Error-Based ILU Preconditioner for the Solution of Linear Equations

Abstract

There are several types of ILU preconditioners based on different fill-in dropping rules that can be used. One must assure that the chosen preconditioner is suitable for the problem, but this is not frequently an easy task. A bad choice will lower the GMRES convergence rate, increasing the floating point operations and GMRES iteration as well, or even fail. Based on that, this paper proposes a fill-in dropping rule to construct an ILU preconditioner for solution of linear equations via GMRES. The rule is based on reducing error in incomplete triangular factors related to full factors and on Doolittle's Method for LU factorization and allows efficient control of nonzero elements (fill-in) in order to improve the preconditioner quality and GMRES performance as well. The resulting preconditioner is referred to as ILUD (D stands for Doolittle) and it is tested on real power systems; single and sequential load flows (associated to multiple simulations - contingency analysis). The results corroborate the simplicity, efficiency, high quality, and robustness of the ILUD preconditioner.