A class of multilevel recursive incomplete LU preconditioning techniques (Q2731124)

Preconditioners based on multilevel block incomplete LU factorization (BILUM) have been shown to possess certain properties that are typically enjoyed by multigrid methods. They are faster and more robust than traditional LU precoditioners. This paper extends BILUM techniques to multilevel recursive ILU preconditioning techniques for solving general sparse systems. This technique is based on a recursive two by two block ILU factorization on the coefficient matrix. The coarse level system is constructed as an Schur complement. A dynamic preconditioner is obtained by solving the Schur complement matrix approximately by a preconditioned Krylov subspace method. This class of preconditioners may be highly robust and scalable.