Schur complement Domain Decomposition in conjunction with Algebraic Multigrid methods based on generic approximate inverses

For decades, Domain Decomposition (DD) techniques have been used for the numerical solution of boundary value problems. In recent years, the Algebraic Multigrid (AMG) method has also seen significant rise in popularity as well as rapid evolution. In this article, a Domain Decomposition method is presented, based on the Schur complement system and an AMG solver, using generic approximate banded inverses based on incomplete LU factorization. Finally, the applicability and effectiveness of the proposed method on characteristic two dimensional boundary value problems is demonstrated and numerical results on the convergence behavior are given.