Multigrid High Order Mesh Refinement Techniques
                for Composite Grid Electrostatics Calculations

                                Thomas L. Beck
                           Department of Chemistry
                           University of Cincinnati
                          Cincinnati, OH 45221-0172

                                   Abstract

A new method for performing high order mesh refinement multigrid computations
in real space is presented.  The method allows for accurate linear scaling
electrostatics calculations over composite domains with local nested fine
patches.

The Full Approximation Scheme (FAS) multigrid technique is utilized for a
sequence of refinement patches of increasing resolution.  Conservation forms
are generated on coarse scales by additional defect correction terms which
counter the local excess fluxes at the boundaries.  Formulas are given for
arbitrary order, extending the existing technique of Bai and Brandt.  Test
calculations are presented for a singular source in three dimensions which
illustrate the multigrid convergence properties, numerical accuracy, and
correct order of the approach.