Discontinuous Coarse Space Corrections (DCS) for Optimized Schwarz Methods

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

In this presentation, we explain why continuous coarse spaces are a suboptimal choice when combined with domain decomposition methods that have discontinuous iterates, like Optimized Schwarz Methods (OSM), or Restricted Additive Schwarz methods (RAS). As an alternative, we propose discontinuous coarse spaces for such domain decomposition methods. For linear problems, we explain the design of one particular discontinuous coarse space and present an algorithm that computes an efficient discontinuous coarse space corrector for the special case of an OSM. While the algorithm is suitable for higher dimensions, it has the special property of con- verging in a single coarse iteration for one-dimensional linear problems. We expect Discontinuous Coarse Spaces (DCS) to become standard practice for methods with discontinous iterates in the coming decade.

Domaines: Analyse numérique [math.NA]

Martin J. Gander, Laurence Halpern, Kévin Santugini-Repiquet. Discontinuous Coarse Space Corrections (DCS) for Optimized Schwarz Methods. The Twenty First International Conference on Domain Decomposition Methods, Jun 2012, Rennes, France. ⟨hal-00765824⟩