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
- 1996
650.
Denk, Georg; Günther, Michael; Simeon, Bernd
Numerische simulation in chip-design und fahrzeugtechnik
Preprint (1841)
1996
Herausgeber: Technische Hochschule Darmstadt649.
GrÄb, Robert; Günther, Michael; Wever, Utz; Zheng, Qinghua
Optimization of parallel multilevel-Newton algorithms on workstation clusters
In Bougé, Luc and Fraigniaud, Pierre and Mignotte, Anne and Robert, Yves, Editor, Euro-Par96 Parallel ProcessingBand1124ausLecture Notes in Computer Science, Seite 91–96
In Bougé, Luc and Fraigniaud, Pierre and Mignotte, Anne and Robert, Yves, Editor
Herausgeber: Springer Berlin Heidelberg
1996648.
GrÄb, Robert; Günther, Michael; Wever, Utz; Zheng, Qinghua
Optimization of parallel multilevel-Newton algorithms on workstation clusters
In L. Bouge and et al., Editor, Euro-Par'96 Parallel Processing: Second International Euro-Par Conference Lyon, France, August 26--29, 1996 Proceedings, Volume II 2Band1124ausLecture Notes in Computer Science, Seite 91--96
Springer Berlin Heidelberg
In L. Bouge and et al., Editor
Herausgeber: Berlin, Springer-Verlag
1996647.
Klamroth, Kathrin; Mengersen, Ingrid
Ramsey numbers of K_3 versus (p,q)-graphs
Ars Combinatoria, 43 :107-120
1996646.
Becker, Karl Heinz; Kleffmann, Jörg; Kurtenbach, Ralf; Wiesen, Peter
Solubility of nitrous acid (HONO) in sulfuric acid solutions
Journal of Physical Chemistry, 100 (36) :14984-14990
1996645.
Becker, Karl Heinz; Kleffmann, Jörg; Kurtenbach, Ralf; Wiesen, Peter
Solubility of nitrous acid (HONO) in sulfuric acid solutions
Journal of Physical Chemistry, 100 (36) :14984-14990
1996644.
Becker, Karl Heinz; Kleffmann, Jörg; Kurtenbach, Ralf; Wiesen, Peter
Solubility of nitrous acid (HONO) in sulfuric acid solutions
Journal of Physical Chemistry, 100 (36) :14984-14990
1996643.
Tausch, Michael W.; Wachtendonk, M.; Porth, H.-R.; Schulze, I.; Wambach, H.
STOFF-FORMEL-UMWELT, CHEMIE S I
Herausgeber: C. C. Buchner, Bamberg
1996642.
G\"unther, Michael; Rentrop, P.
The {NAND-gate} -- a benchmark for the numerical simulation of digital circuits
In W.~Mathis and P.~Noll, Editor, 2.ITG-Diskussionssitzung ''Neue Anwendungen Theoretischer Konzepte in der Elektrotechnik - mit Gedenksitzung zum 50. Todestag von Wilhelm Cauer'', Seite 27--33
In W.~Mathis and P.~Noll, Editor
Herausgeber: Berlin, VDE-Verlag
1996641.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press640.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press639.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996638.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996637.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) Transitions of SbH and SbD
Journal of Molecular Spectroscopy, 179 (1) :79-84
1996
Herausgeber: Academic Press636.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) Transitions of SbH and SbD
Journal of Molecular Spectroscopy, 179 (1) :79-84
1996
Herausgeber: Academic Press635.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press634.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press633.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ → X3Σ- Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press632.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ → X3Σ- transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996631.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ(a2) → X3Σ-(X21) Transitions of SbH and SbD
Journal of Molecular Spectroscopy, 179 (1) :79-84
1996
Herausgeber: Academic Press630.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press629.
Günther, Michael; Rentrop, Peter
The differential-algebraic index concept in electric circuit simulation
, Proceedings of the 3rd International Congress on Industrial and Applied MathematicsBand76, Seite 91–94
Herausgeber: Akademie Verlag Berlin
1996628.
The differential-algebraic index concept in electric circuit simulation
Zeitschrift fur angewandte Mathematik und Mechanik, 76 (1) :91--94
1996627.
Denk, Georg; Günther, Michael
The influence of MOSFET model and network equations on circuit simulation
Preprint (1842)
1996
Herausgeber: Technische Hochschule Darmstadt626.
Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The potential energy surface of H\(_{2}\)\(^{16}\)O
Journal of Chemical Physics, 105 (15) :6490-6497
1996