A BDDC Algorithm for Mortar Discretization of Elasticity Problems

Abstract

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 the 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, Comm. Pure Appl. Math., 59 (2006), pp. 1523–1572] and [H. H. Kim, A FETI-DP Formulation of Three Dimensional Elasticity Problems with Mortar Discretization, Technical report, New York University, 2005]. 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 the material parameters across the subdomain interface. Numerical results are included.