Incomplete lu decompositions based on order matrices

Abstract

A method of incomplete LU decomposition of different accuracy is presented for giving preconditioners to solve large sparse linear systems of equations A x = b where A is obtained from discretization of 2-D elliptic partial differential equations (PDEs). The method is based on a truncated elimination neglecting quantities of small magnitude. Several new concepts, such as the order, the order matrix and the P-order truncated elimination, are presented to explore a systematic way for giving the P-order incomplete LU decomposition of A. Examples are given to show the efficiency of the method when the P-order incomplete LU decomposition is used as the preconditioner for the computation of preconditioned conjugate gradient methods.

Keywords:

• Incomplete factorisation
• row elimination
• order matrix
• P-order influence area
• preconditioner

C.R Categories:

• G.1.7

^∗Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China.

^∗Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China.

Notes

^∗Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China.