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
- 2020
4292.
Doganay, Onur Tanil; Gottschalk, Hanno; Hahn, Camilla; Klamroth, Kathrin; Schultes, Johanna; Stiglmayr, Michael
Gradient based biobjective shape optimization to improve reliability and cost of ceramic components
Optimization and Engineering, 21 (4) :1359-1387
2020
Herausgeber: Springer4291.
Doganay, Onur Tanil; Gottschalk, Hanno; Hahn, Camilla; Klamroth, Kathrin; Schultes, Johanna; Stiglmayr, Michael
Gradient based biobjective shape optimization to improve reliability and cost of ceramic components
Optimization and Engineering, 21 (4) :1359-1387
20204290.
Xue, Chaoyang; Zhang, Chenglong; Ye, Can; Liu, Pengfei; Catoire, Valéry; Krysztofiak, Gisèle; Chen, Hui; Ren, Yangang; Zhao, Xiaoxi; Wang, Jinhe; Zhang, Fei; Zhang, Chongxu; Zhang, Jingwei; An, Junling; Wang, Tao; Chen, Jianmin; Kleffmann, Jörg; Mellouki, Abdelwahid; Mu, Yujing
HONO Budget and Its Role in Nitrate Formation in the Rural North China Plain
Environmental Science \& Technology, 54 (18) :11048--11057
September 2020
ISSN: 0013-936X, 1520-58514289.
Kutzner, Laura; Goloshchapova, Kateryna; Rund, Katharina M.; Jübermann, Martin; Blum, Maximilian; Rothe, Michael; Schunck, Wolf-Hagen; Kühn, Hartmut; Schebb, Nils Helge
Human lipoxygenase isoforms form complex patterns of double and triple oxygenated compounds from eicosapentaenoic acid
Biochimica et Biophysica Acta (BBA) - Molecular and Cell Biology of Lipids, 1865 (12) :158806
2020
ISSN: 1388-19814288.
Burger, Martin; Pinnau, Rene; Totzeck, Claudia; Tse, Oliver; Roth, Andreas
Instantaneous control of interacting particle systems in the mean-field limit
Journal of Computational Physics, 405 :109181
20204287.
Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes -- a dynamic-iteration perspective
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor
Seite 73--90
Herausgeber: Springer
2020
73--904286.
Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes: a dynamic-iteration perspective
Progress in differential-algebraic equations II, Seite 73--90
Springer International Publishing
20204285.
Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes: A dynamic-iteration perspective
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor, Progress in Differential-Algebraic Equations IIausDifferential-Algebraic Equations Forum, Seite 73–90
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor
Herausgeber: Springer Cham
20204284.
Bartel, Andreas; Günther, Michael
Inter/extrapolation-based multirate schemes: A dynamic-iteration perspective
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor, Progress in Differential-Algebraic Equations IIausDifferential-Algebraic Equations Forum, Seite 73–90
In Reis, Timo and Grundel, Sara and Schöps, Sebastian, Editor
Herausgeber: Springer Cham
20204283.
Dietz, Tobias; Klamroth, Kathrin; Kraus, Konstantin; Ruzika, Stefan; Schäfer, Luca E.; Schulze, Britta; Stiglmayr, Michael; Wiecek, Margaret M.
Introducing Multiobjective Complex Systems
European Journal of Operational Research, 280 (2) :581--596
2020
Herausgeber: Elsevier4282.
Kaltenbäck, Michael; Skrepek, Nathanael
Joint functional calculus for definitizable self-adjoint operators on {K}rein spaces
Integral Equations Operator Theory, 92 (4) :Paper No. 29, 36
20204281.
Kaltenbäck, Michael; Skrepek, Nathanael
Joint functional calculus for definitizable self-adjoint operators on Krein spaces
Integral Equations Operator Theory, 92 (4) :Paper No. 29, 36
20204280.
Frommer, Andreas; Jacob, Birgit; Kahl, Karsten; Wyss, Christian; Zwaan, Ian
Krylov type methods exploiting the quadratic numerical range
Electron. Trans. Numer. Anal., 53 :541-561
20204279.
Stiglmayr, Michael
Layout problems with reachability constraint
In J. S. Neufeld and U. Buscher and R. Lasch and D. Möst and J. Schönberger , Editor, Operations Research Proceedings 2019
Operations Research 2019
Dresden
In J. S. Neufeld and U. Buscher and R. Lasch and D. Möst and J. Schönberger , Editor
Herausgeber: Springer, Cham
20204278.
Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Linking Baskakov type operators
CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2019, Seite 23-38
Herausgeber: Prof. Marin Drinov Academic Publishing House
20204277.
[german] Zeller, Diana; Bohrmann-Linde, Claudia
Mit Früchten zum elektrischen Strom! - Dynamische eBooks am Beispiel des Konzepts ''Alternative Solarzellen mit Titandioxid''
Digital Unterrichten Biologie, 3 :10-11
20204276.
Bartel, Andreas; Ehrhardt, Matthias
Modulation of Rayleigh-Benard Convection by Lagrangian Thermal Forcing
APS Division of Fluid Dynamics Meeting Abstracts, Seite T01--008
20204275.
Ferrari, P.; Serra-Capizzano, S.
Multigrid for $\mathbb{Q}_{k}$ Finite Element Matrices using a (block) Toeplitz symbol approach
Mathematics, 8 (1) :Paper No. 5
20204274.
Ferrari, P.; Serra-Capizzano, S.
Multigrid for $\mathbb{Q}_{k}$ Finite Element Matrices using a (block) Toeplitz symbol approach
Mathematics, 8 (1) :Paper No. 5
20204273.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
arXiv preprint arXiv:2009.02484
20204272.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
Preprint
20204271.
Hutzenthaler, Martin; Kruse, Thomas
Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities
SIAM Journal on Numerical Analysis, 58 (2) :929--961
2020
Herausgeber: SIAM4270.
Hutzenthaler, Martin; Kruse, Thomas
Multilevel Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities
SIAM Journal on Numerical Analysis, 58 (2) :929–961
2020
Herausgeber: Society for Industrial and Applied Mathematics4269.
Kawai, M.; Ida, A.; Matsuba, H.; Nakajima, K.; Bolten, Matthias
Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Seite 217-226
Herausgeber: ACM, New York
20204268.
Kawai, M.; Ida, A.; Matsuba, H.; Nakajima, K.; Bolten, M.
Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods
Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, Seite 217-226
Herausgeber: ACM, New York
2020
