Solution of non-linear finite element problems with not well-conditioned stiffness matrices

Abstract

In structural mechanics, there exist many non-linear finite element problems with very ill-conditioned or even singular stiffness matrices. They are often difficult to solve using a usual method. This paper describes a minimal residual Lanczos algorithm for solution of ill-conditioned or singular (but inconsistent) linear systems. With the algorithm, a modification of the Newton-Lanczos method is given to handle effectively the above non-linear problems.