Adaptive Coarse Spaces for FETI-DP in Three Dimensions

An adaptive coarse space approach including a condition number bound for dual primal finite element tearing and interconnecting (FETI-DP) methods applied to three dimensional problems with coefficient jumps inside subdomains and across subdomain boundaries is presented. The approach is based on a known adaptive coarse space approach enriched by a small number of additional local edge eigenvalue problems. These edge eigenvalue problems serve to make the method robust and permit a condition number bound which depends only on the tolerance of the local eigenvalue problems and some properties of the domain decomposition. The introduction of the edge eigenvalue problems thus turns a well-known condition number indicator for FETI-DP and balancing domain decomposition by constraints (BDDC) methods into a condition number estimate. Numerical results are presented for linear elasticity and heterogeneous materials supporting our theoretical findings. The problems considered include those with random coefficients and almost incompressible material components.