An adaptive GDSW coarse space for two-level overlapping Schwarz methods in two dimensions. (English) Zbl 1450.65164
Bjørstad, Petter E. (ed.) et al., Domain decomposition methods in science and engineering XXIV. Proceedings of the 24th international conference, Svalbard, Norway, February 6–10, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 125, 373-382 (2018).
Summary: We propose robust coarse spaces for two-level overlapping Schwarz preconditioners, which are extensions of the energy minimizing coarse space known as GDSW (Generalized Dryja, Smith, Widlund). The resulting two-level methods with adaptive coarse spaces are robust for second order elliptic problems in two dimensions, even in presence of a highly heterogeneous coefficient function, and reduce to the standard GDSW algorithm if no additional coarse basis functions are used.
For the entire collection see [Zbl 1430.65002].
For the entire collection see [Zbl 1430.65002].
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 35J15 | Second-order elliptic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
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