Solving Large Sparse Finite Element Systems of Nonlinear Equations by Explicit SEMI-Direct Methods Based on Approximate Inverse Preconditioners

摘要

A class of generalized approximate inverse presconditioners, based on the concept of adaptable incomplete LU-type decomposition, is presented. Explicit preconiditoned semi-direct methods in conjuction with modified forms of Newton/Picard methods are used for solving nonlinear initial/boundary value problems. The applicability, effectiveness and performance of the proposed hybrid iterative schemes and sparse approximate inverse preconditioners is discussed and numerical results for solving characteristic nonlinear elliptic PDE'S are given.