Parallel and Parareal Deferred Corrections for Temporal Integration of PDEs

Abstract:
  The prospect of parallelizing the numerical solution of PDEs in the time
direction has interested computational scientists for decades but has never
achieved near the success as parallelization in the spatial domain.  The
introduction of the parareal algorithm in 2001 rekindled interest in this
area, but parareal has  yet to be widely accepted.  I will discuss the
parareal algorithm and show how it can be considered one instance of a much
more general class of parallel deferred corrections algorithms which promise
improved parallel efficiency.  The future prospects for combining spatial and
temporal parallelization for large scale PDE simulations will be considered.