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
5063.
Clemens, Markus; Günther, Michael
Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework
2023 International Conference on Electromagnetics in Advanced Applications (ICEAA), Seite 1–1
Herausgeber: IEEE
20235062.
Hilbig, André; Malzahn, Tamara; Losch, Daniel; Seifert, Christian; Weiß, Sabrina
starkeSeiten Informatik 7/8 Ausgabe Nordrhein-Westfalen ab 2021 - Schulbuch Klasse 7/8
Herausgeber: Klett Verlag
2023ISBN: 978-3-12-007534-9
5061.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland5060.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland5059.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland5058.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta–Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics
2023
ISSN: 0168-92745057.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
20235056.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems--a sensitivity-based approach
arXiv preprint arXiv:2301.02019
20235055.
Relton, Samuel D.; Schweitzer, Marcel
Structured level-2 condition numbers of matrix functions
20235054.
Studies on the improvement of the matching uncertainty definition in top-quark processes simulated with Powheg+Pythia 8
CERN, Geneva
20235053.
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
20235052.
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
20235051.
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
20235050.
Günther, Michael; Sandu, Adrian; Schäfers, Kevin; Zanna, Antonella
Symplectic GARK methods for partitioned Hamiltonian systems
20235049.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
20235048.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
20235047.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
20235046.
Bolten, Matthias; Friedhoff, S.; Hahne, J.
Task graph-based performance analysis of parallel-in-time methods
Parallel Comput., 118 :103050
20235045.
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
20235044.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60 :35
20235043.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
20235042.
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
20235041.
Alameddine, Jean-Marco; others
The particle-shower simulation code CORSIKA 8
PoS, ICRC2023 :310
20235040.
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--2395039.
[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 2023
