  In the context of non overlapping domain decomposition methods, several
algebraic approximations of the Dirichlet-to-Neumann (DtN) map are proposed in
[F. X. Roux, et. al. Algebraic approximation of Dirichlet- to-Neumann maps for
the equations of linear elasticity, Comput. Methods Appl. Mech. Engrg., 195,
2006, 3742-3759]. For the case of non overlapping domains, approximation to the
DtN are analogous to the approximation of the Schur complements in the
incomplete multilevel block factorization. In this work, several original and
purely algebraic (based on graph of the matrix) domain decomposition techniques
are investigated for steady state incompressible Navier-Stokes equation defined
on uniform and stretched grid for low viscosity. Moreover, the methods proposed
are highly parallel during both setup and application phase. Spectral and
numerical analysis of the methods are also presented.
