METHODS FOR OVERCOMING BREAKDOWN PROBLEMS IN THE UNSYMMETRIC LANCZOS REDUCTION METHOD

The Unsymmetric Lanczos Reduction (ULR) method is developed to solve t he finite-element-based solution to the contaminant transport problem. The method sometimes suffers from breakdown when at some step divisio n by a pivot which is zero or near zero, causes numerical instability. In this paper, the Maximum-Pivot New-Start Vector method is developed to overcome such breakdowns by constructing a new starting vector wit h the possible maximum pivot. Some cases of instability cannot be reme died by this approach (pathological breakdowns) and the Switch method is developed to complete the solution by changing the algorithm to an Arnoldi reduction approach. Investigation of some two-dimensional exam ples and held problems illustrates the efficiency of the methods and s ubstantial time savings over other existing solution methods. (C) 1998 John Wiley & Sons, Ltd.