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
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Knechtli, F; Striebel, M; Wandelt, M
Symmetric \& Volume Preserving Projection Schemes5374.
Putek, Piotr; Günther, Michael
Topology Optimization and Analysis of a PM synchronous Machine for Electrical Automobiles5373.
Ehrhardt, Matthias; Günther, Michael
Vorhersage-Modelle am Beispiel des Corona-Virus COVID-195372.
Ehrhardt, Matthias
für Angewandte Analysis und Stochastik5371.
Günther, Michael
Lab Exercises for Numerical Analysis and Simulation I: ODEs5370.
Al{\i}, G; Bartel, A
Electrical RLC networks and diodes- 2025
5369.
Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas
Nonlinear Monte Carlo Methods with Polynomial Runtime for Bellman Equations of Discrete Time High-Dimensional Stochastic Optimal Control Problems
Appl. Math. Optim., 91 (1) :26
20255368.
Kiesling, Elisabeth; Bohrmann-Linde, Claudia
Carbon Capture and Storage - Nachweis von adsorbiertem Kohlenstoffdioxid
Naturwissenschaften im Unterricht Chemie, 1/25 :Versuchskarteikarte
20255367.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Constructing Optimal Star Discrepancy Sets
accepted in Proceedings of the AMS
20255366.
Kunze, Markus; Mui, Jonathan; Ploss, David
Elliptic operators with non-local Wentzell-Robin boundary conditions
20255365.
Song, Yongcun; Wang, Ziqi; Zuazua, Enrique
FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning
Neural Network, 181
Januar 20255364.
Kienitz, J; Moodliyar, L
Gaussian views explained
Wilmott, 2025 (135) :72–77
2025
Herausgeber: Wilmott Magazine5363.
Xu, Zhuo; Tucsnak, Marius
Global Exponential Stabilization for a Simplified Fluid-Particle Interaction System
Januar 20255362.
Bartel, Andreas; Schaller, Manuel
Goal-oriented time adaptivity for port-Hamiltonian systems
Journal of Computational and Applied Mathematics, 461 :116450
2025
ISSN: 0377-04275361.
Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
Computer Physics Communications, 309 :109478
2025
ISSN: 0010-46555360.
Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
Computer Physics Communications, 309 :109478
2025
ISSN: 0010-46555359.
Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators and their application to lattice QCD simulations
PoS, LATTICE2024 :025
20255358.
Günther, Michael
Einführung in die Finanzmathematik- 2025
5357.
Storch, Sonja; Campagna, Davide; Aydonat, Simay; Göstl, Robert
Mechanochemical generation of nitrogen-centred radicals for the formation of tertiary amines in polymers
RSC Mechanochemistry, 2
Januar 20255356.
Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators and their application to lattice QCD simulations
PoS, LATTICE2024 :025
20255355.
Frommer, Andreas; Rinelli, Michele; Schweitzer, Marcel
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
Math. Comp., 94 :801-823
20255354.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5353.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5352.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
20255351.
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