Purely algebraic domain decomposition methods for the incompressible Navier-Stokes equations

摘要

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