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



2023

5060.

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
Preprint
2023

5059.

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
2023

5058.

Müller, Mats; Kemper, Svenja; Schlenkhoff, Andreas
Numerical modelling of the hydraulic capacity of grates inlets (OpenFOAM)
E-proceedings of the 40th IAHR World Congress in 2023 in Vienna, Austria.
2023

5057.

Ehrhardt, Matthias; Kozitskiy, Sergey B
On a generalization of the split-step Padé method to the case of unknown vector-functions
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal

5056.

Ehrhardt, Matthias; Kozitskiy, Sergey B
On a generalization of the split-step Padé method to the case of unknown vector-functions
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal

5055.

Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
Integral Equations and Operator Theory, 95 :Paper No. 15
2023

5054.

Soroking, Mikhail; Petrov, Pavel; Budyansky, Maxim; Fayman, Pavel; Didov, Alexandr; Golov, Alexandr; Morgunov, Yuri
On the effect of horizontal refraction caused by an anticyclonic eddy in the case of long-range sound propagation in the Sea of Japan
J. Marine Sci. Eng. , 11 (9)
Juni 2023

5053.

Kraus, Konstantin; Klamroth, Kathrin; Stiglmayr, Michael
On the online path extension problem -- Location and routing problems in board games
2023

5052.

Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Accepted at Numerische Mathematik
2023

5051.

Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numerische Mathematik, 155 (1-2) :1–34
2023
Herausgeber: Springer New York

5050.

Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numerische Mathematik, 155 (1-2) :1–34
2023
Herausgeber: Springer New York

5049.

Bartel, A.; Günther, M.; Jacob, Birgit; Reis, T.
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numer. Math., 155 (1-2) :1-34
2023

5048.

Farkas, Bálint; Jacob, Birgit; Reis, Timo; Schmitz, Merlin
Operator splitting based dynamic iteration for linear infinite-dimensional port-Hamiltonian systems
2023

5047.

Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
arXiv preprint arXiv:2304.01766
2023

5046.

Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
Preprint
2023

5045.

Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
Preprint
2023

5044.

Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael
Operator splitting for semi-explicit differential-algebraic equations and port-Hamiltonian DAEs
Preprint
2023

5043.

Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael
Operator splitting for semi-explicit differential-algebraic equations and port-Hamiltonian DAEs
Preprint
2023

5042.

Doganay, Onur Tanil; Klamroth, Kathrin; Lang, Bruno; Stiglmayr, Michael; Totzeck, Claudia
Optimal control for port-Hamiltonian systems and a new perspective on dynamic network flow problems
2023

5041.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal optimization through multi-objective reformulation
European Journal of Operational Research, 311 (2) :427-443
2023
ISSN: 0377-2217

5040.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Anh Nguyen, Tuan
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Journal of Numerical Mathematics, 31 (1) :1–28
2023
Herausgeber: De Gruyter

5039.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Anh Nguyen, Tuan
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Journal of Numerical Mathematics, 31 (1) :1–28
2023
Herausgeber: De Gruyter

5038.

Alves, A. Augusto; others
Parallel processing of radio signals and detector arrays in CORSIKA 8
PoS, ICRC2023 :469
2023

5037.

Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
Journal of Computational Physics, 488 :112211
2023

5036.

Heldmann, Fabian; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
Journal of Computational Physics, 488 :112211
2023
Herausgeber: Academic Press