Multigrid high-order mesh refinement techniques for composite grid electrostatics calculations

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 that 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 that illustrate the multigrid convergence properties, numerical accuracy, and correct order of the approach.