Volume 49, pp. 28-40, 2018.

Additive average Schwarz with adaptive coarse spaces: scalable algorithms for multiscale problems

Leszek Marcinkowski and Talal Rahman


We present an analysis of the additive average Schwarz preconditioner with two newly proposed adaptively enriched coarse spaces, which were presented at the twenty-third international conference on domain decomposition methods in Korea, for solving second-order elliptic problems with highly varying and discontinuous coefficients. It is shown that the condition number of the preconditioned system is bounded independently of the variations and the jumps in the coefficient while depending only on a prescribed threshold for the eigenvalues of the coarse space, and it depends linearly on the mesh parameter ratio H/h that is the ratio between the subdomain size and the mesh size thereby retaining the same optimality and scalability of the original additive average Schwarz preconditioner.

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Key words

domain decomposition preconditioner, additive average Schwarz method, adaptive coarse space, multiscale finite element

AMS subject classifications

65N55, 65N30, 65N22, 65F08

Links to the cited ETNA articles

[8]Vol. 45 (2016), pp. 524-544 Juan G. Calvo and Olof B. Widlund: An adaptive choice of primal constraints for BDDC domain decomposition algorithms
[24]Vol. 45 (2016), pp. 75-106 Axel Klawonn, Patrick Radtke, and Oliver Rheinbach: A comparison of adaptive coarse spaces for iterative substructuring in two dimensions
[31]Vol. 46 (2017), pp. 273-336 Clemens Pechstein and Clark R. Dohrmann: A unified framework for adaptive BDDC

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