An Interleaved Adaptive Refinement Multigrid Algorithm

                             William F. Mitchell
                National Institute of Standards and Technology
                            Gaithersburg, MD 20899
                            mitchell@cam.nist.gov

                                   Abstract

Multilevel adaptive methods that combine the full multigrid method with
adaptiv e refinement of finite element grids have been shown to be an
effective O(N) method for elliptic partial differential equations.  The
traditional approach is to begin with a very coarse grid and alternate between
phases of adaptive refinement and multigrid cycles until some termination
criterion is met.  In this talk we will describe more tightly in terleaved
approach in which the alternation between adaptive refinement and multigrid
steps occurs at each grid of the multigrid cycle.  While this should have no
effect on the convergence rate or operation count, it can be advantageous in a
distributed memory parallel computing environment by providing increased
opportunity to overlap communication with computation.