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



2024

6995.

Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 2024

6994.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Spectral analysis of a class of linear hyperbolic partial differential equations
03 2024

6993.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Linear-Quadratic optimal control for boundary controlled networks of waves
02 2024

6992.

Celik, I. E.; Mittendorf, Fabia; Gómez-Suárez, Adrián; Kirsch, S. F.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 9
02 2024
Publisher: Elsevier
ISSN: 2666-951X

6991.

Bensberg, Kathrin; Savvidis, Athanasios; Ballaschk, Frederic; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry - A European Journal, 2024 :e202304011
02 2024
Publisher: Wiley
ISSN: 0947-6539

6990.

[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
February 2024

6989.

[english] Wiebel, Michelle; Bensberg, Kathrin; Wende, Luca; Grandrath, Rebecca; Plitzko, Kathrin; Bohrmann-Linde, Claudia; Kirsch, Stefan F.; Schebb, Nils Helge
Efficient and simple extraction protocol for triterpenic acids from apples
Journal of Chemical Education
2024
Publisher: American Chemical Society and Division of Chemical Education, Inc.

6988.

Krhac, Kaja; Maschke, Bernhard; van der Schaft, Arjan
Port-Hamiltonian systems with energy and power ports
2024

6987.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6986.

Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics

6985.

Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics

6984.

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

6983.

Ehrhardt, M; Günther, M; Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

6982.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6981.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6980.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6979.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

6978.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6977.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

6976.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Page 377

6975.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Page 377

6974.

Putek, Piotr; PAPLICKI, Piotr; Pulch, Roland; Maten, Jan; Günther, Michael; PA{\L}KA, Ryszard
NONLINEAR MULTIOBJECTIVE TOPOLOGY OPTIMIZATION AND MULTIPHYSICS ANALYSIS OF A PERMANENT-MAGNET EXCITED SYNCHRONOUS MACHINE

6973.

Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs

6972.

Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model

6971.

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

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