Volume 45, pp. 524-544, 2016.

An adaptive choice of primal constraints for BDDC domain decomposition algorithms

Juan G. Calvo and Olof B. Widlund


An adaptive choice for primal spaces based on parallel sums is developed for BDDC deluxe methods and elliptic problems in three dimensions. The primal space, which forms the global, coarse part of the domain decomposition algorithm and which is always required for any competitive algorithm, is defined in terms of generalized eigenvalue problems related to subdomain edges and faces; selected eigenvectors associated to the smallest eigenvalues are used to enhance the primal spaces. This selection can be made automatic by using tolerance parameters specified for the subdomain faces and edges. Numerical results verify the results and provide a comparison with primal spaces commonly used. They include results for cubic subdomains as well as subdomains obtained by a mesh partitioner. Different distributions for the coefficients are also considered with constant coefficients, highly random values, and channel distributions.

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Key words

elliptic problems, domain decomposition, BDDC deluxe preconditioners, adaptive primal constraints

AMS subject classifications

65F08, 65N30, 65N35, 65N55

Links to the cited ETNA articles

[14]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

ETNA articles which cite this article

Vol. 46 (2017), pp. 273-336 Clemens Pechstein and Clark R. Dohrmann: A unified framework for adaptive BDDC
Vol. 49 (2018), pp. 1-27 Axel Klawonn, Martin Kühn, and Oliver Rheinbach: Adaptive FETI-DP and BDDC methods with a generalized transformation of basis for heterogeneous problems
Vol. 49 (2018), pp. 28-40 Leszek Marcinkowski and Talal Rahman: Additive average Schwarz with adaptive coarse spaces: scalable algorithms for multiscale problems
Vol. 49 (2018), pp. 64-80 Hyea Hyun Kim, Eric Chung, and Junxian Wang: BDDC and FETI-DP algorithms with a change of basis formulation on adaptive primal constraints
Vol. 52 (2020), pp. 43-76 Axel Klawonn, Martin Kühn, and Oliver Rheinbach: Coarse spaces for FETI-DP and BDDC Methods for heterogeneous problems: connections of deflation and a generalized transformation-of-basis approach
Vol. 53 (2020), pp. 562-591 Alexander Heinlein, Axel Klawonn, Martin Lanser, and Janine Weber: A frugal FETI-DP and BDDC coarse space for heterogeneous problems

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