Two-level algebraic domain decomposition preconditioners using Jacobi-Schwarz smoother and adaptive coarse grid corrections

Hua Xiang (1) , Frédéric Nataf (2, 3)

1 Department of Mathematics [Wuhan]
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
3 LJLL - Laboratoire Jacques-Louis Lions

We investigate two-level preconditioners on the extended linear system arising from the domain decomposition method. The additive Schwarz method is used as a smoother, and the coarse grid space is constructed by using the Ritz vectors obtained in the Arnoldi process. The coarse grid space can be improved adaptively as the Ritz vectors become a better approximation of the eigenvectors. Numerical tests on the model problem demonstrate the efficiency.

Domaines: Analyse numérique [math.NA]

Hua Xiang, Frédéric Nataf. Two-level algebraic domain decomposition preconditioners using Jacobi-Schwarz smoother and adaptive coarse grid corrections. Journal of Computational and Applied Mathematics, 2014, 261, pp.1-13. ⟨10.1016/j.cam.2013.10.027⟩. ⟨hal-01094008⟩