Multirate Partial Differential Algebraic Equations
In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and/or frequency change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. On the one hand, the simulation of enveloppe-modulated signals requires the solution of initial-boundary value problems of the MPDAEs. On the other hand, the simulation of quasiperiodic signals implies multiperiodic boundary conditions only for the MPDAEs. In case of quasiperiodic signals, a method of characteristics solves the multirate model efficiently, since the system of partial differential algebraic equations exhibits a hyperbolic structure.
Publications
- 2023
4777.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numerische Mathematik, 155 (1-2) :1–34
2023
Herausgeber: Springer New York4776.
Bartel, A.; Günther, M.; Jacob, Birgit; Reis, T.
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numer. Math., 155 (1-2) :1-34
20234775.
Farkas, Bálint; Jacob, Birgit; Reis, Timo; Schmitz, Merlin
Operator splitting based dynamic iteration for linear infinite-dimensional port-Hamiltonian systems
20234774.
Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
arXiv preprint arXiv:2304.01766
20234773.
Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
Preprint
20234772.
Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael
Operator splitting for semi-explicit differential-algebraic equations and port-Hamiltonian DAEs
Preprint
20234771.
Mayotte, Eric William; others
Measurement of the mass composition of ultra-high-energy cosmic rays at the Pierre Auger Observatory
PoS, ICRC2023 :365
20234770.
Costa, Gustavo Morais Rodrigues; Lobosco, Marcelo; Ehrhardt, Matthias; Reis, Ruy Freitas
Mathematical Analysis and a Nonstandard Scheme for a Model of the Immune Response against COVID-19
20234769.
Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal optimization through multi-objective reformulation
European Journal of Operational Research, 311 (2) :427-443
2023
ISSN: 0377-22174768.
[en] Lauer, Patrick; Arnold, Lukas; Brännström, Fabian
Inverse modelling of pyrolization kinetics with ensemble learning methods
Fire Safety Journal
Januar 2023
ISSN: 037971124767.
Relton, Samuel D.; Schweitzer, Marcel
Structured level-2 condition numbers of matrix functions
20234766.
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
20234765.
[german] Gökkus, Yasemin; Kremer, Richard; Zeller, Diana; Bohrmann-Linde, Claudia
H5P angereicherte Videos für den Chemieunterricht und die Lehrkräfteausbildung
In Bohrmann-Linde, C.; Gökkuş, Y.; Kremer, R.; Zeller, D., Editor, Band Netzwerk Digitalisierter Chemieunterricht. Sammelband NeDiChe-Treff 2021
Seite 9-18
Herausgeber: Chemiedidaktik. Bergische Universität Wuppertal
2023
9-184764.
Morejon, Leonel; Kampert, Karl-Heinz
Implementing hadronic interactions in CRPropa to study bursting sources of UHECRs
PoS, ICRC2023 :285
20234763.
4762.
Petrov, Pavel; Matskovskiy, Andrey; Zakharenko, Alena; Zavorokhin, German; Dosso, Stan
Generalized Pekeris-Buldyrev waveguide and its properties
submitted to J. Acoust. Soc. Am.
Juni 20234761.
Jacob, Birgit; Zwart, Hans
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain: An Introduction
20234760.
Schweitzer, Marcel
Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Linear Algebra Appl., 656 :247-276
20234759.
Schweitzer, Marcel
Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Linear Algebra Appl., 656 :247-276
2023
Herausgeber: Elsevier4758.
Lars, Thun
Investigation of time constraints for quality prediction in arc welding using deep learning
20234757.
Costa, Gustavo Morais Rodrigues; Lobosco, Marcelo; Ehrhardt, Matthias; Reis, Ruy Freitas
Mathematical Analysis and a Nonstandard Scheme for a Model of the Immune Response against COVID-19
20234756.
Abdul Halim, Adila; others
Investigations of a Novel Energy Estimator using Deep Learning for the Surface Detector of the Pierre Auger Observatory
PoS, ICRC2023 :275
20234755.
Albi, Giacomo; Ferrarese, Federica; Totzeck, Claudia
Kinetic based optimization enhanced by genetic dynamics
20234754.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Kompetenzförderung durch Erklärvideos in einem Selbstlernbuch zum Einstieg in die Organische Chemie
MNU-Journal, 01.2023 :48-54
2023
ISSN: 0025-58664753.
[german] Zeller, Diana; Bohrmann-Linde, Claudia
Kritischer Umgang mit Videos im naturwissenschaftlichen Unterricht (KriViNat)
In Wilke, T.; Rubner, I., Editor, Band DiCE-Tagung 2023 - Digitalisation in Chemistry Education
Herausgeber: Friedrich-Schiller-Universität Jena, Institut für Anorganische und Analytische Chemie, Jena
2023