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



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: Elsevier

5384.

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 2025

5383.

[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
191-204

ISBN: 9783839471203

5382.

Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Searching Permutations for Constructing Uniformly Distributed Point Sets
PNAS
2025

5381.

Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
2025

5380.

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 2025

5379.

Arora, Sahiba; Mui, Jonathan
Smoothing of operator semigroups under relatively bounded perturbations
2025

5378.

Santos, Daniela Dos; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the Multiobejctive Quasi-Clique Problem
European Journal of Operational Research, 323 :409—424
2025

5377.

Elghazi, Bouchra; Jacob, Birgit; Zwart, Hans
Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation
Januar 2025

5376.

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

5375.

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

5374.

Günther, Michael
Einführung in die Finanzmathematik

5373.

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

5372.

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

5371.

Ehrhardt, Matthias
für Angewandte Analysis und Stochastik

5370.

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

5369.


High order tensor product interpolation in the Combination Technique
preprint, 14 :25

5368.

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

5367.

Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers

5366.

Günther, Michael
Lab Exercises for Numerical Analysis and Simulation I: ODEs

5365.

Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics

5364.

Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics

5363.

Ehrhardt, Matthias; Günther, Michael
Mathematical Study of Grossman's model of investment in health capital

5362.

Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

5361.


Model Order Reduction Techniques for Basket Option Pricing