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A BDDC algorithm for mortar discretization of elasticity problems. (English) Zbl 1226.74046

Summary: A balancing domain decomposition by constraints (BDDC) algorithm is developed for compressible elasticity problems in three dimensions with mortar discretization on geometrically nonconforming subdomain partitions. Material parameters of elasticity problems may have jump across the subdomain interface. Coarse basis functions in the BDDC algorithm are constructed from primal constraints on faces, which are similar to the average matching condition and the moment matching condition considered in [A. Klawonn and O. B. Widlund, Commun. Pure Appl. Math. 59, No. 11, 1523–1572 (2006; Zbl 1110.74053)]. A condition number bound is proved to be \(C(1+\log (H/h))^3\) for geometrically nonconforming partitions, and to be \(C(1+\log (H/h))^2\) for geometrically conforming partitions. The bound is not affected by the jump of material parameters across the subdomain interface. Numerical results are included.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs

Citations:

Zbl 1110.74053
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