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



2024

5277.

[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Diekmann, Charlotte; Schrader, Claudia
Virtual Reality für den Chemieunterricht
Nachrichten aus der Chemie, 72 (6) :15-22
2024

5276.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Steopoaie, Ancuta Emilia
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov operators
Applicable Analysis and Discrete Mathematics :1-16
2024
2023

5275.

Haussmann, N.; Stroka, S.; Mazaheri, S.; Clemens, M.
Using Point Clouds for Material Properties Smoothing in Low-Frequency Numerical Dosimetry Simulations
21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024)
Jeju, South Korea
Dezember 2023

5274.

Kähne, B.; Clemens, M.
A GPU Accelerated Semi-Implicit Method for Large-Scale Nonlinear Eddy-Current Problems Using Adaptive Time Step Control
21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024)
Jeju, South Korea
Dezember 2023

5273.

[en] Börger, Kristian; Ellingham, Jennifer; Belt, Alexander; Schultze, Thorsten; Bieder, Stefan; Weckman, Elizabeth; Arnold, Lukas
Assessing performance of LEDSA and Radiance method for measuring extinction coefficients in real-scale fire environments
Fire Safety Journal, 141
Dezember 2023
ISSN: 03797112

5272.

[en] Hehnen, Tristan; Arnold, Lukas
PMMA pyrolysis simulation – from micro- to real-scale
Fire Safety Journal, 141
Dezember 2023
ISSN: 03797112

5271.

Gernandt, Hannes; Hinsen, Dorothea; Cherifi, Karim
The difference between port-Hamiltonian, passive and positive real descriptor systems
Mathematics of Control, Signals, and Systems
Dezember 2023

5270.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Voronovskaja formula for Aldaz–Kounchev–Render operators: uniform convergence
Analysis and Mathematical Physics, 14 (1)
Dezember 2023
ISSN: 1664-235X

5269.

Stroka, S.; Kasolis, F.; Haussmann, N.; Clemens, M.
Efficient Low-Frequency Human Exposure Assessment with the Maximum Entropy Snapshot Sampling
21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024)
Jeju, Korea
November 2023

5268.

Xuan, Mingjun; Fan, Jilin; Khiêm, Vu Ngoc; Zou, Miancheng; Brenske, Kai-Oliver; Mourran, Ahmed; Vinokur, Rostislav; Zheng, Lifei; Itskov, Mikhail; Göstl, Robert; Herrmann, Andreas
Polymer Mechanochemistry in Microbubbles
Advanced Materials, 35 (47) :2305130
November 2023
ISSN: 1521-4095

5267.

Stroka, S.; Haussmann, N.; Clemens, M.
Efficient Assessment of High-Resolution Low-Frequency Magnetic Field Exposure Scenarios Using Reduced Order Models
15th Scientific Computing in Electrical Engineering (SCEE 2024)
Darmstadt, Germany
November 2023

5266.

Alameddine, Jean-Marco; Albrecht, Johannes; Dembinski, Hans; Gutjahr, Pascal; Kampert, Karl-Heinz; Rhode, Wolfgang; Sackel, Maximilian; Sandrock, Alexander; Soedingrekso, Jan
Improvements in charged lepton and photon propagation for the software PROPOSAL
November 2023

5265.

[german] Grandrath, Rebecca
Videoschnitt für Einsteiger:innen
Unterricht Biologie - Das Schülerarbeitsheft, 51 :32-36
November 2023

5264.

[german] Kiesling, Elisabeth; Kremer, Richard; Pereira Vaz, Nuno; Venzlaff, Julian; Bohrmann-Linde, Claudia
Wege aus der Klimakrise – ein BNE-Schülerlaborangebot mit mehrdimensionalem Zugang
MNU Journal, 76 (06/2023) :464 - 471
November 2023
ISSN: 0025-5866

5263.

He, Siyang; Schog, Simon; Chen, Ying; Ji, Yuxin; Panitz, Sinan; Richtering, Walter; Göstl, Robert
Photoinduced Mechanical Cloaking of Diarylethene-Crosslinked Microgels
Advanced Materials, 35 (41) :2305845
Oktober 2023
ISSN: 1521-4095

5262.

Springer, Bastian L.; Holzschneider, K.; Mohr, Fabian; Kirsch, S. F.
Phenanthro[9,10‑d]imidazoles: An Unexpected Synthetic Route
Synthesis, 55 (24) :4224-4230
Oktober 2023
Herausgeber: Thieme
ISSN: 0039-7881

5261.

Abdul Halim, A.; others
Demonstrating Agreement between Radio and Fluorescence Measurements of the Depth of Maximum of Extensive Air Showers at the Pierre Auger Observatory
Oktober 2023

5260.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Genuine Bernstein–Durrmeyer type operators preserving 1 and $x^j$
Annals of Functional Analysis, 15 (1)
Oktober 2023
Herausgeber: Springer Science and Business Media LLC
ISSN: 2008-8752

5259.

Rajkovic, Michelle; Benter, Thorsten; Wissdorf, Walter
Molecular Dynamics-Based Modeling of Ion-Neutral Collisions in an Open Ion Trajectory Simulation Framework
Journal of the American Society for Mass Spectrometry, 34 (10) :2156—2165
Oktober 2023
ISSN: 1044-0305, 1879-1123

5258.

Sánchez-Rodríguez, Antonio R.; Gómez-Álvarez, Elena; Méndez, José M.; Skiba, Ute M.; Jones, Davey L.; Chadwick, Dave R.; Del Campillo, María C.; Fernandes, Raphael Ba.; Kleffmann, Jörg; Barrón, Vidal
Photocatalytic fixation of NOx in soils
Chemosphere, 338 :139576
Oktober 2023
ISSN: 00456535

5257.

Abdul Halim, A.; others
Radio Measurements of the Depth of Air-Shower Maximum at the Pierre Auger Observatory
Oktober 2023

5256.

Göstl, Robert
Trendbericht: Makromolekulare Chemie 2023
Nachrichten aus der Chemie, 71 (10) :48--54
September 2023
ISSN: 1868-0054

5255.

Kordon, Florian; Stiglmayr, Michael; Maier, Andreas; Vicario, Celia Mart{\'{\i}}n; Pertlwieser, Tobias; Kunze, Holger
A principled representation of elongated structures using heatmaps
Scientific Reports, 13 (15253)
September 2023

5254.

Meinert, Janning; Morej\'on, Leonel; Sandrock, Alexander; Eichmann, Björn; Kreidelmeyer, Jonas; Kampert, Karl-Heinz
Modified temperature redshift relation and UHECR propagation
September 2023

5253.

[en] Börger, Kristian; Belt, Alexander; Schultze, Thorsten; Arnold, Lukas
Remote Sensing of the Light-Obscuring Smoke Properties in Real-Scale Fires Using a Photometric Measurement Method
Fire Technology
September 2023
ISSN: 0015-2684, 1572-8099