Applied and Computational Mathematics (ACM)

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



2021

4516.

Anchordoqui, Luis A.; others
Hunting super-heavy dark matter with ultra-high energy photons
Astropart. Phys., 132 :102614
2021

4515.

Schultes, Johanna; Stiglmayr, Michael; Klamroth, Kathrin; Hahn, Camilla
Hypervolume Scalarization for Shape Optimization to Improve Reliability and Cost of Ceramic Components
Optimization and Engineering, 22 (2) :1203-1231
2021

4514.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Iterates of convolution-type operators
Positivity, 25 :495-506
2021

4513.

Zeller, Diana
Kursbuch Gase und Überraschungen. Eine Lerneinheit des Konzepts KriViNat
Herausgeber: Chemiedidaktik. Bergische Universität Wuppertal
2021
online

4512.

Jacob, Birgit; Partington, Jonathan R.; Pott, Sandra; Rydhex, Eskil; Schwenninger, Felix L.
Laplace-Carleson embeddings and infinity-norm admissibility
2021

4511.

Ehrhardt, Matthias
Lattice Kinetic Algorithms for relativistic flows: a unified treatment
University of Cyprus
2021

4510.

Rautenberg, Julian
Limits on ultra-high energy photons with the Pierre Auger Observatory
PoS, ICRC2019 :398
2021

4509.

Sandu, Adrian; Günther, Michael; Roberts, Steven
Linearly implicit GARK schemes
Applied Numerical Mathematics, 161 :286--310
2021
Herausgeber: North-Holland

4508.

Sandu, Adrian; Günther, Michael; Roberts, Steven
Linearly implicit GARK schemes
Applied Numerical Mathematics, 161 :286–310
2021
Herausgeber: Elsevier

4507.

Sandu, Adrian; Günther, Michael; Roberts, Steven
Linearly implicit GARK schemes
Applied Numerical Mathematics, 161 :286–310
2021
Herausgeber: Elsevier

4506.

Beckermann, Bernhard; Cortinovis, Alice; Kressner, Daniel; Schweitzer, Marcel
Low-rank updates of matrix functions II: Rational Krylov methods
SIAM J. Numer. Anal., 59 (3) :1325-1347
2021

4505.

Beckermann, Bernhard; Cortinovis, Alice; Kressner, Daniel; Schweitzer, Marcel
Low-rank updates of matrix functions II: Rational Krylov methods
SIAM J. Numer. Anal., 59 (3) :1325-1347
2021

4504.

Beckermann, Bernhard; Cortinovis, Alice; Kressner, Daniel; Schweitzer, Marcel
Low-rank updates of matrix functions II: Rational Krylov methods
SIAM J. Numer. Anal., 59 (3) :1325-1347
2021

4503.

Haussmann, N.; Zang, M.; Mease, R.; Clemens, M.; Schmuelling, B.
Magnetic Dosimetry Simulations of Wireless Power Transfer Systems with High Resolution Voxel Models Utilizing the Co-Simulation Scalar Potential Finite Difference Scheme
The 12th International Symposium on Electric and Magnetic Fields (EMF 2021), Online Conference, 06.-08.07.2021. Abstract accepted.
2021

4502.

Zang, M.; Haussmann, N.; Mease, R.; Clemens, M.; Schmuelling, B.
Magnetic Field Exposure Simulations of Human Bodies close by a Wireless Power Transfer System of an Elec-trically Powered Taxi
The 12th International Symposium on Electric and Magnetic Fields (EMF 2021), Online Conference, 06.-08.07.2021. Abstract accepted.
2021

4501.

Araújo, Adérito; Ehrhardt, Matthias
Mathematical models of the spread and consequences of the SARS-CoV-2 pandemics: Effects on health, society, industry, economics and technology
Journal of Mathematics in Industry, 11 :1–2
2021
Herausgeber: Springer Verlag

4500.

Araújo, Adérito; Ehrhardt, Matthias
Mathematical models of the spread and consequences of the SARS-CoV-2 pandemics: Effects on health, society, industry, economics and technology
Journal of Mathematics in Industry, 11 :1–2
2021
Herausgeber: Springer Verlag

4499.

Araújo, Adérito; Ehrhardt, Matthias
Mathematical models of the spread and consequences of the SARS-CoV-2 pandemics: Effects on health, society, industry, economics and technology
2021

4498.

Bannenberg, Marcus WFM; Kasolis, Fotios; Günther, Michael; Clemens, Markus
Maximum entropy snapshot sampling for reduced basis modelling
COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 41 (3) :954--966
2021
Herausgeber: Emerald Publishing Limited

4497.

Burger, Martin; Pinnau, Rene; Totzeck, Claudia; Tse, Oliver
Mean-field optimal control and optimality conditions in the space of probability measures
SIAM Journal of Control and Optimization, 59 (2) :977-1006
2021

4496.

Burger, Martin; Kreusser, Lisa Maria; Totzeck, Claudia
Mean-field optimal control for biological pattern formation
ESAIM COCV, 27 (40)
2021

4495.

Aab, Alexander; others
Measurement of the Fluctuations in the Number of Muons in Extensive Air Showers with the Pierre Auger Observatory
Phys. Rev. Lett., 126 (15) :152002
2021

4494.

Gesell, H.; Gutt, R.; Janssen, N.; Janoske, U.
Modeling of the Aluminium Electrolysis Process: Feeding and Dissolution of Alumina Particles
presented at NAFEMS World Congress 2022
Oktober 2021

4493.

Pereira Vaz, Nuno; Bohrmann-Linde, Claudia
Modellexperiment Treibhauseffekt 2.0
Naturwissenschaften im Unterricht Chemie, 5/21 (32) :26--31
2021

4492.

Abreu, Pedro; others
Monte Carlo simulations for the Pierre Auger Observatory using the VO auger grid resources
PoS, ICRC2021 :232
2021