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
- 2022
4889.
Abreu, Pedro; others
A Search for Photons with Energies Above 2 x 10^{17} eV Using Hybrid Data from the Low-Energy Extensions of the Pierre Auger Observatory
Astrophys. J., 933 (2) :125
20224888.
Glück, Jochen; Roth, Stefan; Spodarev, Evgeny
A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages
Scand. J. Stat. :30 pages
20224887.
Villena, Guillermo; Kleffmann, Jörg
A source for the continuous generation of pure and quantifiable HONO mixtures
Atmospheric Measurement Techniques, 15 (3) :627--637
Februar 2022
ISSN: 1867-85484886.
Voss C., Janoske U.
A surrogate approach to rapidly predict particle collection on single fiber using computational fluid dynamics and machine learning
Machine Learning und Artificial Intelligence in Strömungsmechanik und Strukturanalyse
Herausgeber: NAFEMS
Mai 20224885.
Bolten, M.; Donatelli, M.; Ferrari, P.; Furci, I.
A symbol based analysis for multigrid methods for block-circulant and block-Toeplitz Systems
SIAM J. Matrix Anal. Appl., 43 (1) :405-438
20224884.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
A symbol-based analysis for multigrid methods for block-circulant and block-Toeplitz systems
SIAM J. Matrix Anal. Appl., 43 (1) :405-438
2022
ISSN: 0895-47984883.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
A symbol-based analysis for multigrid methods for block-circulant and block-Toeplitz systems
SIAM J. Matrix Anal. Appl., 43 (1) :405-438
2022
ISSN: 0895-47984882.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A two-dimensional port-Hamiltonian model for coupled heat transfer
Mathematics, 10 (24) :4635
2022
Herausgeber: MDPI4881.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A two-dimensional port-Hamiltonian model for coupled heat transfer
Mathematics, 10 (24) :4635
2022
Herausgeber: MDPI4880.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A two-dimensional port-Hamiltonian model for coupled heat transfer
Mathematics, 10 (24) :4635
2022
Herausgeber: MDPI4879.
Jäschke, Jens; Ehrhardt, M.; Günther, M.; Jacob, Birgit
A Two-Dimensional Port-Hamiltonian Model for Coupled Heat Transfer
Mathematics, 10(24) :4635
20224878.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A Two-Dimensional Port-Hamiltonian Model for Coupled Heat Transfer
Mathematics, 10 (24) :4635
2022
Herausgeber: MDPI4877.
Yoda, R.; Bolten, Matthias; Nakajima, K.; Fujii, A.
Acceleration of optimized coarse-grid operators by spatial redistribution for multigrid reduction in time
In Groen, Derek and de Mulatier, Clelia and Paszynski, Maciej and Krzhizhanovskaya, Valeria V. and Dongarra, Jack J. and Sloot, Peter M. A., Editor, Computational Science - ICCS 2022, Seite 214-221
In Groen, Derek and de Mulatier, Clelia and Paszynski, Maciej and Krzhizhanovskaya, Valeria V. and Dongarra, Jack J. and Sloot, Peter M. A., Editor
Herausgeber: Springer International Publishing, Cham
20224876.
Yoda, R.; Bolten, M.; Nakajima, K.; Fujii, A.
Acceleration of optimized coarse-grid operators by spatial redistribution for multigrid reduction in time
In Groen, Derek and de Mulatier, Clelia and Paszynski, Maciej and Krzhizhanovskaya, Valeria V. and Dongarra, Jack J. and Sloot, Peter M. A., Editor, Computational Science - ICCS 2022, Seite 214-221
In Groen, Derek and de Mulatier, Clelia and Paszynski, Maciej and Krzhizhanovskaya, Valeria V. and Dongarra, Jack J. and Sloot, Peter M. A., Editor
Herausgeber: Springer International Publishing, Cham
20224875.
Ehrhardt, Matthias
An efficient second-order method for the linearized Benjamin-Bona-Mahony equation with artificial boundary conditions
Preprint IMACM
2022
Herausgeber: Bergische Universität Wuppertal4874.
Ehrhardt, Matthias
An efficient second-order method for the linearized Benjamin-Bona-Mahony equation with artificial boundary conditions
Preprint IMACM
2022
Herausgeber: Bergische Universität Wuppertal4873.
Ehrhardt, Matthias
An efficient second-order method for the linearized Benjamin-Bona-Mahony equation with artificial boundary conditions
20224872.
Arora, Sahiba; Glück, Jochen
An operator theoretic approach to uniform (anti-)maximum principles
J. Differential Equations, 310 :164--197
20224871.
4870.
Schneider, Lukas; Kaul, Matthias; Braschke, Kamil; Eilts, Peter; Schmidt, Eberhard; Janoske, Uwe
Ash Behaviour in Wall-Flow Filters
In Bargende, Michael and Reuss, Hans-Christian and Wagner, Andreas, Editor, 22. Internationales Stuttgarter Symposium, Seite 629--646
In Bargende, Michael and Reuss, Hans-Christian and Wagner, Andreas, Editor
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2022ISBN: 978-3-658-37009-1
4869.
Yoda, R.; Bolten, M.; Nakajima, K.; Fujii, A.
Assignment of idle processors to spatial redistributed domains on coarse levels in multigrid reduction in time
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Seite (accepted)
20224868.
Yoda, R.; Bolten, Matthias; Nakajima, K.; Fujii, A.
Assignment of idle processors to spatial redistributed domains on coarse levels in multigrid reduction in time
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Seite 41-51
20224867.
Yoda, R.; Bolten, M.; Nakajima, K.; Fujii, A.
Assignment of idle processors to spatial redistributed domains on coarse levels in multigrid reduction in time
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Seite 41-51
20224866.
Sch\"afers, Torben; Teng, Long
Asymmetry in stochastic volatility models with threshold and time-dependent correlation
Studies in Nonlinear Dynamics \& Econometrics
20224865.
Xue, Chaoyang; Ye, Can; Kleffmann, Jörg; Zhang, Chenglong; Catoire, Valéry; Bao, Fengxia; Mellouki, Abdelwahid; Xue, Likun; Chen, Jianmin; Lu, Keding; Zhao, Yong; Liu, Hengde; Guo, Zhaoxin; Mu, Yujing
Atmospheric measurements at Mt. Tai – Part I: HONO formation and its role in the oxidizing capacity of the upper boundary layer
Atmospheric Chemistry and Physics, 22 (5) :3149—3167
März 2022
ISSN: 1680-7324