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Two-level preconditioning for h-version boundary element approximation of hypersingular operator with GenEO

Pierre Marchand 1, 2, 3 Xavier Claeys 1, 2, 3 Pierre Jolivet 4, 5 Frédéric Nataf 1, 5, 2, 3 Pierre-Henri Tournier 5, 2, 3
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 IRIT-APO - Algorithmes Parallèles et Optimisation
IRIT - Institut de recherche en informatique de Toulouse
Abstract : In the present contribution, we consider symmetric positive definite operators stemming from boundary integral equation (BIE), and we study a two-level preconditioner where the coarse space is built using local generalized eigenproblems in the overlap. We will refer to this coarse space as the GenEO coarse space.
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Pierre Marchand, Xavier Claeys, Pierre Jolivet, Frédéric Nataf, Pierre-Henri Tournier. Two-level preconditioning for h-version boundary element approximation of hypersingular operator with GenEO. Numerische Mathematik, Springer Verlag, 2020, 146, pp.597-628. ⟨10.1007/s00211-020-01149-5⟩. ⟨hal-02188771⟩

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