Dr. Michael Minion, Lawrence Berkeley National Laboratory
I will explain how current trends in super computer architectures, due to the breakdown of Dennard scaling, are spurring research into new approaches for the temporal integration of partial differential equations. In particular, there is a need for higher-order methods suitable for problems with multiple physical processes or time scales. In addition, finding methods that can exploit parallelism in the time direction is currently an active research area. I will provide an introduction and overview of research into multilevel, iterative methods for the temporal integration of ODEs, and PDEs based on spectral deferred corrections (SDC) that provide a framework for constructing methods that are both higher-order and provide the potential for temporal parallelism.