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
4641.
Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A Gradient Descent Algorithm for the Heston model
arXiv preprint arXiv:2110.14370
20214640.
Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
A homeomorphism theorem for sums of translates
20214639.
Kühn, Jan; Bartel, Andreas; Putek, Piotr
A hysteresis loss model for Tellinen’s scalar hysteresis model
In van Beurden, Martijn and Budko, Neil and Schilders, Wil, Editor, Scientific Computing in Electrical Engineering: SCEE 2020, Eindhoven, The Netherlands, February 2020ausMathematics in Industry, Seite 241–250
In van Beurden, Martijn and Budko, Neil and Schilders, Wil, Editor
Herausgeber: Springer Cham
20214638.
Kühn, Jan; Bartel, Andreas; Putek, Piotr
A Hysteresis Loss Model for Tellinen’s Scalar Hysteresis Model
Scientific Computing in Electrical Engineering: SCEE 2020, Eindhoven, The Netherlands, February 2020
Seite 241--250
Herausgeber: Springer International Publishing Cham
2021
241--2504637.
Schnepper, Teresa; Klamroth, Kathrin; Puerto, Justo; Stiglmayr, Michael
A Local Analysis to Determine All Optimal Solutions of p-k-max Location Problems on Networks
Discrete Applied Mathematics, 296 :217-234
20214636.
Kapllani, Lorenc; Teng, Long; Ehrhardt, Matthias
A multistep scheme to solve backward stochastic differential equations for option pricing on GPUs
In Dimov, Ivan and Fidanova, Stefka, Editor, Advances in High Performance Computing: Results of the International Conference on “High Performance Computing” Borovets, Bulgaria, 2019, Seite 196–208
In Dimov, Ivan and Fidanova, Stefka, Editor
Herausgeber: Springer Cham
20214635.
Kapllani, Lorenc; Teng, Long; Ehrhardt, Matthias
A multistep scheme to solve backward stochastic differential equations for option pricing on GPUs
In Dimov, Ivan and Fidanova, Stefka, Editor, Advances in High Performance Computing: Results of the International Conference on “High Performance Computing” Borovets, Bulgaria, 2019, Seite 196–208
In Dimov, Ivan and Fidanova, Stefka, Editor
Herausgeber: Springer Cham
20214634.
Kapllani, Lorenc; Teng, Long; Ehrhardt, Matthias
A multistep scheme to solve backward stochastic differential equations for option pricing on gpus
, Advances in High Performance Computing: Results of the International Conference on “High Performance Computing” Borovets, Bulgaria, 2019Band902, Seite 196--208
Springer International Publishing
20214633.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-equilibrium bounce-back boundary condition for thermal multispeed LBM
Journal of Computational Science, 53 :101364
2021
Herausgeber: Elsevier4632.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-equilibrium bounce-back boundary condition for thermal multispeed LBM
J. Comput. Sci., 53 :101364
2021
Herausgeber: Elsevier {BV}4631.
4630.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
A parallel sparse grid combination technique using the Parareal Algorithm
Preprint IMACM
2021
Herausgeber: Bergische Universität Wuppertal4629.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
A parallel sparse grid combination technique using the Parareal Algorithm
Preprint IMACM
2021
Herausgeber: Bergische Universität Wuppertal4628.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
A parallel sparse grid combination technique using the Parareal Algorithm
Preprint IMACM
2021
Herausgeber: Bergische Universität Wuppertal4627.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
A parallel Sparse Grid Combination Technique using the Parareal Algorithm
20214626.
Teng, Long
A review of tree-based approaches to solve forward-backward stochastic differential equations
Journal of Computational Finance, 25 (3) :125–159
2021
Herausgeber: Incisive Media4625.
Teng, Long
A review of tree-based approaches to solve forward-backward stochastic differential equations
JCF, 25 (3) :125--159
20214624.
Caracas, Ioana Alexandra; others
A tau scenario application to a search for upward-going showers with the Fluorescence Detector of the Pierre Auger Observatory
PoS, ICRC2021 :1145
20214623.
Kühn, Jan; Bartel, Andreas; Putek, Piotr
A thermal extension and loss model for Tellinen’s hysteresis model
COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 40 (2) :126–141
2021
Herausgeber: Emerald Group Publishing4622.
Kühn, Jan; Bartel, Andreas; Putek, Piotr
A thermal extension and loss model for Tellinen’s hysteresis model
COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 40 (2) :126--141
2021
Herausgeber: Emerald Publishing Limited4621.
Clemens, Markus; Kasolis, Fotios; Henkel, M-L; Kähne, B; Günther, Michael
A two-step Darwin model time-domain formulation for quasi-static electromagnetic field calculations
IEEE Transactions on Magnetics, 57 (6) :1--4
2021
Herausgeber: IEEE4620.
Clemens, Markus; Kasolis, Fotios; Henkel, M-L; Kähne, B; Günther, Michael
A two-step Darwin model time-domain formulation for quasi-static electromagnetic field calculations
IEEE Transactions on Magnetics, 57 (6) :1–4
2021
Herausgeber: IEEE4619.
Clemens, Markus; Kasolis, Fotios; Henkel, M-L; Kähne, B; Günther, Michael
A two-step Darwin model time-domain formulation for quasi-static electromagnetic field calculations
IEEE Transactions on Magnetics, 57 (6) :1–4
2021
Herausgeber: IEEE4618.
Janssen, N.; Gesell, H.; Gutt, R.; Janoske, U.
Adaption of the Aluminium Electrolysis to Volatile Power Supply: Development of a Predictive Model to Investigate the Thermal Behavior of a Cell
presented at NAFEMS World Congress 2022
Oktober 20214617.
Hahne, J.; Friedhoff, S.; Bolten, M.
Algorithm 1016: PyMGRIT: a Python package for the parallel-in-time method MGRIT
ACM Trans. Math. Software, 47 (2) :Art. 19, 22
2021