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



2023

4737.

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

4736.

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

4735.

[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

4734.

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

4733.

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

4732.

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

4731.

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

4730.

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

4729.

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

4728.

[english] Venzlaff, Julian; Kosumi, Kaltrina; Zeller, Diana; Bohrmann-Linde, Claudia
Education for Sustainable Development and Experiments involving Titanium Dioxide
World Journal of Chemical Education, 11 (3) :80-86
August 2023

4727.

[english] Brunnert, Rainer; Tausch, Michael W.
Green Chemistry in STEM Education: Light for Basic Concepts
World Journal of Chemical Education, 11 (3) :65-73
August 2023

4726.

Desai, Prachi; Dasgupta, Anshuman; Sofias, Alexandros Marios; Peña, Quim; Göstl, Robert; Slabu, Ioana; Schwaneberg, Ulrich; Stiehl, Thomas; Wagner, Wolfgang; Jockenhövel, Stefan; Stingl, Julia; Kramann, Rafael; Trautwein, Christian; Brümmendorf, Tim H.; Kiessling, Fabian; Herrmann, Andreas; Lammers, Twan
Transformative Materials for Interfacial Drug Delivery
Advanced Healthcare Materials, 12 (20) :2301062
August 2023
ISSN: 2192-2659

4725.

Haussmann, N.; Stroka, S.; Clemens, M.
Anwendung neuronaler Netze in der Bestimmung der Exposition gegenüber niederfrequenten Magnetfeldern bei induktiven Ladesystemen
URSI e.V. Deutschland 2023 Kleinheubacher Tagung (KHB 2023)
Miltenberg, Germany
07 2023

4724.

Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A numerical study of the impact of variance boundary conditions for the Heston model
IMACM preprint 23/11
Juli 2023

4723.

Stroka, S.; Haussmann, N.; Clemens, M.
Bewertung niederfrequenter Magnetfeldexpositionen unter Einsatz ordnungsreduzierender Modelle
URSI e.V. Deutschland 2023 Kleinheubacher Tagung (KHB 2023)
Miltenberg, Germany
06 2023

4722.

[german] Venzlaff, Julian; Bohrmann-Linde, Claudia
Photoreformierung – grüner Wasserstoff aus Alkohol, Zucker und Stärke
CHEMKON, 30 (6) :254-259
Juni 2023

4721.

Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry, 2023 (21) :4574-4577
05 2023
Herausgeber: RSC

4720.

Haussmann, N.; Stroka, S.; Tiemann, M.; David, A.; Schmuelling, B.; Clemens, M.
Vorstellung des MILAS Projektes: Autonome induktiv geladene Elektro-Shuttles im öffentlichen Nahverkehr
5. Wissenschaftsforum Mobilität 2023, „Next Chapter in Mobility“
Duisburg, Germany
5 2023

4719.

Kähne, B.; Clemens, M.
A ROW-Type Method for GPU-Accelerated Large-Scale Finite Element Simulations of Nonlinear Eddy Current Problems
The 13th International Symposium on Electric and Magnetic Fields (EMF 2023)
Marseilles, France
5 2023

4718.

Haussmann, N.; Stroka, S.; Clemens, M.
Reduction of the Numerical Error in High-Resolution Low-Frequency Magnetic-Field Exposure Scenarios of Human Models Utilizing Smoothing Methods
The 13th International Symposium on Electric and Magnetic Fields (EMF 2023)
Marseilles, France, 29.-31.08.2023
04 2023

4717.

Zhou, Yu; Centeno, Silvia P.; Zhang, Kuan; Zheng, Lifei; Göstl, Robert; Herrmann, Andreas
Fracture Detection in Bio-Glues with Fluorescent-Protein-Based Optical Force Probes
Advanced Materials, 35 (16) :2210052
April 2023
ISSN: 1521-4095

4716.

Bensberg, Kathrin; Kunz, K.; Kirsch, Stefan F.
Thermolysis of Geminal Diazido Malonamides: Simple Access to Tetrazoles and Functionalization of In Situ Formed Isocyanates
European Journal of Organic Chemistry, 26 (18) :e2023002
04 2023
Herausgeber: Wiley
ISSN: 1434-193X

4715.

Küng, Robin; Germann, Anne; Krüsmann, Marcel; Niggemann, Louisa P.; Meisner, Jan; Karg, Matthias; Göstl, Robert; Schmidt, Bernd M.
Mechanoresponsive Metal-Organic Cage-Crosslinked Polymer Hydrogels
Chemistry – A European Journal, 29 (18) :e202300079
März 2023
ISSN: 1521-3765

4714.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Dem Apfel ans Leder
Nachrichten aus der Chemie, 71 :12-14
März 2023

4713.

Ponce, Cristobal; Wu, Yongxin; Le Gorrec, Yann; Ramirez, Hector
Port-Hamiltonian modeling of multidimensional flexible mechanical structures defined by linear elastic relations
November 2023

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