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
5052.
Al{\i}, G; Bartel, A; Günther, M
Electrical RLC networks and diodes5051.
Gjonaj, Erion; Bahls, Christian Rüdiger; Bandlow, Bastian; Bartel, Andreas; Baumanns, Sascha; Belzen, F; Benderskaya, Galina; Benner, Peter; Beurden, MC; Blaszczyk, Andreas; others
Feldmann, Uwe, 143 Feng, Lihong, 515 De Gersem, Herbert, 341 Gim, Sebasti{\'a}n, 45, 333
MATHEMATICS IN INDUSTRY 14 :5875050.
Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik5049.
Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik5048.
Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations5047.
Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :255046.
Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25- 2024
5045.
Kapllani, Lorenc; Teng, Long
{A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations}
20245044.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Diekmann, Charlotte; Schrader, Claudia
Virtual Reality für den Chemieunterricht
Nachrichten aus der Chemie, 72 (6) :15-22
20245043.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388- 2024
5042.
Arslan, Bahar; Relton, Samuel D.; Schweitzer, Marcel
Structured level-2 condition numbers of matrix functions
Electron. J. Linear Algebra, 40 :28-47
20245041.
Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
Preprint
20245040.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Constructing Optimal Star Discrepancy Sets
20245039.
Jacob, Birgit; Glück, Jochen; Meyer, Annika; Wyss, Christian; Zwart, Hans
Stability via closure relations with applications to dissipative and port-Hamiltonian systems
J. Evol. Equ., 24 :Paper No. 62
20245038.
Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
Structural Aspects of Electromagneto-Quasistatic Field Formulations of Darwin-Type Derived in the Port-Hamiltonian System Framework
TechRxiv
2024
Herausgeber: IEEE5037.
Günther, M.; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
Band 43
Herausgeber: Springer, Cham.
van Beurden, M., Budko, N.V., Ciuprina, G., Schilders, W., Bansal, H., Barbulescu, R. Edition
20245036.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-Preserving Identification of Port-Hamiltonian Systems—A Sensitivity-Based Approach
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor, Scientific Computing in Electrical Engineering SCEE 2022, Amsterdam, The Netherlands, July 2022ausMathematics in Industry, Seite 167–174
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor
Herausgeber: Springer Cham
20245035.
Ghasemzadeh, Mohammadamin; Amirfazli, Alidad
Study of Insect Impact on an Aerodynamic Body Using a Rotary Wing Simulator
Fluids, 9 (1)
2024
ISSN: 2311-55215034.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
To appear in International Journal of Uncertainty Quantification
2024
Herausgeber: Begell5033.
Schäfers, Kevin; Peardon, Michael; Günther, Michael
A modified Cayley transform for SU (3)
Preprint
20245032.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics
20245031.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics, 101 (9-10) :1094–1112
2024
Herausgeber: Taylor & Francis5030.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences5029.
Rohde, Martin; Burgmann, Sebastian; Janoske, Uwe
The impact of a two-dimensional vibration excitation on the critical incident flow velocity of a sessile droplet
International Journal of Multiphase Flow, 171 :104663
2024
Herausgeber: Pergamon5028.
Reiter, Kendra; Schmidt, Marie; Stiglmayr, Michael
The Line-Based Dial-a-Ride Problem
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)Band123ausOpen Access Series in Informatics (OASIcs), Seite 14:1—14:20
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs)
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor
Herausgeber: Schloss Dagstuhl — Leibniz-Zentrum für Informatik, Dagstuhl, Germany
2024