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

4903.

Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
2022

4902.

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: Elsevier

4901.

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
5–27

4900.

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--27

4899.

Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Publisher: Springer Netherlands

4898.

Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on {GPU}
JMI, 12 (5)
2022

4897.

Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Publisher: Springer Netherlands

4896.

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 Verlag

4895.

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 Press

4894.

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: Elsevier

4893.

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--27

4892.

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: Elsevier

4891.

Jäschke, J.; Skrepek, N.; Ehrhardt, M.
Mixed-Dimensional Geometric Coupling of Port-{Hamiltonian} Systems
IMACM preprint 22/04
February 2022

4890.

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: Elsevier

4889.

Gerlach, Moritz; Glück, Jochen
On characteristics of the range of integral operators
2022

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 Press

4887.

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 Press

4886.

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 Press

4885.

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 Press

4884.

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
2022

4883.

Glück, Jochen; Martin, Florian G.
Uniform convergence of stochastic semigroups
Israel J. Math., 247 (1) :1--19
2022

4882.

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--194

4881.

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
2022

4880.

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

4879.

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