Abstract
The use of volume-agglomeration for introducing one or several levels of coarse grids in an Additive Schwarz multi-domain algorithm is revisited. The purpose is to build an algorithm applicable to elliptic and convective models. The sub-domain solver is ILU. We rely on algebraic coupling between the coarse grid and the Schwarz preconditioner. The Deflation Method and the Balancing Domain Decomposition (BDD) Method are experimented for a coarse grid as well as domain-by-domain coarse gridding. Standard coarse grids are built with the characteristic functions of the sub-domains. We also consider the building of a set of smooth basis functions (analog to smoothed-aggregation methods). The test problem is the Poisson problem with a discontinuous coefficicent. The two options are compared for the standpoint of coarse-grid consistency and for the gain in scability of the global Schwarz iteration.
MSC2010: 65F04, 65F05
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Alcin, H., Allain, O., Dervieux, A. (2011). Volume-Agglomeration Coarse Grid In Schwarz Algorithm. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_1
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