Applied and Computational Mathematics (ACM)

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

4853.

Kienitz, J.; McWalter, T. A.; Rudd, R.; Platen, E.
Quantization methods for stochastic differential equations
In Günther, Michael and Schilders, Wil, Editor from Mathematics in Industry
Page 299–329
Publisher: Springer Cham
2022
299–329

4852.

Amin Zargaran, Uwe Janoske
Prediction of the mixing efficiency in rotor-stator system for high viscous mixtures based on a combined Lagrangian particle approach with an Immersed-Boundary Method
September 2022

4851.


Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor from Mathematics in Industry
Publisher: Springer Cham
2022

ISBN: 978-3-031-11817-3

4850.


Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor from Mathematics in Industry
Publisher: Springer Cham
2022

ISBN: 978-3-031-11817-3

4849.


Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor from Mathematics in Industry
Publisher: Springer Cham
2022

ISBN: 978-3-031-11817-3

4848.

Ehrhardt, Matthias; Günther, Michael
Progress in Industrial Mathematics at ECMI 2021
2022

4847.

Kääpä, Alex; Kampert, Karl-Heinz; Mayotte, Eric
Propagation of extragalactic cosmic rays in the Galactic magnetic field
PoS, EPS-HEP2021 :088
2022

4846.

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
Publisher: Academic Press

4845.

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
Publisher: Academic Press

4844.

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
Publisher: Academic Press

4843.

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
Publisher: Abstract accepted
2022

4842.

Kienitz, J.; McWalter, T. A.; Rudd, R.; Platen, E.
Quantization methods for stochastic differential equations
In Günther, Michael and Schilders, Wil, Editor from Mathematics in Industry
Page 299–329
Publisher: Springer Cham
2022
299–329

4841.

Addazi, A.; others
Quantum gravity phenomenology at the dawn of the multi-messenger era-A review
Prog. Part. Nucl. Phys., 125 :103948
2022

4840.

Kienitz, Jörg
Semi-analytical conditional expectations
Risk Cutting Edge, 7
2022
Publisher: Incisive Media

4839.

Bensberg, Kathrin; Kirsch, S. F.
Reactions with Geminal Diazides: Long Known, Full of Surprises, and New Opportunities
Synthesis, 54 (20) :4447-4460
2022
Publisher: Thieme
ISSN: 0039-7881

4838.

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
Publisher: SpringerOpen

4837.

Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :12
2022
Publisher: Springer Verlag

4836.

Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :12
2022
Publisher: Springer Verlag

4835.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems
arXiv preprint arXiv:2206.03772
2022

4834.

Rudd, Ralph; McWalter, Thomas; Kienitz, Jörg; Platen, Eckhard
Robust product Markovian quantization
The Journal of Computational Finance, 25 (4) :55–78
2022
Publisher: Incisive Media

4833.

Vorländer, Anna
Search for high-mass resonances in dilepton final states with associated b-jets at the ATLAS experiment
2022

4832.

Austrup, Volker Andreas
Search for scalar and vector leptoquarks decaying into quarks and leptons of different generations
Bergische Universitaet Wuppertal
2022

4831.

Roggel, Jens
Search for vector-like partners of the top and bottom quarks with the ATLAS experiment
Wuppertal U.
2022

4830.

Abreu, Pedro; others
Searches for Ultra-High-Energy Photons at the Pierre Auger Observatory
Universe, 8 (11) :579
2022

4829.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research :1--23
2022
Publisher: Springer