Preconditioned iterative methods for solving 3D boundary value problems

A new class of approximate LU-type factorization procedures for solving spa rse linear systems of irregular structure, which are derived from the finit e element method of Partial Differential Equations in three space variables , is introduced. Theoretical results on the convergence rate of approximate matrix factorization semi-direct methods for three space variables are int roduced. Applications of the method on a three dimensional linear boundary value problem is discussed and numerical results are given.