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



2022

4878.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies
AAMM, 14 (2) :528--538
2022
ISSN: 2075-1354

4877.

Kienitz, Jörg
Stochastic volatility – a story of two decades of SABR and Wilmott magazine
Wilmott, 2022 (121) :24–26
2022
Publisher: Wilmott Magazine

4876.

Muniz, M.; Ehrhardt, M.; Günther, M.; Winkler, R.
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
IMACM preprint 22/14
June 2022

4875.

[english] Mertineit, Ann-Kathrin; Schaper, Klaus; Bohrmann-Linde, Claudia; Burdinski, Dirk; Zulauf, Bert; Meuter, Nico; Hackradt, Hans; Kremer, Richard
Teaching Software Skills Using a Freely Accessible Learning Space - an OER Approach
Page 7073-7081
2022

ISBN: 978-84-09-42484-9

4874.

Alvarez, Elena Gómez; Carslaw, Nicola; Dusanter, Sébastien; Edwards, Pete; Gábor Mihucz, Viktor; Heard, Dwayne; Kleffmann, Jörg; Nehr, Sascha; Schoemacker, Coralie; Venables, Dean
Techniques for measuring indoor radicals and radical precursors
Applied Spectroscopy Reviews :1--45
June 2022
ISSN: 0570-4928, 1520-569X

4873.

Kääpä, Alex; Kampert, Karl-Heinz; Mayotte, Eric
The effects of the GMF on the transition from Galactic to extragalactic cosmic rays
PoS, ICRC2021 :004
2022

4872.

Albrecht, Johannes; others
The Muon Puzzle in cosmic-ray induced air showers and its connection to the Large Hadron Collider
Astrophys. Space Sci., 367 (3) :27
2022

4871.

Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
The parareal algorithm and the sparse grid combination technique in the application of the Heston model
Progress in Industrial Mathematics at ECMI 2021, Page 477–483
Publisher: Springer Cham
2022

4870.

Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
The parareal algorithm and the sparse grid combination technique in the application of the Heston model
Progress in Industrial Mathematics at ECMI 2021, Page 477–483
Publisher: Springer Cham
2022

4869.

Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael
The Parareal Algorithm and the Sparse Grid Combination Technique in the Application of the Heston Model
Progress in Industrial Mathematics at ECMI 2021
Page 477--483
Publisher: Springer International Publishing Cham
2022
477--483

4868.

Gerlach, Moritz; Glück, Jochen; Kunze, Markus
Stability of transition semigroups and applications to parabolic equations
To appear in Trans. Amer. Math. Soc.
2022

4867.

Bolten, Matthias; Ekström, S.-E.; Furci, I.; Serra-Capizzano, S.
Toeplitz Momentary Symbols: definition, results, and limitations in the spectral analysis of structured matrices
Linear Algebra Appl., 651 :51-82
2022

4866.

Bolten, M.; Ekström, S.-E.; Furci, I.; Serra-Capizzano, S.
Toeplitz Momentary Symbols: definition, results, and limitations in the spectral analysis of structured matrices
Linear Algebra Appl., 651 :51-82
2022

4865.

Mittendorf, Fabia; Celik, I. E.; Kirsch, S. F.
Total Synthesis of Cryptoconcatone D via Construction of 1,3-Diol Units Using Chiral Horner–Wittig Reagents
The Journal of Organic Chemistry, 87 (21) :14899–14908
2022

4864.

Maharjan, Drishti; Zaspel, Peter
Toward data-driven filters in paraview
JFV, 29 (3)
2022

4863.

Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Tracing locally Pareto optimal points by numerical integration
SIAM Journal on Control and Optimization, 59 (5) :3302-3328
2022

4862.

Ehrhardt, Matthias
Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line
Physics Letters, Section A, 423 :127822
2022
Publisher: Elsevier

4861.

Ehrhardt, Matthias
Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line
Physics Letters, Section A, 423 :127822
2022
Publisher: Elsevier

4860.


Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line
Physics Letters A, 423 :127822
2022
Publisher: North-Holland

4859.

Ud Din, Bashir
Validation of Monte Carlo simulated processes from pp collisions at the LHC using neural networks
2022

4858.

Acu, Ana-Maria; Dancs, Madalina; Heilmann, Margareta; Raşa, Ioan; Paşca, Vlad
Voronovskaya type results for special sequences of operators
RACSAM, 116,19
2022

4857.

Bannenberg, Marcus WFM; Kasolis, Fotios; Günther, Michael; Clemens, Markus
Maximum entropy snapshot sampling for reduced basis modelling
COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 41 (3) :954–966
2022
Publisher: Emerald Publishing

4856.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Stochastic Runge-Kutta-Munthe-Kaas methods in the modelling of perturbed rigid bodies
Advances in Applied Mathematics and Mechanics, 14 (2) :528–538
2022
Publisher: Global Science Press

4855.

Arora, Sahiba; Glück, Jochen
Stability of (eventually) positive semigroups on spaces of continuous functions
C. R., Math., Acad. Sci. Paris, 360 :771--775
2022

4854.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Seserman, Andra
Poisson approximation to the binomial distribution: extensions to the convergence of positive operators
2022