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
- 2022
4552.
Heyden, von der, Lisa; Wissdorf, Walter; Kurtenbach, Ralf; Kleffmann, Jörg
A relaxed eddy accumulation (REA) LOPAP system for flux measurements of nitrous acid (HONO)
Atmospheric Measurement Techniques, 15 (6) :1983--2000
März 2022
ISSN: 1867-85484551.
Schweitzer, Marcel
Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian
Electron. Trans. Numer. Anal., 55 :438-454
20224550.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
A deep smoothness WENO method with applications in option pricing
Progress in Industrial Mathematics at ECMI 2021
Seite 417--423
Herausgeber: Springer International Publishing Cham
2022
417--4234549.
Wahdan, Shayma
Measurements of observables sensitive to colour reconnection in $t\bar{t}$ events with the ATLAS detector at $\sqrt{s}$ = 13 TeV
Bergische Universitaet Wuppertal
20224548.
Budde, Christian; Dobrick, Alexander; Glück, Jochen; Kunze, Markus
A monotone convergence theorem for strong Feller semigroups
20224547.
Hermle, Patrick; Kreidler, Henrik
A Halmos-von Neumann theorem for actions of general groups
20224546.
Edeko, Nikolai; Kreidler, Henrik; Nagel, Rainer
A dynamical proof of the van der Corput inequality
Dynamical Systems, 37 :648-665
20224545.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
A deep smoothness WENO method with applications in option pricing
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021, Seite 417–423
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224544.
Kossaczk{\'a}, Tatiana; Ehrhardt, Matthias; Günther, Michael
A deep smoothness WENO method with applications in option pricing
Progress in Industrial Mathematics at ECMI 2021
Seite 417--423
Herausgeber: Springer International Publishing Cham
2022
417--4234543.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A combined method for stability analysis of linear time invariant and nonlinear continuous-time control systems based on the Hermite-Fujiwara matrix and Cholesky decomposition
20224542.
Kossaczka, T; Ehrhardt, Matthias; Günther, Michael
A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing4541.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A combined method for stability analysis of linear time invariant and nonlinear continuous-time control systems based on the Hermite-Fujiwara matrix and Cholesky decomposition
20224540.
Arora, Sahiba; Glück, Jochen
A characterization of the individual maximum and anti-maximum principle
20224539.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A Characteristic Boundary Condition for Multispeed Lattice Boltzmann Methods
Accepted at Commun. Comput. Phys.
20224538.
Acu, Ana-Maria; Dancs, Madalina; Heilmann, Margareta; Raşa, Ioan; Paşca, Vlad
A Bernstein-Schnabl type operator
Applicable Analysis and Discrete Mathematics, 16(2) :495-507
20224537.
[german] Zeller, Diana; Bohrmann-Linde, Claudia
#debunk YouTube-Videos - Ein didaktisches Konzept zum Einsatz von Videos im Chemieunterricht zur Stärkung der Digital Scientific Literacy
MNU journal, 75 (03) :197-201
20224536.
Burgmann, Sebastian; Krämer, Veronika; Dues, Michael; Steinbock, Jonas; Büttner, Lars; Czarske, Juergen; Janoske, Uwe
tm - Technisches Messen, 89 (3) :178--188
20224535.
Kossaczka, T; Ehrhardt, M; Günther, M
A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing LLC4534.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-reflecting boundary condition for multispeed lattice Boltzmann methods
In M. Ehrhardt and M. Günther, Editor, Accepted at Progress in Industrial Mathematics at ECMI 2021
Herausgeber: Springer-Verlag, Berlin
2022ISBN: 978-3-031-11817-3
4533.
Jacob, Birgit; Schwenninger, Felix; Wintermayr, Jens
A refinement of Boillon's theorem on maximal regularity
Studia Math., 263 (2) :141-158
20224532.
Berkhahn, Sarah; Ehrhardt, Matthias
A physics-informed neural network to model COVID-19 infection and hospitalization scenarios
Advances in Continuous and Discrete Models, 2022 (1) :61
2022
Herausgeber: Springer International Publishing Cham4531.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78–94
2022
Herausgeber: Taylor & Francis4530.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78--94
2022
Herausgeber: Taylor \& Francis4529.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A Port-Hamiltonian Formulation of Coupled Heat Transfer
Math. Comput. Model. Dyn. Syst., 28 (1) :78-94
20224528.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78--94
2022
Herausgeber: Taylor & Francis