Applied and Computational Mathematics (ACM)

Multirate

Highly integrated electric cicuits show a phenomenon called latency. That is, a processed signal causes activity only in a small subset of the whole circuit (imagine a central processing unit), whereas the other part of the system behaves almost constant over some time - is latent. Such an electric system can be described as coupled system, where the waveforms show different time scales, also refered to as multirate.

More generally, any coupled problem formulation due to coupled physical effects, may cause a multirate problem: image the simulation of car driving on the road, there you need a model for the wheel, the chassis, the dampers, the road,... (cf. co-simulation). Again each system is covered by their own time constant, which might vary over several orders of magnitude comparing different subsystems.

Classical methods cannot exploit this multirate potential, but resolve everything on the finest scale. This causes an over sampling of the latent components. In constrast, Co-simulation or especially dedicated multirate methods are designed to use the inherent step size to resolve the time-domain behaviour of each subystem with the required accuracy. This requires a time-stepping for each.

Group members working in that field

  • Andreas Bartel
  • Michael Günther

Former and ongoing Projects

  • CoMSON
  • ICESTARS
  • 03GUNAVN

Cooperations

Publications



2021

4489.

Donatelli, Marco; Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano; Sesana, Debora
Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2356, 20
2021
ISSN: 1070-5325

4488.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; others
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Partial Differential Equations and Applications, 2 (6) :1--31
2021
Publisher: Springer

4487.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; others
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Partial Differential Equations and Applications, 2 (6) :1–31
2021
Publisher: Springer International Publishing

4486.

Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix sequences
Electron. J. Linear Algebra, 37 :370-386
2021

4485.

Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix sequences
Electron. J. Linear Algebra, 37 :370-386
2021

4484.

Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix sequences
Electron. J. Linear Algebra, 37 :370-386
2021

4483.

Hachtel, Christoph; Bartel, Andreas; Günther, Michael; Sandu, Adrian
Multirate implicit Euler schemes for a class of differential--algebraic equations of index-1
Journal of Computational and Applied Mathematics, 387 :112499
2021
Publisher: North-Holland

4482.

Hachtel, Christoph; Bartel, Andreas; Günther, Michael; Sandu, Adrian
Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
Journal of Computational and Applied Mathematics, 387 :112499
2021
Publisher: North-Holland

4481.

Hachtel, Christoph; Bartel, Andreas; Günther, Michael; Sandu, Adrian
Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
Journal of Computational and Applied Mathematics, 387 :112499
2021
Publisher: North-Holland

4480.

Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :1--33
2021
Publisher: Springer Netherlands

4479.

Lübke, Marco
Neuartige multifunktionelle Tenside auf Basis nachwachsender Rohstoffe
2021

4478.

Claus, L.; Bolten, Matthias
Non-overlapping block smoothers for the Stokes equations
Num. Lin. Alg. Appl., 28 (6) :e2389
2021

4477.

Claus, L.; Bolten, M.
Non-overlapping block smoothers for the Stokes equations
Num. Lin. Alg. Appl., 28 (6) :e2389
2021

4476.

Claus, L.; Bolten, M.
Non-overlapping block smoothers for the Stokes equations
Num. Lin. Alg. Appl., 28 (6) :e2389
2021

4475.

Eichfelder, Gabriele; Klamroth, Kathrin; Niebling, Julia
Nonconvex constrained optimization by a filtering branch and bound
Journal of Global Optimization, 80 :31-61
2021

4474.

Mironchenko, Andrii; Kawan, Christoph; Glück, Jochen
Nonlinear small-gain theorems for input-to-state stability of infinite interconnections
Math. Control Signals Systems, 33 (4) :573--615
2021

4473.

Krämer, Veronika; Barwari, Beawer; Burgmann, Sebastian; Rohde, Martin; Rentschler, Simon; Holzknecht, Christopher; Gmelin, Christoph; Janoske, Uwe
Numerical analysis of an adhering droplet applying an adapted feedback deceleration technique
International Journal of Multiphase Flow, 145 :103808
December 2021
Publisher: Elsevier {BV}

4472.

Jacob, Birgit; Zwart, Hans
Observability for port-Hamiltonian systems
European Control Conference (ECC) :2052-2057
2021

4471.

Markert, Clara; Thinius, Marco; Lehmann, Laura; Heintz, Chris; Stappert, Florian; Wissdorf, Walter; Kersten, Hendrik; Benter, Thorsten; Schneider, Bradley B.; Covey, Thomas R.
Observation of charged droplets from electrospray ionization (ESI) plumes in API mass spectrometers
Analytical and Bioanalytical Chemistry
July 2021
ISSN: 1618-2642, 1618-2650

4470.

Friedhoff, S.; Southworth, B. S.
On "optimal" $h$-independent convergence of parareal and multigrid-reduction-in-time using Runge-Kutta time integration
Numer. Linear Algebra Appl., 28 (3)
2021

4469.

Friedhoff, S.; Southworth, B. S.
On "optimal" $h$-independent convergence of parareal and multigrid-reduction-in-time using Runge-Kutta time integration
Numer. Linear Algebra Appl., 28 (3) :Paper No. e2301, 30
2021

4468.

Friedhoff, S.; Southworth, B. S.
On "optimal" $h$-independent convergence of parareal and multigrid-reduction-in-time using Runge-Kutta time integration
Numer. Linear Algebra Appl., 28 (3) :Paper No. e2301, 30
2021

4467.

Farkas, Bálint; Friesen, Martin; Rüdiger, Barbara; Schroers, Dennis
On a class of stochastic partial differential equations with multiple invariant measures
NoDEA
2021

4466.

Glück, Jochen
On disjointness, bands and projections in partially ordered vector spaces
Positivity and its applications from Trends Math.
Page 141--171
Publisher: Birkhäuser/Springer, Cham
2021
141--171

4465.

Glück, Jochen
On the decoupled Markov group conjecture
Bull. Lond. Math. Soc., 53 (1) :240--247
2021