Comparison of Some Domain Decomposition Methods

A progressive research in domain decomposition in the last several decades has been motivated by inceasing availability of multicore, parallel computers. In this contribution we focus on an iterative substructuring class of the domain decomposition methods. Some of the most popular methods are formulated under so-called minimalist assumptions. This allows for their effective comparison, which reveales that some of the methods are equivalent or even the same. Finally, the theory is used to develop an adaptive method that significantly improves convergence of two most advanced methods, BDDC and FETI-DP.