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
4680.
Bülow, Friedrich; Hahn, Yannik; Meyes, Richard; Meisen, Tobias; others
Transparent and Interpretable State of Health Forecasting of Lithium-Ion Batteries with Deep Learning and Saliency Maps
International Journal of Energy Research, 2023
2023
Herausgeber: Hindawi4679.
[english] Rendon-Enriquez, Ibeth; Palma-Cando, Alex; Körber, Florian; Niebisch, Felix; Forster, Michael; Tausch, Michael W.; Scherf, Ullrich
Thin Polymer Films by Oxidative or Reductive Electropolymerization and Their Application in Electrochromic Windows and Thin-Film Sensors
molecules, 28 (2) :883
Januar 20234678.
Bolten, Matthias; Donatelli, M.; Ferrari, P.; Furci, I.
Symbol based convergence analysis in block multigrid methods with applications for Stokes problems
Appl. Numer. Math., 193 :109-130
20234677.
Guerreiro, Andreia P.; Klamroth, Kathrin; Fonseca, Carlos M.
Theoretical aspects of subset selection in multi-objective optimization
In Brockhoff, D. and Emmerich, M. and Naujoks, B. and Purshouse, R., Editor aus Natural Computing Series
Seite 213--239
Herausgeber: Springer
2023
213--2394676.
Alameddine, Jean-Marco; others
The particle-shower simulation code CORSIKA 8
PoS, ICRC2023 :310
20234675.
Meinert, Janning; Morej\'on, Leonel; Sandrock, Alexander; Eichmann, Björn; Kreidelmeyer, Jonas; Kampert, Karl-Heinz
The impact of a modified CMB photon density on UHECR propagation
PoS, ICRC2023 :322
20234674.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
20234673.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60 :35
20234672.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
20234671.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
20234670.
Bolten, Matthias; Friedhoff, S.; Hahne, J.
Task graph-based performance analysis of parallel-in-time methods
Parallel Comput., 118 :103050
20234669.
Synthesis and evaluation of radioiodinated estrogens for diagnosis and therapy of male urogenital tumours
Organic & Biomolecular Chemistry, 2023 (21) :3090-3095
2023
Herausgeber: RSC
ISSN: 1477-05394668.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
20234667.
Günther, Michael; Sandu, Adrian; Schäfers, Kevin; Zanna, Antonella
Symplectic GARK methods for partitioned Hamiltonian systems
20234666.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
20234665.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
20234664.
[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, 1572-80994663.
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
arXiv preprint arXiv:2302.01810
20234662.
Göhring, Timo
Ratio of Electron and Muon Pair Production at High Invariant Mass in Association with a b-jet
20234661.
Yusupov, JR; Ehrhardt, Matthias; Matyokubov, Kh Sh; Matrasulov, DU
Driven transparent quantum graphs
Preprint arXiv
20234660.
Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Seserman, Andra
Convergence of linking Durrmeyer type modifications of generalized Baskakov operators
Bulletin of the Malaysian Math. Sciences Society, 46 (3)
20234659.
Jacob, Birgit; Mironchenko, Andrii; Partington, Jonathan R.; Wirth, Fabian
Corrigendum: Noncoercive Lyapunov functions for input-to-state stability of infinite-dimensional systems
SIAM J. Control Optim., 61 (2) :723-724
20234658.
Aerdker, S.; others
CRPropa 3.2: a public framework for high-energy astroparticle simulations
PoS, ICRC2023 :1471
20234657.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
arXiv preprint arXiv:2301.03924
20234656.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep FDM: Enhanced finite difference methods by deep learning
Franklin Open, 4 :100039
2023
Herausgeber: Elsevier
