GRAPH PERTURBATIONS

Recently, attention has been drawn to the ordering of the unknowns to use in conjunction with approximate factorizations of Stieltjes matrices used as preconditioners in iterative elliptic solvers because this ordering is an important issue for parallel or vector implementation while it also has a strong influence on the convergence behaviour. Consistent orderings have attractive properties in this respect because they partition the unknowns into subsets of unknowns which can be handled in parallel. However such orderings may lead to poorly bounded conditioning 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 offdiagonal or graph perturbations. The analysis of simple examples displays the interest of this new technique.