How does the partition of unity influence SORAS preconditioner?

Marcella Bonazzoli (1) , Xavier Claeys (2) , Frédéric Nataf (3) , Pierre-Henri Tournier (3)

1 IDEFIX - Inversion of Differential Equations For Imaging and physiX
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations

We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reaction-convection-diffusion equation. We focus on two kinds of partitions of unity, and study the dependence on the overlap and on the number of subdomains. In particular, the second kind of partition of unity, which is non-zero in the interior of the whole overlapping region, gives more favorable convergence properties, especially when increasing the overlap width, in comparison with the first kind of partition of unity, whose gradient is zero on the subdomain interfaces and which would be the natural choice for ORAS solver instead.

Mots clés: Partition of unity; Optimized Schwarz preconditioners; Overlapping domain decomposition

Domaines: Analyse numérique [math.NA]

Marcella Bonazzoli, Xavier Claeys, Frédéric Nataf, Pierre-Henri Tournier. How does the partition of unity influence SORAS preconditioner?. Domain Decomposition Methods in Science and Engineering XXVII, 149, Springer Nature Switzerland, pp.61-68, 2024, Lecture Notes in Computational Science and Engineering, ⟨10.1007/978-3-031-50769-4_6⟩. ⟨hal-03882577v2⟩