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
5431.
Vinod, Vivin; Zaspel, Peter
Assessing Non-Nested Configurations of Multifidelity Machine Learning for Quantum-Chemical Properties
Machine Learning: Science and Technology, 5 (4) :045005
20245430.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195-208
Juli 2024
ISSN: 0898-12215429.
[English] Schrader, Claudia; Diekmann, Charlotte; Schulz, Paulina; Mack, Nils; Bohrmann, Claudia; Zeller, Diana
Hands-on training: Effects on virtual presence, learning-centered emotions, cognitive load and learning outcome when learning with virtual reality
Computers in Human Behavior Reports (100487)
September 20245428.
Reiter, Kendra; Schmidt, Marie; Stiglmayr, Michael
The Line-Based Dial-a-Ride Problem
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)Band123ausOpen Access Series in Informatics (OASIcs), Seite 14:1—14:20
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs)
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor
Herausgeber: Schloss Dagstuhl — Leibniz-Zentrum für Informatik, Dagstuhl, Germany
20245427.
Vinod, Vivin; Kleinekathöfer, Ulrich; Zaspel, Peter
Optimized multifidelity machine learning for quantum chemistry
Mach. Learn.: Sci. Technol., 5 (1) :015054
20245426.
Ghasemzadeh, Mohammadamin; Amirfazli, Alidad
Study of Insect Impact on an Aerodynamic Body Using a Rotary Wing Simulator
Fluids, 9 (1)
2024
ISSN: 2311-55215425.
[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 20245424.
Rohde, Martin; Burgmann, Sebastian; Janoske, Uwe
The impact of a two-dimensional vibration excitation on the critical incident flow velocity of a sessile droplet
International Journal of Multiphase Flow, 171 :104663
2024
Herausgeber: Pergamon- 2023
5423.
Petrov, Pavel; Matskovskiy, Andrey; Zakharenko, Alena; Zavorokhin, German; Dosso, Stan
Generalized Pekeris-Buldyrev waveguide and its properties
submitted to J. Acoust. Soc. Am.
Juni 20235422.
Stroka, S.; Haussmann, N.; Clemens, M.
Bewertung niederfrequenter Magnetfeldexpositionen unter Einsatz ordnungsreduzierender Modelle
URSI e.V. Deutschland 2023 Kleinheubacher Tagung (KHB 2023)
Miltenberg, Germany
Juni 20235421.
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 20235420.
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
Mai 20235419.
Kapllani, Lorenc; Teng, Long
Deep Learning algorithms for solving high-dimensional nonlinear Backward Stochastic Differential Equations
Discrete Contin. Dyn. Syst. - B
2023
ISSN: 1531-34925418.
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
Mai 20235417.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Accepted at Numerische Mathematik
20235416.
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
April 20235415.
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
April 2023
Herausgeber: Wiley
ISSN: 1434-193X5414.
Mui, Jonathan
Spectral properties of locally eventually positive operator semigroups
Semigroup Forum, 106 :460-480
20235413.
Stroka, S.; Haussmann, N.; Zang, M.; Schmuelling, B.; Clemens, M.
GPU-Based Near Real-Time Estimation of the Human Body Penetrating Low-Frequency Magnetic Fields Using Free-Space Field Measurements
IEEE Transactions on Magnetics, 59 (5) :1-4
20235412.
Vinod, Vivin; Maity, Sayan; Zaspel, Peter; Kleinekathöfer, Ulrich
Multifidelity Machine Learning for Molecular Excitation Energies
J. Chem. Theory Comput., 19 (21) :7658-7670
20235411.
Haussmann, Norman; Stroka, Steven; Schmuelling, Benedikt; Clemens, Markus
GPU-accelerated body-internal electric field exposure simulation using low-frequency magnetic field sampling points
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 42 (5) :982-992
Januar 2023
Herausgeber: Emerald Publishing Limited
ISSN: 0332-16495410.
Braun, Feodor; Jaschinski, M.; Kirsch, Stefan F.; Schomäcker, Klaus
Synthesis and evaluation of radioiodinated estrogens for diagnosis and therapy of male urogenital tumours
Organic & Biomolecular Chemistry, 21 :3090-3095
März 2023
Herausgeber: RSC
ISSN: 1477-05395409.
David, Amelie; Stroka, Steven; Haussmann, Norman; Schmülling, Benedikt; Clemens, Markus
Überprüfung der elektromagnetischen Umweltverträglichkeit bei induktiver Ladung
In Proff, Heike and Clemens, Markus and Marrón, Pedro J. and Schmülling, Benedikt, Editor
Seite 143-180
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2023
143-1805408.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
20235407.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Submitted to SIAM-ASA J. Uncertain. Quantif.
2023