GRAPH PERTURBATIONS

Recently, attention has been drawn to the ordering of the unknowns to use in conjunction with approximate factorizations of Stieltjes matric es used as preconditioners in iterative elliptic solvers because this ordering is an important issue for parallel or vector implementation w hile it also has a strong influence on the convergence behaviour. Cons istent orderings have attractive properties in this respect because th ey partition the unknowns into subsets of unknowns which can be handle d in parallel. However such orderings may lead to poorly bounded condi tioning properties that cannot be improved by the diagnal perturbation techniques generally used by MILU methods. A new remedy is therefore proposed here, which consists in the (additional) introduction of offd iagonal or graph perturbations. The analysis of simple examples displa ys the interest of this new technique.