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

4616.

Hahne, J.; Friedhoff, S.; Bolten, Matthias
Algorithm 1016: PyMGRIT: a Python package for the parallel-in-time method MGRIT
ACM Trans. Math. Software, 47 (2) :Art. 19, 22
2021

4615.

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

4614.

Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
An ADI Sparse Grid method for pricing efficiently American options under the Heston model
Advances in Applied Mathematics and Mechanics, 13 (6) :1384–1397
2021
Herausgeber: Global Science Press

4613.

Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
An ADI Sparse Grid method for pricing efficiently American options under the Heston model
Advances in Applied Mathematics and Mechanics, 13 (6) :1384–1397
2021
Herausgeber: Global Science Press

4612.

Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
An ADI Sparse Grid method for pricing efficiently American options under the Heston model
Advances in Applied Mathematics and Mechanics, 13 (6) :1384–1397
2021
Herausgeber: Global Science Press

4611.


An ADI Sparse Grid method for Pricing Efficiently American Options under the Heston Model
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 13 (6) :1384--1397
2021
Herausgeber: GLOBAL SCIENCE PRESS Office B, 9/F, Kings Wing Plaza2, No. 1 On Kwan St~…
ISSN: 2075-1354

4610.

Treibert, Sarah; Ehrhardt, Matthias
An Unsupervised Physics-Informed Neural Network to Model COVID-19 Infection and Hospitalization Scenarios
2021

4609.

Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions
SIAM J. Matrix Anal. Appl., 42 (3) :1290-1318
2021

4608.

Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions
SIAM J. Matrix Anal. Appl., 42 (3) :1290-1318
2021

4607.

Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions
SIAM J. Matrix Anal. Appl., 42 (3) :1290-1318
2021

4606.

Braschke, Kamil; Zoller, Julian; Zargaran, Amin; Dittler, Achim; Janoske, Uwe
Analytical and numerical calculation of the detachment of particle structures from fibers
Aerosol Science and Technology :1--11
September 2021
Herausgeber: Informa {UK} Limited

4605.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Approximating correlation matrices using stochastic Lie group methods
Mathematics, 9 (1) :94
2021
Herausgeber: MDPI

4604.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Approximating correlation matrices using stochastic Lie group methods
Mathematics, 9 (1) :94
2021
Herausgeber: MDPI

4603.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Approximating correlation matrices using stochastic Lie group methods
Mathematics, 9 (1) :94
2021
Herausgeber: MDPI

4602.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Approximating Correlation Matrices Using Stochastic Lie Group Methods
Mathematics, 9 (1) :94
Januar 2021
Herausgeber: MDPI AG
ISSN: 2227-7390

4601.

[english] Kremer, Richard; Bohrmann-Linde, Claudia; Tausch, Michael W.
Artificial Photosynthesis in Chemical Education - Photocatalytic Generation of Hydrogen in Classroom Experiments
Education Quimica, 32 (3)
2021

4600.

Ferrari, Paola; Serra-Capizzano, Stefano
Asymptotic spectra of large matrices coming from the symmetrization of Toeplitz structure functions and applications to preconditioning
Numer. Linear Algebra Appl., 28 (1) :Paper No. e2332, 16
2021

4599.

Ferrari, Paola; Serra-Capizzano, Stefano
Asymptotic spectra of large matrices coming from the symmetrization of Toeplitz structure functions and applications to preconditioning
Numer. Linear Algebra Appl., 28 (1) :Paper No. e2332, 16
2021

4598.

Hahne, J.; Southworth, B. S.; Friedhoff, S.
Asynchronous Truncated Multigrid-reduction-in-time (AT-MGRIT)
2021

4597.

Hahne, J.; Southworth, B. S.; Friedhoff, S.
Asynchronous Truncated Multigrid-reduction-in-time (AT-MGRIT)
2021

4596.

Hahne, J.; Southworth, B. S.; Friedhoff, S.
Asynchronous Truncated Multigrid-reduction-in-time (AT-MGRIT)
2021

4595.

Xue, Chaoyang; Ye, Can; Kleffmann, Jörg; Zhang, Chenglong; Catoire, Valéry; Bao, Fengxia; Mellouki, Abdelwahid; Xue, Likun; Chen, Jianmin; Lu, Keding; Zhao, Yong; Liu, Hengde; Guo, Zhaoxin; Mu, Yujing
Atmospheric Measurements at the Foot and the Summit of Mt. Tai – Part I: HONO Formation and Its Role in the Oxidizing Capacity of the Upper Boundary Layer
aus preprint
Gases/Field Measurements/Troposphere/Chemistry (chemical composition and reactions)
Juli 2021

4594.

Illmann, Niklas; Gibilisco, Rodrigo Gastón; Bejan, Iustinian Gabriel; Patroescu-Klotz, Iulia; Wiesen, Peter
Atmospheric oxidation of α,β-unsaturated ketones: kinetics and mechanism of the OH radical reaction
Atmospheric Chemistry and Physics, 21 (17) :13667--13686
September 2021
ISSN: 1680-7324

4593.

Illmann, Niklas; Gibilisco, Rodrigo Gastón; Bejan, Iustinian Gabriel; Patroescu-Klotz, Iulia; Wiesen, Peter
Atmospheric oxidation of α,β-unsaturated ketones: kinetics and mechanism of the OH radical reaction
Atmospheric Chemistry and Physics, 21 (17) :13667--13686
September 2021
ISSN: 1680-7324

4592.

Haussmann, N.; Zang, M.; Clemens, M.; B., Schmülling
Bestimmung der Exposition des menschlichen Körpers durch niederfrequente Magnetfelder in der Umgebung induktiv geladener Elektrotaxis – ein Überblick am Beispiel des TALAKO-Projekts
Abstract at URSI e.V. Deutschland 2020 Kleinheubacher Tagung (KHB 2021)
September 2021