research-article

Preconditioned Dynamic Iteration for Coupled Differential-Algebraic Systems

Authors:

Michael GüntherAuthors Info & Claims

Volume 41, Issue 1

Pages 1 - 25

https://doi.org/10.1023/A:1021909032551

Published: 01 January 2001 Publication History

Abstract

The network approach to the modelling of complex technical systems results frequently in a set of differential-algebraic systems that are connected by coupling conditions. A common approach to the numerical solution of such coupled problems is based on the coupling of standard time integration methods for the subsystems. As a unified framework for the convergence analysis of such multi-rate, multi-method or dynamic iteration approaches we study in the present paper the convergence of a dynamic iteration method with a (small) finite number of iteration steps in each window. Preconditioning is used to guarantee stability of the coupled numerical methods. The theoretical results are applied to quasilinear problems from electrical circuit simulation and to index-3 systems arising in multibody dynamics.

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Cited By

Eguillon YLacabanne BTromeur-Dervout D(2023)MISSILESJournal of Computational and Applied Mathematics10.1016/j.cam.2022.115013424:COnline publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.cam.2022.115013
Bartel AGünther MJacob BReis T(2023)Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systemsNumerische Mathematik10.1007/s00211-023-01369-5155:1-2(1-34)Online publication date: 20-Sep-2023
https://dl.acm.org/doi/10.1007/s00211-023-01369-5
Eguillon YLacabanne BTromeur-Dervout D(2022)FORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilitiesEngineering with Computers10.1007/s00366-022-01610-z38:5(4501-4543)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00366-022-01610-z
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Index Terms

Preconditioned Dynamic Iteration for Coupled Differential-Algebraic Systems
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Computations on matrices

Index terms have been assigned to the content through auto-classification.

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cover image BIT

BIT Volume 41, Issue 1

Jan 2001

214 pages

ISSN:0006-3835

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Copyright © 2001 Swets & Zeitlinger.

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BIT Computer Science and Numerical Mathematics

United States

Publication History

Published: 01 January 2001

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Cited By

Eguillon YLacabanne BTromeur-Dervout D(2023)MISSILESJournal of Computational and Applied Mathematics10.1016/j.cam.2022.115013424:COnline publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.cam.2022.115013
Bartel AGünther MJacob BReis T(2023)Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systemsNumerische Mathematik10.1007/s00211-023-01369-5155:1-2(1-34)Online publication date: 20-Sep-2023
https://dl.acm.org/doi/10.1007/s00211-023-01369-5
Eguillon YLacabanne BTromeur-Dervout D(2022)FORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilitiesEngineering with Computers10.1007/s00366-022-01610-z38:5(4501-4543)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00366-022-01610-z
Hafner IPopper N(2021)Convergence Properties of Hierarchical Co-simulation ApproachesSoftware Engineering and Formal Methods. SEFM 2021 Collocated Workshops10.1007/978-3-031-12429-7_12(156-172)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.1007/978-3-031-12429-7_12
Gomes CThule CBroman DLarsen PVangheluwe H(2018)Co-SimulationACM Computing Surveys10.1145/317999351:3(1-33)Online publication date: 23-May-2018
https://dl.acm.org/doi/10.1145/3179993
Gomes CThule CDeantoni JLarsen PVangheluwe H(2018)Co-simulation: The Past, Future, and Open ChallengesLeveraging Applications of Formal Methods, Verification and Validation. Distributed Systems10.1007/978-3-030-03424-5_34(504-520)Online publication date: 5-Nov-2018
https://dl.acm.org/doi/10.1007/978-3-030-03424-5_34
Kassiotis CIbrahimbegovic ANiekamp RMatthies H(2011)Nonlinear fluid---structure interaction problem. Part IComputational Mechanics10.1007/s00466-010-0545-647:3(305-323)Online publication date: 1-Mar-2011
https://dl.acm.org/doi/10.1007/s00466-010-0545-6

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