Fast normalized approximate inverse preconditioning for solving non-linear finite element systems

摘要

A new class of inner-outer iterative procedures in conjunction with Picard/Newton methods based on normalized explicit preconditioning methods for solving sparse non-linear finite element systems of irregular structure is presented. The proposed preconditioning methods, based on the explicit computation of a class of normalized optimized approximate inverse finite element matrix techniques, are particularly effective for solving non-linear initial/boundary value problems in three dimensions. Isomorphic methods in conjunction with normalized explicit preconditioned conjugate gradient schemes are presented for the efficient solution of non-linear finite element systems. Applications on characteristic non-linear initial/boundary value problems in three dimensions are discussed and numerical results are given.