MPI based Multigrid/Schwarz Splitting Software Libraries

Barry Smith

Abstract

In the past few years a beautiful framework has emerged that unifies much of the mathematical theory explaining multigrid, multilevel, and domain decomposition methods for linear elliptic PDEs. A small number of suitable mathematical concepts can be used to define and completely analyze a wide variety of these methods. The same small set of building blocks may be used in the design and implementation of software libraries for the numerical solution of elliptic PDEs. The use of the unifying concepts allow small software efforts to support almost the full range of Schwarz type methods.