BDDC and FETI-DP methods with enriched coarse spaces for elliptic problems with oscillatory and high contrast coefficients

Abstract

BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithms with adaptively enriched coarse spaces are developed and analyzed for second order elliptic problems with high contrast and random coefficients. Among many approaches to form adaptive coarse spaces, we consider an approach using eigenvectors of generalized eigenvalues problems defined on each subdomain interface, see Mandel and Sousedík (2007), Galvis and Efendiev (2010), Spillane et al. (2011), Spillane et al. (2013), Klawonn et al. (2015).