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Communication Dans Un Congrès Année : 2022

On the links between observed and theoretical convergence rates for Schwarz waveform relaxation algorithm for the time-dependent problems

Résumé

In the framework of linear problems, a usual approach to study the convergence of Schwarz algorithms is to calculate the convergence rate in the frequency domain. However, for time-dependent problems, this tool provides results not fully representative of the observed behaviour of the algorithm. In this article we highlight differences between the theoretical convergence rate and the convergence observed in the physical space-time domain. We also explain how the theoretical convergence rate can be used to provide bounds to the observed convergence rate obs. For problems defined on time windows of finite size, we recall that the bounds usually considered to study the convergence are empirical estimates albeit robust. In conclusion of this paper, numerical experiments are carried out to illustrate the relevance of the theoretical analysis.
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Dates et versions

hal-03654199 , version 1 (28-04-2022)

Identifiants

  • HAL Id : hal-03654199 , version 1

Citer

Sophie Thery. On the links between observed and theoretical convergence rates for Schwarz waveform relaxation algorithm for the time-dependent problems. DD2020 - 26th International Domain Decomposition Conference, Dec 2020, Hong Kong, China. pp.1-9. ⟨hal-03654199⟩
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