Deflation techniques in conjunction with generic factored approximate sparse inverse preconditioning

Abstract

A class of Modified Generic Factored Approximate Sparse Inverse matrix, based on sparsity patterns and a column-wise computational approach, has been recently proposed and used for solving general sparse linear systems. For certain classes of problems the number of nonzero elements increases rapidly as the "levels of fill" parameter is increased in the process of computing the sparsity pattern of the approximate inverse. In order to improve the approximate inverse preconditioning schemes without increasing the nonzero elements, deflation techniques are also introduced. The basis vectors for the deflation are computed algebraically based on separating the graph corresponding to the matrix into well partitioned sets. Furthermore, various graph partitioning methods are used in order to choose better basis vectors for the deflation method. Finally, the applicability of the proposed schemes is examined and numerical results are given.