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



6931.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

6930.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov Operators
submitted
2024

6929.

Hoang, Manh Tuan; Ehrhardt, Matthias
A second-order nonstandard finite difference method for a general Rosenzweig-MacArthur predator--prey model
Journal of Computational and Applied Mathematics :115752
2024
Publisher: Elsevier

6928.

Jacob, Birgit; Günther, Michael; Ehrhardt, Matthias
Analysis and Numerics of port-Hamiltonian systems Schedule (Start of Seminar: Oct 26, 2022)

6927.

Ehrhardt, M
Asymptotische Analysis Vorlesungszeiten

6926.

Ehrhardt, Matthias
Computerunterstützte Mathematik Zeiten

6925.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society

6924.

Tripiccione, Betreuer Raffaele; Ehrhardt, Matthias; Alexandrou, Constantia; Toschi, Federico; Simma, Hubert; Schifano, Co-Betreuer Sebastiano Fabio
Daniele Simeoni 1836010

6923.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

6922.

Günther, Michael
Einführung in die Finanzmathematik

6921.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Page 388

6920.

Al{\i}, G; Bartel, A; Günther, M
Electrical RLC networks and diodes

6919.

Gjonaj, Erion; Bahls, Christian Rüdiger; Bandlow, Bastian; Bartel, Andreas; Baumanns, Sascha; Belzen, F; Benderskaya, Galina; Benner, Peter; Beurden, MC; Blaszczyk, Andreas; others
Feldmann, Uwe, 143 Feng, Lihong, 515 De Gersem, Herbert, 341 Gim, Sebasti{\'a}n, 45, 333
MATHEMATICS IN INDUSTRY 14 :587

6918.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6917.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6916.

Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations

6915.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6914.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6913.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

6912.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

6911.

Günther, Michael; Kossaczk{\`y}, Igor
Lab Exercises for Numerical Analysis and Simulation I: ODEs

6910.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Publisher: Springer

6909.

Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
arXiv preprint arXiv:2401.17954
2024

6908.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Publisher: World Scientific

6907.

Günther, M; Ehrhardt, M; Knechtli, F; Shcherbakov, D; Striebel, M; Wandelt, M
Symmetric \& Volume Preserving Projection Schemes

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