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
4903.
Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
20224902.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-nume\-rical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
J. Energy Storage, 45 :103746
2022
Publisher: Elsevier4901.
Bartel, Andreas; Günther, Michael
Multirate schemes—an answer of numerical analysis to a demand from applications
In Günther, Michael and Schilders, Wil, Editor from Mathematics in Industry
Page 5–27
Publisher: Springer Cham
2022
5–274900.
Bartel, Andreas; Günther, Michael
Multirate Schemes -- An Answer of Numerical Analysis to a Demand from Applications
In Michael Günther and Wil Schilders, Editor, Novel Mathematics Inspired by Industrial Challenges
Page 5--27
Publisher: Springer
2022
5--274899.
Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Publisher: Springer Netherlands4898.
Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on {GPU}
JMI, 12 (5)
20224897.
Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Publisher: Springer Netherlands4896.
Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on GPU
Journal of Mathematics in Industry, 12 (1) :1–22
2022
Publisher: Springer Verlag4895.
Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 507 (1) :125761
2022
Publisher: Academic Press4894.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
Journal of Energy Storage, 45 :103746
2022
Publisher: Elsevier4893.
Bartel, Andreas; Günther, Michael
Multirate schemes—an answer of numerical analysis to a demand from applications
Novel Mathematics Inspired by Industrial Challenges
Page 5--27
Publisher: Springer International Publishing Cham
2022
5--274892.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
Journal of Energy Storage, 45 :103746
2022
Publisher: Elsevier4891.
Jäschke, J.; Skrepek, N.; Ehrhardt, M.
Mixed-Dimensional Geometric Coupling of Port-{Hamiltonian} Systems
IMACM preprint 22/04
February 20224890.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
Journal of Energy Storage, 45 :103746
2022
Publisher: Elsevier4889.
4888.
Ehrhardt, Matthias
On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215–228
2022
Publisher: IOS Press4887.
Ehrhardt, Matthias
On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215–228
2022
Publisher: IOS Press4886.
Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 507 (1) :125761
2022
Publisher: Academic Press4885.
Ehrhardt, Matthias
On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215--228
2022
Publisher: IOS Press4884.
Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
On intertwining of maxima of sum of translates functions with nonsingular kernels
Trudy Inst. Mat. Mekh. UrO RAN
20224883.
Glück, Jochen; Martin, Florian G.
Uniform convergence of stochastic semigroups
Israel J. Math., 247 (1) :1--19
20224882.
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
Page 173--194
Publisher: Springer Fachmedien Wiesbaden, Wiesbaden
2022
173--1944881.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
The parareal algorithm and the sparse grid combination technique in the application of the Heston model
Progress in Industrial Mathematics at ECMI 2021, Page 477–483
Publisher: Springer Cham
20224880.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Stochastic Runge-Kutta-Munthe-Kaas methods in the modelling of perturbed rigid bodies
Advances in Applied Mathematics and Mechanics, 14 (2) :528–538
2022
Publisher: Global Science Press4879.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Stochastic Runge-Kutta-Munthe-Kaas methods in the modelling of perturbed rigid bodies
Advances in Applied Mathematics and Mechanics, 14 (2) :528–538
2022
Publisher: Global Science Press