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
5089.
[en] Hehnen, Tristan; Arnold, Lukas
PMMA pyrolysis simulation – from micro- to real-scale
Fire Safety Journal, 141
Dezember 2023
ISSN: 037971125088.
Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Seserman, Andra
Poisson approximation to the binomial distribution: extensions to the convergence of positive operators
Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117
20235087.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-{H}amiltonian Systems Modelling in Electrical Engineering
arXiv preprint arXiv:2301.02024
20235086.
5085.
Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
20235084.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian Systems Modelling in Electrical Engineering
arXiv preprint arXiv:2301.02024
20235083.
Bahja, Ali Rida
Pose Estimation using Deep Learning and Systematic Dataset Generation for Industrial Manufacturing
20235082.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Positive linear operators preserving certain monomials on [0, ∞)
Dolomites Research Notes on Approximation, 16 :1-9
2023
ISSN: 2035-68035081.
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: 004565355080.
Morejon, Leonel; Condorelli, Antonio; Biteau, Jonathan; Kampert, Karl-Heinz
Propagation of Ultra High-Energy Cosmic Rays in light of the latest EBL constraints
PoS, ICRC2023 :283
20235079.
Ahmed, Mustafa
Quantifizierung der Genauigkeit der Co-Simulation Scalar Potential Finite Difference Methode bei der Expositionsbestimmung von Menschen durch die vernachlässigte Rückwirkung der körperinduzierten Ströme auf das magnetische Quellfeld
20235078.
Abdul Halim, Adila; others
Radio Interferometry applied to air showers recorded by the Auger Engineering Radio Array
PoS, ICRC2023 :380
20235077.
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 20235076.
Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
SIAM J. Matrix Anal. Appl., 44 :1073-1095
20235075.
Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
SIAM J. Matrix Anal. Appl., 44 (3) :1073-1095
20235074.
Göhring, Timo
Ratio of Electron and Muon Pair Production at High Invariant Mass in Association with a b-jet
20235073.
[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, 1572-80995072.
Asatryan, Hayk; Gaul, Daniela; Gottschalk, Hanno; Klamroth, Kathrin; Stiglmayr, Michael
Ridepooling and public bus services: A comparative case-study
Submitted to Transportation
2023
Herausgeber: arXiv5071.
Wintermayr, Jens; Kerner, Joachim; Täufer, Matthias
Robustness of Flat Bands on the Perturbed Kagome and the Perturbed Super-Kagome Lattice
Annales Henri Poincare :19
Dezember 20235070.
Thielmann, Oliver
Search for flavour-changing neutral current interactions in the top-quark Higgs boson sector in multi-lepton final states with the ATLAS detector at the LHC at $\sqrt{s} = 13\,\text{TeV}$
Bergische Universität Wuppertal
20235069.
Aad, Georges; others
Search for pair-produced scalar and vector leptoquarks decaying into third-generation quarks and first- or second-generation leptons in pp collisions with the ATLAS detector
JHEP, 2306 :188
20235068.
Aad, Georges; others
Search for pair-produced vector-like top and bottom partners in events with large missing transverse momentum in pp collisions with the ATLAS detector
Eur. Phys. J. C, 83 (8) :719
20235067.
Abreu, P.; others
Search for photons above 10^{19} eV with the surface detector of the Pierre Auger Observatory
JCAP, 05 :021
20235066.
Abdul Halim, Adila; others
Search for primary photons at tens of PeV with the Pierre Auger Observatory
PoS, ICRC2023 :238
20235065.
Abdul Halim, Adila; others
Search for Ultra-high-energy Photons from Gravitational Wave Sources with the Pierre Auger Observatory
Astrophys. J., 952 (1) :91
2023
