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
- 2019
4091.
Schöps, Sebastian; Duque Guerra, David J; De Gersem, Herbert; Bartel, Andreas; Günther, Michael; Pulch, Roland
Non-Intrusive methods for the cosimulation of coupled problems
In ter Maten, E. Jan W. and Brachtendorf, Hans-Georg and Pulch, Roland and Schoenmaker, Wim and De Gersem, Herbert, Editor aus Mathematics in Industry
Seite 131–159
Herausgeber: Springer Cham
2019
131–1594090.
Putek, Piotr
Nonlinear magnetoquasistatic interface problem in a perma\-nent-magnet machine with stochastic partial differential equation constraints
Engineering Optimization :1--24
März 20194089.
Putek, Piotr
Nonlinear magnetoquasistatic interface problem in a permanent-magnet machine with stochastic partial differential equation constraints
Engineering Optimization, 51 (12) :2169–2192
2019
Herausgeber: Taylor & Francis4088.
Adam, Ahmad Y.; Jensen, Per; Yachmenev, Andrey; Yurchenko, Sergey N.
Nonresonant Raman spectra of the methyl radical \(^{12}\)CH\(_{3}\) simulated in variational calculations
Journal of Molecular Spectroscopy, 362 :77-83
2019
Herausgeber: Academic Press4087.
Adam, Ahmad Y.; Jensen, Per; Yachmenev, Andrey; Yurchenko, Sergey N.
Nonresonant Raman spectra of the methyl radical \(^{12}\)CH\(_{3}\) simulated in variational calculations
Journal of Molecular Spectroscopy, 362 :77-83
2019
Herausgeber: Academic Press4086.
Adam, Ahmad Y.; Jensen, Per; Yachmenev, Andrey; Yurchenko, Sergey N.
Nonresonant Raman spectra of the methyl radical 12CH3 simulated in variational calculations
Journal of Molecular Spectroscopy, 362 :77-83
2019
Herausgeber: Academic Press4085.
Bolten, Matthias; Gottschalk, H.; Hahn, C.; Saadi, M.
Numerical shape optimization to decrease failure probability of ceramic structures
Comput. Vis. Sci., 21 :1-10
20194084.
Bolten, M.; Gottschalk, H.; Hahn, C.; Saadi, M.
Numerical shape optimization to decrease failure probability of ceramic structures
Comput. Vis. Sci., 21 :1-10
20194083.
Bolten, M.; Gottschalk, H.; Hahn, C.; Saadi, M.
Numerical shape optimization to decrease failure probability of ceramic structures
Comput. Vis. Sci., 21 :1-10
20194082.
Jacob, Birgit; Schwenninger, Felix L.; Zwart, Hans
On continuity of solutions for parabolic control systems and input-to-state stability
J. Differential Equations, 266 (10) :6284--6306
20194081.
Jacob, Birgit; Kaiser, Julia T.
On Exact Controllability of Infinite-Dimensional Linear Port-{H}amiltonian Systems
IEEE Control Systems Letters, 3 (3) :661-666
20194080.
Jacob, Birgit; Kaiser, Julia T.
On Exact Controllability of Infinite-Dimensional Linear Port-Hamiltonian Systems
IEEE Control Systems Letters, 3 (3) :661-666
20194079.
Weinan, E; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
Journal of Scientific Computing, 79 (3) :1534--1571
2019
Herausgeber: Springer4078.
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
Journal of Scientific Computing, 79 (3) :1534–1571
2019
Herausgeber: Springer New York4077.
Harbrecht, Helmut; Zaspel, Peter
On the Algebraic Construction of Sparse Multilevel Approximations of Elliptic Tensor Product Problems
J. Sci. Comput., 78 (2) :1272-1290
2019
ISSN: 1573-76914076.
Calore, E; Gabbana, A; Schifano, SF; Tripiccione, R
Optimization of lattice Boltzmann simulations on heterogeneous computers
The International Journal of High Performance Computing Applications, 33 (1) :124–139
2019
Herausgeber: SAGE Publications4075.
Organometallic gold catalysis in combination with enzyme, organo-, or transition-metal catalysis
Science of Synthesis, Knowledge Updates (1) :1–64
20194074.
Ballaschk, Frederic
Oxidation of secondary alcohols using solid-supported hypervalent iodine catalysts
Green Chemistry :5896–5903
2019
ISSN: 1463-92704073.
Brunnert, Rainer; Bohrmann-Linde, Claudia; Meuter, Nico; Pereira Vaz, Nuno; Spinnen, Sebastian; Yurdanur, Yasemin; Tausch, Michael W.
Photons and Molecules: Basic Concepts of Photochemistry in Video Tutorials
, EPA Newsletter Band 96 aus EPA Newsletter
Seite 70-77
Herausgeber: Norbert Hoffmann
2019
70-774072.
Ehrhardt, Matthias
Preprint Elliptical and Archimedean copula models: an application to the price estimation of portfolio credit derivatives
20194071.
Bartel, Andreas; Günther, Michael
Preprint Inter/extrapolation-based multirate schemes—perspective
20194070.
Ehrhardt, Matthias; Vázquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89–90
Herausgeber: Universidade da Coruña
20194069.
Ehrhardt, Matthias; Vázquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89–90
Herausgeber: Universidade da Coruña
20194068.
Rivela, Cynthia B.; Tovar, Carmen M.; Gibilisco, Rodrigo G.; Teruel, Mariano A.; Barnes, Ian; Wiesen, Peter; Blanco, Mar{í}a B.
Product distribution and mechanism of the OH\(^{-}\) initiated tropospheric degradation of three CFC replacement candidates: CH\(_{3}\)CF=CH\(_{2}\), (CF\(_{3}\))\(_{2}\)C=CH\(_{2}\) and (E/Z)-CF\(_{3}\)CF=CHF
RSC Advances, 9 (10) :5592-5598
20194067.
Rivela, Cynthia B.; Tovar, Carmen M.; Gibilisco, Rodrigo G.; Teruel, Mariano A.; Barnes, Ian; Wiesen, Peter; Blanco, Mar{í}a B.
Product distribution and mechanism of the OH\(^{-}\) initiated tropospheric degradation of three CFC replacement candidates: CH\(_{3}\)CF=CH\(_{2}\), (CF\(_{3}\))\(_{2}\)C=CH\(_{2}\) and (E/Z)-CF\(_{3}\)CF=CHF
RSC Advances, 9 (10) :5592-5598
2019
