Continuous Analysis of the Additive Schwarz Method: a Stable Decomposition in $H^1$

Martin J. Gander (1) , Laurence Halpern (2) , Kévin Santugini-Repiquet (3, 4)

1 Section de mathématiques [Genève]
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 IMB - Institut de Mathématiques de Bordeaux
4 MC2 - Modélisation, contrôle et calcul

The classical convergence result for the additive Schwarz preconditioner with coarse grid is based on a stable decomposition. The result holds for discrete versions of the Schwarz preconditioner, and states that the preconditioned operator has a uniformly bounded condition number that depends only on the number of colors of the domain decomposition, and the ratio between the average diameter of the subdomains and the overlap width.

Domaines: Analyse numérique [math.NA]

Martin J. Gander, Laurence Halpern, Kévin Santugini-Repiquet. Continuous Analysis of the Additive Schwarz Method: a Stable Decomposition in $H^1$. 2010. ⟨hal-00462006v1⟩