Abstract
We describe a BDDC algorithm, see e.g., [1], and an adaptive coarse space enforced by a transformation of basis for the iterative solution of scalar diffusion problems with a discontinuous diffusion coefficient. The coefficient varies over several orders of magnitude both inside of the subdomains and along the interface. A related algorithm for FETI-DP with a balancing preconditioner has been already described in [6, 7]. Other adaptive coarse space constructions for FETI, FETI-DP, and BDDC methods have been proposed in [8, 10]. We also present some preliminary numerical results for different scalings, including the recent deluxe scaling; cf., [2].
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Klawonn, A., Radtke, P., Rheinbach, O. (2016). Adaptive Coarse Spaces for BDDC with a Transformation of Basis. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_29
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DOI: https://doi.org/10.1007/978-3-319-18827-0_29
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