Natural Domain Decomposition Algorithms for the Solution of Time-Harmonic Elastic Waves

@article{Brunet2019NaturalDD,
  title={Natural Domain Decomposition Algorithms for the Solution of Time-Harmonic Elastic Waves},
  author={Romain Brunet and Victorita Dolean and Martin J. Gander},
  journal={SIAM J. Sci. Comput.},
  year={2019},
  volume={42},
  pages={A3313-A3339}
}
We study for the first time Schwarz domain decomposition methods for the solution of the Navier equations modeling the propagation of elastic waves. These equations in the time harmonic regime are difficult to solve by iterative methods, even more so than the Helmholtz equation. We first prove that the classical Schwarz method is not convergent when applied to the Navier equations, and can thus not be used as an iterative solver, only as a preconditioner for a Krylov method. We then introduce… 

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