SOLUTION OF NONLINEAR FINITE-ELEMENT PROBLEMS WITH NOT WELL-CONDITIONED STIFFNESS MATRICES

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