BDDC and FETI-DP Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity

Abstract

We construct and study a BDDC (Balancing Domain Decomposition by Constraints) algorithm, see [1, 2], for the system of almost incompressible elasticity discretized with Gauss Lobatto Legendre (GLL) spectral elements. Related FETIDP algorithms could be considered as well. We show that sets of primal constraints can be found so that these methods have a condition number that depends only weakly on the polynomial degree, while being independent of the number of subdomains (scalability) and of the Poisson ratio and Youngs modulus of the material considered (robustness).