DDFV Schwarz Ventcell algorithms

Martin J. Gander (1) , Laurence Halpern (2) , Florence Hubert (3) , Stella Krell (4, 5)

1 Section de mathématiques [Genève]
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 I2M - Institut de Mathématiques de Marseille
4 COFFEE - COmplex Flows For Energy and Environment
5 LJAD - Laboratoire Jean Alexandre Dieudonné

Over the last five years, classical and optimized Schwarz methods with Robin transmission conditions have been developed for anisotropic elliptic problems discretized by Discrete Duality Finite Volume (DDFV) schemes. We present here the case of higher order transmission conditions in the framework of DDFV. We prove convergence of the algorithm for a large class of symmetric transmission operators, including the discrete Ventcell operator. We also illustrate numerically that using optimized Ventcell transmission conditions leads to much faster algorithms than when using Robin transmission conditions, especially in case of anisotropic elliptic operators.

Mots clés: Discrete Duality Finite Volume schemes; Ventcell transmission conditions; Schwarz algorithms

Domaines: Analyse numérique [math.NA]

Martin J. Gander, Laurence Halpern, Florence Hubert, Stella Krell. DDFV Schwarz Ventcell algorithms. 22nd International Conference on Domain Decomposition Methods, Institute of Computational Science (ICS) of the Università della Svizzera italiana (USI - University of Lugano) Sep 2013, Lugano, Switzerland. ⟨10.1007/978-3-319-18827-0⟩. ⟨hal-01271251⟩