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
5041.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-{H}amiltonian Systems Modelling in Electrical Engineering
arXiv preprint arXiv:2301.02024
20235040.
5039.
Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
20235038.
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian Systems Modelling in Electrical Engineering
arXiv preprint arXiv:2301.02024
20235037.
Bahja, Ali Rida
Pose Estimation using Deep Learning and Systematic Dataset Generation for Industrial Manufacturing
20235036.
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: 2035-68035035.
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: 004565355034.
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
20235033.
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
20235032.
Abdul Halim, Adila; others
Radio Interferometry applied to air showers recorded by the Auger Engineering Radio Array
PoS, ICRC2023 :380
20235031.
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 20235030.
Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
SIAM J. Matrix Anal. Appl., 44 :1073-1095
20235029.
Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
SIAM J. Matrix Anal. Appl., 44 (3) :1073-1095
20235028.
Göhring, Timo
Ratio of Electron and Muon Pair Production at High Invariant Mass in Association with a b-jet
20235027.
[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, 1572-80995026.
Asatryan, Hayk; Gaul, Daniela; Gottschalk, Hanno; Klamroth, Kathrin; Stiglmayr, Michael
Ridepooling and public bus services: A comparative case-study
Submitted to Transportation
2023
Herausgeber: arXiv5025.
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 20235024.
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
20235023.
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
20235022.
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
20235021.
Abreu, P.; others
Search for photons above 10^{19} eV with the surface detector of the Pierre Auger Observatory
JCAP, 05 :021
20235020.
Abdul Halim, Adila; others
Search for primary photons at tens of PeV with the Pierre Auger Observatory
PoS, ICRC2023 :238
20235019.
Abdul Halim, Adila; others
Search for Ultra-high-energy Photons from Gravitational Wave Sources with the Pierre Auger Observatory
Astrophys. J., 952 (1) :91
20235018.
Schweitzer, Marcel
Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds
SIAM J. Matrix Anal. Appl., 44 (3) :1321-1348
20235017.
Schweitzer, Marcel
Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds
SIAM J. Matrix Anal. Appl., 44 (3) :1321-1348
2023
