Incomplete factorization by local exact factorization (ILUE)

This study proposes a new preconditioning strategy for symmetric positive (semi-)definite SP(S)D matrices referred to as incomplete factorization by local exact factorization (ILUE). The investigated technique is based on exact LU decomposition of small-sized local matrices associated with a splitting of the domain into overlapping or non-overlapping subdomains. The ILUE preconditioner is defined and its relative condition number estimated. Numerical tests on linear systems arising from the finite element (FE) discretization of a second order elliptic boundary value problem in mixed form demonstrate the advantage of the new algorithm, even for problems with highly oscillatory permeability coefficients, against the classical ILU(p) and ILUT(τ) incomplete factorization preconditioners.