Domain decomposition methods : algorithms and theory The scope of this text is to offer a comprehensive and self sufficient presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. Strong emphasis is put both on their algorithmic and mathematical aspects. Some important methods that are not treated in other available monographs on domain decomposition such as FETI methods Balancing Neumann Neumann methods and algorithms for spectral element approximations are covered in this book