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
4541.
Tovar, Carmen M.; Haack, Alexander; Barnes, Ian; Bejan, Iustinian Gabriel; Wiesen, Peter
Experimental and theoretical study of the reactivity of a series of epoxides with chlorine atoms at 298 K
Physical Chemistry Chemical Physics, 23 (9) :5176-5186
20214540.
Grandrath, Rebecca; Bohrmann-Linde, Claudia
Experimentalkurs zu Biologischen Brennstoffzellen. Begleitendes E-Book für die Sekundarstufe II [Schülerversion]
20214539.
Grandrath, Rebecca; Bohrmann-Linde, Claudia
Experimentalkurs zu Biologischen Brennstoffzellen.Begleitendes E-Book für die Sekundarstufe II [Lehrerversion]
20214538.
Explicit high order one-step methods for decoupled forward backward stochastic differential equations
Adv. Appl. Math. Mech, 13 :1293--1317
20214537.
Aab, Alexander; others
Extraction of the muon signals recorded with the surface detector of the Pierre Auger Observatory using recurrent neural networks
JINST, 16 (07) :P07016
20214536.
Ferrari, Paola; Garoni, Carlo; Serra-Capizzano, Stefano
Fast parallel solver for the space-time IgA-DG discretization of the diffusion equation
J. Sci. Comput., 89 (1) :Paper No. 20, 21
20214535.
Ferrari, Paola; Garoni, Carlo; Serra-Capizzano, Stefano
Fast parallel solver for the space-time IgA-DG discretization of the diffusion equation
J. Sci. Comput., 89 (1) :Paper No. 20, 21
20214534.
[german] Bohrmann-Linde, Claudia; Meuter, Nico; Kremer, Richard; Pereira Vaz, Nuno; Venzlaff, Julian
Forschung trifft Schule - Chemie-Labothek als innovatives, vernetzendes Format
Lehrkräftebildung neu gedacht
Seite 108-112
Herausgeber: Marcus Kubsch, Stefan Sorge, Julia Arnold, Nicole Graulich, Waxmann, Münster
2021
108-112ISBN: 978-3-8309-4349-5
4533.
Grira, A.; Kalalian, C.; Illmann, J.N.; Patroescu-Klotz, I.; El Dib, G.; Coddeville, P.; Canosa, A.; Coeur, C.; Wiesen, P.; Roth, E.; Chakir, A.; Tomas, A.
Gas-phase ozonolysis of trans-2-hexenal: Kinetics, products, mechanism and SOA formation
Atmospheric Environment, 253 :118344
Mai 2021
ISSN: 135223104532.
Illmann, Jan Niklas; Patroescu-Klotz, Iulia; Wiesen, Peter
Gas-phase reactivity of acyclic α,β-unsaturated carbonyls towards ozone
Physical Chemistry Chemical Physics, 23 (5) :3455--3466
2021
ISSN: 1463-9076, 1463-90844531.
Wandelt, Mich{\`e}le; Günther, Michael; Muniz, Michelle
Geometric integration on Lie groups using the Cayley transform with focus on lattice QCD
Journal of Computational and Applied Mathematics, 387 :112495
2021
Herausgeber: North-Holland4530.
Backhaus, Jan; Bolten, Matthias; Tanil Doganay, Onur; Ehrhardt, Matthias; Engel, Benedikt; Frey, Christian; Gottschalk, Hanno; Günther, Michael; Hahn, Camilla; Jäschke, Jens; others
GivEn - Shape optimization for gas turbines in volatile energy networks
Mathematical Modeling, Simulation and Optimization for Power Engineering and Management :71–106
2021
Herausgeber: Springer Cham4529.
Backhaus, J.; Bolten, Matthias; Doganay, O. T.; Ehrhardt, M.; Engel, B.; Frey, Ch.; Gottschalk, H.; Günther, M.; Hahn, C.; Jäschke, J.; Jaksch, P.; Klamroth, K.; Liefke, A.; Luft, D.; Mäde, L.; Marciniak, V.; Reese, M.; Schultes, J.; Schulz, V.
GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks
In S. Göttlich and M. Herty and A. Milde, Editor, Mathematical Modeling, Simulation and Optimization for Power Engineering and ManagementBand34ausMathematics in Industry
In S. Göttlich and M. Herty and A. Milde, Editor
Herausgeber: Springer, Cham
20214528.
Backhaus, J.; Bolten, M.; Doganay, O. T.; Ehrhardt, M.; Engel, B.; Frey, Ch.; Gottschalk, H.; Günther, M.; Hahn, C.; Jäschke, J.; Jaksch, P.; Klamroth, K.; Liefke, A.; Luft, D.; Mäde, L.; Marciniak, V.; Reese, M.; Schultes, J.; Schulz, V.
GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks
In S. Göttlich and M. Herty and A. Milde, Editor, Mathematical Modeling, Simulation and Optimization for Power Engineering and ManagementBand34ausMathematics in Industry
In S. Göttlich and M. Herty and A. Milde, Editor
Herausgeber: Springer, Cham
20214527.
Backhaus, Jan; Bolten, Matthias; Tanil Doganay, Onur; Ehrhardt, Matthias; Engel, Benedikt; Frey, Christian; Gottschalk, Hanno; Günther, Michael; Hahn, Camilla; Jäschke, Jens; others
GivEn - Shape optimization for gas turbines in volatile energy networks
Mathematical Modeling, Simulation and Optimization for Power Engineering and Management :71–106
2021
Herausgeber: Springer Cham4526.
Backhaus, Jan; Bolten, Matthias; Tanil Doganay, Onur; Ehrhardt, Matthias; Engel, Benedikt; Frey, Christian; Gottschalk, Hanno; Günther, Michael; Hahn, Camilla; Jäschke, Jens; others
GivEn - Shape optimization for gas turbines in volatile energy networks
Mathematical Modeling, Simulation and Optimization for Power Engineering and Management :71–106
2021
Herausgeber: Springer Cham4525.
Backhaus, J.; Bolten, M.; Doganay, O.T.; Ehrhardt, M.; Engel, B.; Frey, C.; Gottschalk, H.; Günther, M.; Hahn, C.; Jäschcke, J.; Jaksch, P.; Klamroth, K.; Liefke, A.; Luft, D.; Mäde, L.; Marciniak, V.; Reese, M.; Schultes, J.; Schulz, V.; Schmitz, S.; Steiner, J.; Stiglmayr, M.
GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks
In S. Goettlich, M. Herty and A. Milde, Editor, Mathematical MSO for Power Engineering and Management aus Mathematics in Industry
Herausgeber: Springer Berlin/Heidelberg
20214524.
Backhaus, J.; Bolten, M.; Doganay, O. T.; Ehrhardt, M.; Engel, B.; Frey, Ch.; Gottschalk, H.; Günther, M.; Hahn, C.; Jäschke, J.; Jaksch, P.; Klamroth, K.; Liefke, A.; Luft, D.; Mäde, L.; Marciniak, V.; Reese, M.; Schultes, J.; Schulz, V.
GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks
In S. Göttlich and M. Herty and A. Milde, Editor, Mathematical Modeling, Simulation and Optimization for Power Engineering and ManagementBand34ausMathematics in Industry
In S. Göttlich and M. Herty and A. Milde, Editor
Herausgeber: Springer, Cham
20214523.
Backhaus, Jan; Bolten, Matthias; Tanil Doganay, Onur; Ehrhardt, Matthias; Engel, Benedikt; Frey, Christian; Gottschalk, Hanno; Günther, Michael; Hahn, Camilla; Jäschke, Jens; others
GivEn—Shape optimization for gas turbines in volatile energy networks
Mathematical Modeling, Simulation and Optimization for Power Engineering and Management :71--106
2021
Herausgeber: Springer International Publishing4522.
Reininghaus, Maximilian; others
GPU Accelerated optical light propagation in CORSIKA 8
PoS, ICRC2021 :705
20214521.
Kroflič, Ana; Anders, Janine; Drventić, Ivana; Mettke, Peter; Böge, Olaf; Mutzel, Anke; Kleffmann, Jörg; Herrmann, Hartmut
Guaiacol Nitration in a Simulated Atmospheric Aerosol with an Emphasis on Atmospheric Nitrophenol Formation Mechanisms
ACS Earth and Space Chemistry, 5 (5) :1083--1093
Mai 2021
ISSN: 2472-3452, 2472-34524520.
Alves, Antonio Augusto Alves; others
Hadron cascades in CORSIKA 8
PoS, ICRC2021 :474
20214519.
Teng, Long; Zhao, Weidong
High-order combined multi-step scheme for solving forward backward stochastic differential equations
Journal of Scientific Computing, 87 (3) :1–25
2021
Herausgeber: Springer New York4518.
Teng, Long; Zhao, Weidong
High-order combined multi-step scheme for solving forward backward stochastic differential equations
JSC, 87 (81)
20214517.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher Strong Order Methods for It$\backslash$\^{} o SDEs on Matrix Lie Groups
arXiv preprint arXiv:2102.04131
2021