Session

DescriptionThis minisymposium will explore the tension between high-order discretisation methods for PDEs and the fact that many physical phenomena are non-smooth. We will also investigate connections to machine learning, such as the use of reduced precision arithmetics in both domains. High order discretisations in space and time can make optimal use of FLOP-bound exascale hardware and have the potential to unlock additional parallelism. However, it is an open question how these methods can be applied to time-dependent PDEs with elliptic constraints. Off-the-shelf preconditioners are not sufficient and multigrid methods are being developed to solve the resulting large sparse linear systems of equations. Implementing advanced reliable and performance portable PDE based simulation tools requires the combined expertise of specialists from different domains. Real-life codes are starting to use novel discretisation techniques: the UK Met Office explores the solution of the equations of atmospheric fluid dynamics with hybridised finite elements, non-nested multigrid preconditioners and parallel-in-time methods. The ADER-DG ExaHype engine is being extended to include elliptic constraints and support implicit timestepping for astrophysics simulations. A discussion session will explore how the advantages of sophisticated PDE solvers and Machine Learning can be combined productively.