FETI-DP Methods with an Adaptive Coarse Space

A coarse space is constructed for the dual-primal finite element tearing and interconnecting (FETI-DP) domain decomposition method applied to highly heterogeneous problems by solving local generalized eigenvalue problems. For certain problems with highly varying coefficients, e.g., from multiscale simulations, the coefficient jump will appear in the condition number bound even if standard techniques such as scaling and the weighting of constraints are used. The FETI-DP theory is revisited and two central estimates are identified where the dependency on the coefficient contrast can enter the condition number bound. The first is a Poincaré inequality and the second an extension theorem. These estimates are replaced by local eigenvalue problems. Enriching the FETI-DP coarse space by a few numerically computed eigenvectors yields independence of the contrast of the coefficients even in challenging situations.