Applied and Computational Mathematics (ACM)

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

5036.

Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
2023

5035.

Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
2023

5034.

Bolten, Matthias; Friedhoff, S.; Hahne, J.
Task graph-based performance analysis of parallel-in-time methods
Parallel Comput., 118 :103050
2023

5033.

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
2023

5032.

Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60 :35
2023

5031.

Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
2023

5030.

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
2023

5029.

Alameddine, Jean-Marco; others
The particle-shower simulation code CORSIKA 8
PoS, ICRC2023 :310
2023

5028.

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--239

5027.

[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

5026.

Ehrhardt, Matthias
Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction
Journal of Marine Science and Engineering, 11 (10) :1922
2023
Herausgeber: MDPI

5025.

Ehrhardt, Matthias
Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction
Journal of Marine Science and Engineering, 11 (10) :1922
2023
Herausgeber: MDPI

5024.

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: Hindawi

5023.

Ehrhardt, Matthias
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters, Section A, 459 :128611
2023
Herausgeber: North-Holland

5022.

Ehrhardt, Matthias
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters, Section A, 459 :128611
2023
Herausgeber: North-Holland

5021.


Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters A :128611
2023
Herausgeber: North-Holland

5020.

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: 1868-7776

5019.

David, Amelie; Stroka, Steven; Haussmann, Norman; Schmülling, Benedikt; Clemens, Markus
Überprüfung der elektromagnetischen Umweltverträglichkeit bei induktiver Ladung
In Proff, Heike and Clemens, Markus and Marrón, Pedro J. and Schmülling, Benedikt, Editor
Seite 143-180
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2023
143-180

5018.

Dobrick, Alexander; Hölz, Julian; Kunze, Markus
Ultra Feller operators from a functional analytic perspective
2023

5017.

Wiesen, Peter; Illmann, Jan Niklas
Umweltchemie: Methan in der Atmosphäre
Nachrichten aus der Chemie, 71 (2) :70—73
Februar 2023
ISSN: 1439-9598, 1868-0054

5016.

Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Submitted to SIAM-ASA J. Uncertain. Quantif.
2023

5015.

Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
2023

5014.

Dobrick, Alexander; Hölz, Julian
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
2023

5013.

Abdul Halim, Adila; others
Update on the Offline Framework for AugerPrime and production of reference simulation libraries using the VO Auger grid resources
PoS, ICRC2023 :248
2023

5012.

Ehrhardt, Matthias
Use of interference patterns to control sound field focusing in shallow water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI