber: Springer, Cham
20193999.
Janssen, Rick; Gillon, Renaud; Wieers, Aarnout; Deleu, Frederik; Guegnaud, Hervé; Reynier, Pascal; Schoenmaker, Wim; Maten, E. Jan W.
Validation of simulation results on coupled problems
In ter Maten, E. Jan W. and Brachtendorf, Hans-Georg and Pulch, Roland and Schoenmaker, Wim and De Gersem, Herbert, Editor aus Mathematics in Industry
Seite 517–563
Herausgeber: Springer Cham
2019
517–5633998.
Adam, Ahmad Y.; Yachmenev, Andrey; Yurchenko, Sergey N.; Jensen, Per
Variationally Computed IR Line List for the Methyl Radical CH\(_{3}\)
The Journal of Physical Chemistry A, 123 (22) :4755-4763
2019
Herausgeber: American Chemical Society3997.
Adam, Ahmad Y.; Yachmenev, Andrey; Yurchenko, Sergey N.; Jensen, Per
Variationally Computed IR Line List for the Methyl Radical CH\(_{3}\)
The Journal of Physical Chemistry A, 123 (22) :4755-4763
2019
Herausgeber: American Chemical Society3996.
Adam, Ahmad Y.; Yachmenev, Andrey; Yurchenko, Sergey N.; Jensen, Per
Variationally Computed IR Line List for the Methyl Radical CH3
The Journal of Physical Chemistry A, 123 (22) :4755-4763
2019
Herausgeber: American Chemical Society3995.
Weichold, Cathrerine; Behler, Ansgar; Melchior, David; Busch, Stefan; Kling, Hans-Willi; Lange, Karsten; Jakob, Bernd
Verfahren zur Herstellung einer oberflächenaktiven Mischung umfassend Kondensationsprodukte von alpha-Hydroxycarbonsäuren mit 1,2-Alkandiolen
20193994.
Weichold, Cathrerine; Behler, Ansgar; Melchior, David; Busch, Stefan; Kling, Hans-Willi; Lange, Karsten; Jakob, Bernd
Verwendung von 1,2-Alkandiolen als Schaumverbesserer für Citronensäureestertenside umfassend ethoxylierte Alkohole
20193993.
Ankirchner, Stefan; Kruse, Thomas; Urusov, Mikhail
Wasserstein convergence rates for random bit approximations of continuous Markov processes
Journal of Mathematical Analysis and Applications, 493 (2) :124543
2019
Herausgeber: Academic Press3992.
Ankirchner, Stefan; Kruse, Thomas; Urusov, Mikhail
Wasserstein convergence rates for random bit approximations of continuous Markov processes
Journal of Mathematical Analysis and Applications, 493 (2) :124543
2019
Herausgeber: Academic Press