User Guide for Ogmg: A Multigrid Solver for Overlapping Grids Version 1.00

Abstract: This is the user guide to Ogmg, the Overlapping-Grid-MultiGrid-solver. This guide describes how to use Ogmg to solve elliptic boundary value problems. The various parameters associated with the solver are explained. The Overlapping-Grid-MultiGrid-solver, Ogmg, that can be used to obtain solutions to elliptic boundary value problems. Ogmg solves problems in two and three space dimensions on composite overlapping grids. Second and fourth-order accurate approximations are supported. Given an overlapping grid generated from the Ogen grid generator, Ogmg will generate the coarse grid multigrid levels using an automatic coarsening algorithm. The equations on the coarse grids can be determined automatically using a Galerkin averaging procedure. The multigrid solution algorithm has been optimised for some commonly occuring problems such as equations defined with the Laplace operator. Smoothers include Red-Black, Jacobi, Gauss-Seidel, line-zebra and line-Jacobi. Ogmg is particularly efficient when a majority of the grid points belong to cartesian component grids; this is often the case when grids become sufficiently fine. The fourth-order accurate approximations are solved directly with multigrid (as opposed to using a defect correction scheme). Convergence rates for the fourth-order approximations are often nearly as good as the convergence rates for second-order discretizations