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



scheduled 2023

6180.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer
scheduled 2023

6179.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

6178.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6177.

Teng, Long; Ehrhardt, Matthias; G\"unther, Michael
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific
scheduled 2023

6176.

{Duffy, D.; Kienitz, J.}
Monte Carlo Frameworks - Building Customisable and High-performance C++ Applications
Herausgeber: {John Wiley \& Sons, Chichester}

6175.

{Kienitz, J.}
Stochastic Processes in Finance I
{Wilmott Magazine}

6174.

{Kienitz, J.}
Stochastic Processes in Finance II
{Wilmott Magazine}, {6}

6173.

{Kienitz, J.}
Stochastic Processes in Finance III
{Wilmott Magazine}
{2009}

6172.

{Beyer, P.; Kienitz, J.}
{Pricing {F}orward {S}tart {O}ption in {M}odels based on {L}évy {P}rocesses}
{The Icfai University Journal of Derivatives Markets}, {6(2)} :{7--23}
{2009}

6171.

{Kienitz, J.}
{The {CGMY} model}
{The Encyclopedia of Quantitative Finance (ed. Cont), Wiley}
{2009}

6170.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

6169.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

6168.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

6167.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer
2023

6166.

Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
2023

6165.

Bauß, Julius; Stiglmayr, Michael
Augmenting Biobjective Branch \& Bound with Scalarization-Based Information
Submitted to Mathematical Methods of Operations Research
2023
Herausgeber: arXiv

6164.

Carrillo, Jose Antonio; Totzeck, Claudia; Vaes, Urbain
Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints
, Modeling and Simulation for Collective Dynamics,Lecture Notes Series, Institute for Mathematical Sciences, NUS Band 40
2023

6163.

[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Kompetenzförderung durch Erklärvideos in einem Selbstlernbuch zum Einstieg in die Organische Chemie
MNU-Journal, 01.2023 :48-54
2023
ISSN: 0025-5866

6162.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6161.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Mit Lactase und Lactose zum elektrischen Strom - enzymatische Brennstoffzellen auf Filterpapierbasis für den Chemieunterricht.
CHEMKON, 30 (1) :37-41
Januar 2023

6160.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
2023

6159.

[english] Rendon-Enriquez, Ibeth; Palma-Cando, Alex; Körber, Florian; Niebisch, Felix; Forster, Michael; Tausch, Michael W.; Scherf, Ullrich
Thin Polymer Films by Oxidative or Reductive Electropolymerization and Their Application in Electrochromic Windows and Thin-Film Sensors
molecules, 28 (2) :883
Januar 2023

6158.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6157.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6156.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

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