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
- 2025
5385.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5384.
Sinani, Mario; Wynn, Andrew; Palacios, Rafael
Physics-Informed Data-Driven Modelling of Nonlinear Aerodynamic Forces of the Pazy Wing
AIAA SciTech Forum, 6-10 January
01 20255383.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Schrader, Claudia
Produktion eigener VR-Lernsettings im Projekt FoPro-VR. Ein interdisziplinärer Lehransatz für die Lehramtsausbildung
In Mrohs, Lorenz; Franz, Julia; Herrmann, Dominik; Lindner, Konstantin; Staake, Thorsten, Editor, Digitales Lehren und Lernen an der Hochschule. Strategien - Bedingungen - Umsetzung
Seite 191-204
Herausgeber: transcript, Bielefeld
2025
191-204ISBN: 9783839471203
5382.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Searching Permutations for Constructing Uniformly Distributed Point Sets
PNAS
20255381.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
20255380.
Liu, Qian; Yanchang, Zhang; Zuan, Wang; Wang, Miao; Zhao, Xiaowei
Small-signal stability of sequence-decomposed grid-forming IBRs with DC-link voltage dynamics
Februar 20255379.
Arora, Sahiba; Mui, Jonathan
Smoothing of operator semigroups under relatively bounded perturbations
20255378.
Santos, Daniela Dos; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the Multiobejctive Quasi-Clique Problem
European Journal of Operational Research, 323 :409—424
20255377.
Elghazi, Bouchra; Jacob, Birgit; Zwart, Hans
Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation
Januar 20255376.
Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society5375.
Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings5374.
Günther, Michael
Einführung in die Finanzmathematik5373.
Al{\i}, G; Bartel, A
Electrical RLC networks and diodes5372.
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 :5875371.
Ehrhardt, Matthias
für Angewandte Analysis und Stochastik5370.
Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations5369.
High order tensor product interpolation in the Combination Technique
preprint, 14 :255368.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 3885367.
Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers5366.
Günther, Michael
Lab Exercises for Numerical Analysis and Simulation I: ODEs5365.
Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics5364.
Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics5363.
Ehrhardt, Matthias; Günther, Michael
Mathematical Study of Grossman's model of investment in health capital5362.
Bartel, PD Dr A
Mathematische Modellierung in Anwendungen5361.
Model Order Reduction Techniques for Basket Option Pricing