SOME ASPECTS OF MULTIGRID METHODS ON NON-STRUCTURED MESHES

                               Herve Guillard.
                           INRIA, Sophia-Antipolis,
                           2004 Route des Lucioles,
                        BP 93, 06902 Sophia-Antipolis
                                    France
                       e-mail:  Herve.Guillard@inria.fr

                                   Abstract

To solve a given fine mesh problem, the design of a multigrid method requires
the definition of the coarse levels, the associated coarse grid operators and
the inter-grid transfer operators.  For non-structured simplicial meshes,
these definitions can rely on the use of non-nested triangulations.  Another
possibility is to base these definitions on agglomeration/aggregation
techniques in a purely algebraic manner.  In this type of method, the
informations on the differential problem at hand are usually lost, resulting
in a decrease of the efficiency of the multigrid algorithm.  We show that
provided the inter-grid transfers are properly defined, the m ultigrid
agglomeration method is in some sense equivalent to a non-nested multi-grid
algorithm.  This allo ws to analyze the multigrid agglomeration method in a
classical setting.