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

6956.

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, 2024
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X

6955.

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 Eropean Journal, e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-6539

6954.

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

6953.

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

6952.

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

6951.

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

6950.

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

6949.

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

6948.

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

6947.

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

6946.

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

6945.

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

6944.

Petrov, Pavel S; Ehrhardt, Matthias; Kozitskiy, Sergey B
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration :118304
2024
Herausgeber: Elsevier

6943.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csomós, Petra; Faragó, István; Fekete, Imre; others
Invited Papers

6942.

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

6941.

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

6940.

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

6939.

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

6938.

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

6937.

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

6936.

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

6935.

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

6934.

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

6933.

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

6932.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csom{\'o}s, Petra; Farag{\'o}, Istv{\'a}n; Fekete, Imre; others
Invited Papers

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