Volume 51, pp. 432-450, 2019.

Preconditioning the coarse problem of BDDC methods ‐ three-level, algebraic multigrid, and vertex-based preconditioners

Axel Klawonn, Martin Lanser, Oliver Rheinbach, and Janine Weber


A comparison of three Balancing Domain Decomposition by Constraints (BDDC) methods with an approximate coarse space solver using the same software building blocks is attempted for the first time. The comparison is made for a BDDC method with an algebraic multigrid preconditioner for the coarse problem, a three-level BDDC method, and a BDDC method with a vertex-based coarse preconditioner. It is new that all methods are presented and discussed in a common framework. Condition number bounds are provided for all approaches. All methods are implemented in a common highly parallel scalable BDDC software package based on PETSc to allow for a simple and meaningful comparison. Numerical results showing the parallel scalability are presented for the equations of linear elasticity. For the first time, this includes parallel scalability tests for a vertex-based approximate BDDC method.

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Key words

approximate BDDC, three-level BDDC, multilevel BDDC, vertex-based BDDC

AMS subject classifications

68W10, 65N22, 65N55, 65F08, 65F10, 65Y05

Links to the cited ETNA articles

[13]Vol. 49 (2018), pp. 244-273 Axel Klawonn, Martin Lanser, and Oliver Rheinbach: Nonlinear BDDC Methods with approximate solvers

ETNA articles which cite this article

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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