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Title: Adaptive time-step control for a monolithic multirate scheme coupling the heat and wave equation
Author(s): Soszyńska, Martyna
Richter, ThomasLook up in the Integrated Authority File of the German National Library
Issue Date: 2021
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-1031426
Subjects: Multirate time-stepping
Galerkin time discretization
A posteriori error estimation
Partitioned solution
Abstract: We study the dynamics of a parabolic and a hyperbolic equation coupled on a common interface.We develop time-stepping schemes that can use different time-step sizes for each of the subproblems. The problem is formulated in a strongly coupled (monolithic) space-time framework. Coupling two different step sizes monolithically gives rise to large algebraic systems of equations. There, multiple states of the subproblems must be solved at once. For efficiently solving these algebraic systems, we inherit ideas from the partitioned regime. Therefore we present two decoupling methods, namely a partitioned relaxation scheme and a shooting method. Furthermore, we develop an a posteriori error estimator serving as a mean for an adaptive time-stepping procedure. The goal is to optimally balance the time-step sizes of the two subproblems. The error estimator is based on the dual weighted residual method and relies on the space-time Galerkin formulation of the coupled problem. As an example, we take a linear set-up with the heat equation coupled to the wave equation. We formulate the problem in a monolithic manner using the space-time framework. In numerical test cases, we demonstrate the efficiency of the solution process and we also validate the accuracy of the a posteriori error estimator and its use for controlling the time-step sizes.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2021
Journal Title: BIT
Publisher: Springer Science + Business Media B.V
Publisher Place: Dordrecht [u.a.]
Volume: 61
Original Publication: 10.1007/s10543-021-00854-3
Page Start: 1367
Page End: 1396
Appears in Collections:Fakultät für Mathematik (OA)

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