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
5260.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Genuine Bernstein–Durrmeyer type operators preserving 1 and $x^j$
Annals of Functional Analysis, 15 (1)
Oktober 2023
Herausgeber: Springer Science and Business Media LLC
ISSN: 2008-87525259.
Rajkovic, Michelle; Benter, Thorsten; Wissdorf, Walter
Molecular Dynamics-Based Modeling of Ion-Neutral Collisions in an Open Ion Trajectory Simulation Framework
Journal of the American Society for Mass Spectrometry, 34 (10) :2156—2165
Oktober 2023
ISSN: 1044-0305, 1879-11235258.
Sánchez-Rodríguez, Antonio R.; Gómez-Álvarez, Elena; Méndez, José M.; Skiba, Ute M.; Jones, Davey L.; Chadwick, Dave R.; Del Campillo, María C.; Fernandes, Raphael Ba.; Kleffmann, Jörg; Barrón, Vidal
Photocatalytic fixation of NOx in soils
Chemosphere, 338 :139576
Oktober 2023
ISSN: 004565355257.
Abdul Halim, A.; others
Radio Measurements of the Depth of Air-Shower Maximum at the Pierre Auger Observatory
Oktober 20235256.
Göstl, Robert
Trendbericht: Makromolekulare Chemie 2023
Nachrichten aus der Chemie, 71 (10) :48--54
September 2023
ISSN: 1868-00545255.
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 20235254.
Meinert, Janning; Morej\'on, Leonel; Sandrock, Alexander; Eichmann, Björn; Kreidelmeyer, Jonas; Kampert, Karl-Heinz
Modified temperature redshift relation and UHECR propagation
September 20235253.
[en] Börger, Kristian; Belt, Alexander; Schultze, Thorsten; Arnold, Lukas
Remote Sensing of the Light-Obscuring Smoke Properties in Real-Scale Fires Using a Photometric Measurement Method
Fire Technology
September 2023
ISSN: 0015-2684, 1572-80995252.
[english] Venzlaff, Julian; Kosumi, Kaltrina; Zeller, Diana; Bohrmann-Linde, Claudia
Education for Sustainable Development and Experiments involving Titanium Dioxide
World Journal of Chemical Education, 11 (3) :80-86
August 20235251.
[english] Brunnert, Rainer; Tausch, Michael W.
Green Chemistry in STEM Education: Light for Basic Concepts
World Journal of Chemical Education, 11 (3) :65-73
August 20235250.
Desai, Prachi; Dasgupta, Anshuman; Sofias, Alexandros Marios; Peña, Quim; Göstl, Robert; Slabu, Ioana; Schwaneberg, Ulrich; Stiehl, Thomas; Wagner, Wolfgang; Jockenhövel, Stefan; Stingl, Julia; Kramann, Rafael; Trautwein, Christian; Brümmendorf, Tim H.; Kiessling, Fabian; Herrmann, Andreas; Lammers, Twan
Transformative Materials for Interfacial Drug Delivery
Advanced Healthcare Materials, 12 (20) :2301062
August 2023
ISSN: 2192-26595249.
Lichtenberg, Nils; Lutz, Valerie; Jessen, Wilhelm; Klein, Andreas; Kurtenbach, Ralf; Villena, Guillermo; Kleffmann, Jörg
TunNOx – Entwicklung eines photokatalytischen Reaktors zur Reduktion von Stickoxiden in Straßentunneln
Immissionsschutz (3) :8
August 2023
ISSN: 1868-77765248.
Haussmann, N.; Stroka, S.; Clemens, M.
Anwendung neuronaler Netze in der Bestimmung der Exposition gegenüber niederfrequenten Magnetfeldern bei induktiven Ladesystemen
URSI e.V. Deutschland 2023 Kleinheubacher Tagung (KHB 2023)
Miltenberg, Germany
Juli 20235247.
Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A numerical study of the impact of variance boundary conditions for the Heston model
IMACM preprint 23/11
Juli 20235246.
Stroka, S.; Haussmann, N.; Clemens, M.
Bewertung niederfrequenter Magnetfeldexpositionen unter Einsatz ordnungsreduzierender Modelle
URSI e.V. Deutschland 2023 Kleinheubacher Tagung (KHB 2023)
Miltenberg, Germany
Juni 20235245.
[german] Venzlaff, Julian; Bohrmann-Linde, Claudia
Photoreformierung – grüner Wasserstoff aus Alkohol, Zucker und Stärke
CHEMKON, 30 (6) :254-259
Juni 20235244.
Petrov, Pavel; Matskovskiy, Andrey; Zakharenko, Alena; Zavorokhin, German; Dosso, Stan
Generalized Pekeris-Buldyrev waveguide and its properties
submitted to J. Acoust. Soc. Am.
Juni 20235243.
Tyshchenko, Andrey; Kozitskiy, Sergey; Kazak, Mikhail; Petrov, Pavel
Modern methods of sound propagation modelling based on the expansion of acoustic fields over normal modes
Acoustical Physics (accepted, to appear in 2023), 69 (5)
Juni 20235242.
Soroking, Mikhail; Petrov, Pavel; Budyansky, Maxim; Fayman, Pavel; Didov, Alexandr; Golov, Alexandr; Morgunov, Yuri
On the effect of horizontal refraction caused by an anticyclonic eddy in the case of long-range sound propagation in the Sea of Japan
J. Marine Sci. Eng. , 11 (9)
Juni 20235241.
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 20235240.
Makarov, Denis; Petrov, Pavel; Uleysky, Mikhail
Random matrix theory for sound propagation in a shallow-water acoustic waveguide with sea bottom roughness
submitted to J. Marine Sci. Eng.
Juni 20235239.
Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry, 2023 (21) :4574-4577
Mai 2023
Herausgeber: RSC5238.
Haussmann, N.; Stroka, S.; Tiemann, M.; David, A.; Schmuelling, B.; Clemens, M.
Vorstellung des MILAS Projektes: Autonome induktiv geladene Elektro-Shuttles im öffentlichen Nahverkehr
5. Wissenschaftsforum Mobilität 2023, „Next Chapter in Mobility“
Duisburg, Germany
Mai 20235237.
Kähne, B.; Clemens, M.
A ROW-Type Method for GPU-Accelerated Large-Scale Finite Element Simulations of Nonlinear Eddy Current Problems
The 13th International Symposium on Electric and Magnetic Fields (EMF 2023)
Marseilles, France
Mai 20235236.
Baptista, Andrea; Gibilisco, Rodrigo G.; Patroescu-Klotz, Iulia; Illmann, Niklas; Wiesen, Peter; Blanco, María B.; Teruel, Mariano A.
Product study of the reactions of γ-caprolactone and γ-heptalactone initiated by OH radicals at 298 K and atmospheric pressure: Formation of acyl peroxynitrates (APN).
Chemosphere, 323 :138156
Mai 2023
ISSN: 00456535