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
4602.
Ehrhardt, Matthias; Günther, Michael
Progress in Industrial Mathematics at ECMI 2021
20224601.
Ehrhardt, Matthias; Günther, Michael
Progress in Industrial Mathematics at ECMI 2021
20224600.
Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor aus Mathematics in Industry
Herausgeber: Springer Cham
2022ISBN: 978-3-031-11817-3
4599.
Kääpä, Alex; Kampert, Karl-Heinz; Mayotte, Eric
Propagation of extragalactic cosmic rays in the Galactic magnetic field
PoS, EPS-HEP2021 :088
20224598.
Ankirchner, Stefan; Kruse, Thomas; Löhr, Wolfgang; Urusov, Mikhail
Properties of the EMCEL scheme for approximating irregular diffusions
Journal of Mathematical Analysis and Applications, 509 (1) :125931
2022
Herausgeber: Academic Press4597.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems
arXiv preprint arXiv:2206.03772
20224596.
Sabirov, KK; Yusupov, JR; Ehrhardt, M; Matrasulov, DU
Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line
Physics Letters A, 423 :127822
2022
Herausgeber: North-Holland4595.
Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Tracing locally Pareto optimal points by numerical integration
SIAM Journal on Control and Optimization, 59 (5) :3302-3328
20224594.
Haussmann, N.; Clemens, M.
Quantifizierung der Unsicherheit bei der Expositionsbestimmung des menschlichen Körpers durch niederfrequente Magnetfelder auf GPUs mit Monte-Carlo Simulationen
URSI e.V. Deutschland 2022 Kleinheubacher Tagung (KHB 2022)
Miltenberg, Germany
Herausgeber: Abstract accepted
20224593.
Addazi, A.; others
Quantum gravity phenomenology at the dawn of the multi-messenger era-A review
Prog. Part. Nucl. Phys., 125 :103948
20224592.
Maharjan, Drishti; Zaspel, Peter
Toward data-driven filters in paraview
JFV, 29 (3)
20224591.
Reactions with Geminal Diazides: Long Known, Full of Surprises, and New Opportunities
Synthesis, 54 (20) :4447-4460
2022
Herausgeber: Thieme
ISSN: 0039-78814590.
Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :1--13
2022
Herausgeber: SpringerOpen4589.
Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :12
2022
Herausgeber: Springer Verlag4588.
Zang, Martin; Haussmann, Norman; Mease, Robin; Stroka, Steven; Clemens, Markus; Burkert, Amelie; Popp, Alexander; Schmülling, Benedikt
Personenschutz bei induktivem Laden von Fahrzeugbatterien -- Ansätze zur praktikablen Echtzeitbestimmung der magneto-quasistatischen Körperexposition
In Proff, Heike, Editor
Seite 173--194
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2022
173--1944587.
Voss C., Janoske U.
A surrogate approach to rapidly predict particle collection on single fiber using computational fluid dynamics and machine learning
Machine Learning und Artificial Intelligence in Strömungsmechanik und Strukturanalyse
Herausgeber: NAFEMS
Mai 20224586.
Jäschke, J.; Skrepek, N.; Ehrhardt, M.
Mixed-Dimensional Geometric Coupling of Port-{Hamiltonian} Systems
IMACM preprint 22/04
Februar 20224585.
4584.
Villena, Guillermo; Kleffmann, Jörg
A source for the continuous generation of pure and quantifiable HONO mixtures
Atmospheric Measurement Techniques, 15 (3) :627--637
Februar 2022
ISSN: 1867-85484583.
Bolten, M.; Donatelli, M.; Ferrari, P.; Furci, I.
A symbol based analysis for multigrid methods for block-circulant and block-Toeplitz Systems
SIAM J. Matrix Anal. Appl., 43 (1) :405-438
20224582.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
A symbol-based analysis for multigrid methods for block-circulant and block-Toeplitz systems
SIAM J. Matrix Anal. Appl., 43 (1) :405-438
2022
ISSN: 0895-47984581.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
A symbol-based analysis for multigrid methods for block-circulant and block-Toeplitz systems
SIAM J. Matrix Anal. Appl., 43 (1) :405-438
2022
ISSN: 0895-47984580.
Jäschke, Jens; Ehrhardt, M.; Günther, M.; Jacob, Birgit
A Two-Dimensional Port-Hamiltonian Model for Coupled Heat Transfer
Mathematics, 10(24) :4635
20224579.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A Two-Dimensional Port-Hamiltonian Model for Coupled Heat Transfer
Mathematics, 10 (24) :4635
2022
Herausgeber: MDPI4578.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A Two-Dimensional Port-Hamiltonian Model for Coupled Heat Transfer
Mathematics, 10 (24) :4635
2022
Herausgeber: MDPI