Parallel Multigrid Methods

           Dr. Jim E. Jones
   Center for Applied Scientific Computing
   Lawrence Livermore National Laboratory

Computer simulations play an increasingly important role in scientific
investigations, supplementing (and in some cases, supplanting) traditional
experiments. These simulations of complex three-dimensional phenomenon
are possible, in part, because of the dramatic increase in computing
power provided by large parallel machines. Although parallel processing
is necessary for the numerical solution of these problems, it is
not sufficient; one also needs scalable numerical algorithms.  By
"scalable" we generally mean the ability to use additional computational
resources effectively to solve increasingly larger problems.
This talk will discuss the parallel multigrid solvers work being
done within CASC. This work is aimed at providing scalable
linear solvers for use in these large simulation codes. I will begin
with a brief discussion of the basic multigrid algorithm. In the
main part of the talk, I will discuss some of the CASC research
efforts to develop multigrid solvers for difficult physics
simulations.