Preconditioning Operators on Unstructured Grid

                             S.V. Nepomnyaschikh

                    Computing Center of Siberian Division
                        of Russian Academy of Sciences
                                Lavrentieva 6
                             Novosibirsk, 630090
                                    Russia
                         E-mail: svnep@comcen.nsk.su

Abstract:  Preconditioning operators for the iterative solution of systems of
grid equations approximating elliptic boundary value prodlems in domains with
piecewise-smooth boundaries are presented.  This construction is based on the
fictitious space method.  Using this method, the original problem is reduced
to the problem on structured but not hierarchical grid.  Then, using the
multilevel technique on the fictitious hierarchical grid, the final
preconditioner is suggested.  The rate of convergence of the preconditioned
iterative process is independent of the grid size and the cost of the action
of the preconditioning operator is proportional to the number of nodes of the
grid domain.