Multigrid methods are important techniques for efficiently solving huge systems and they have already been shown to scale effectively on millions of cores. However, one of the major challenges facing computational science with future architectures is that faster compute speeds will be achieved through greater concurrency (more “cores”), since clock speeds are no longer increasing. Current petascale computers already have millions of cores, but future exascale machines are expected to have billions. This immense degree of parallelism requires a similar level of concurrency in the algorithms that run on them. One consequence of this is that time integration by traditional time marching will become a sequential bottleneck.
In this talk, we will discuss the multigrid method, its role in scientific computing, and some of our current research directions. We will also discuss our efforts to develop multigrid algorithms for parallel time integration. The approach we use is based on multigrid reduction techniques and has the advantage of being easily integrated into existing codes because it builds directly on the original time-stepping scheme. Results for a variety of applications will be presented.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Bio: Rob Falgout is a computational mathematician in the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory (LLNL) and the project leader for the Scalable Linear Solvers Project and software effort, hypre. He earned his Ph.D. in applied mathematics at the University of Virginia in 1991 under the direction of James Ortega and joined LLNL as a postdoc that same year. He served on the editorial boards for the SIAM Journal on Scientific Computing and Numerical Linear Algebra with Applications and currently co-chairs the Copper Mountain Conference on Multigrid Methods. He has mentored 18 student interns and 4 postdocs. He has more than 27 years of experience developing parallel multigrid methods and software.