An efficient parallel multirate model of the Great Barrier Reef

The development of fast and suitable time integration methods for ocean modeling constitutes an important challenge. No single time-discretisation works well for all physical processes in a complex marine model, as different subsystems have widely different characteristics in terms of time scales, dynamic behavior, and accuracy requirements. Our research team has developed a hydrodynamic model of the whole Great Barrier Reef (GBR). A discontinuous Galerkin finite element method based on unstructured meshes is used for the spatial representation. Explicit time stepping schemes are very attractive for the time integration but they are severely constrained by the Courant–Friedrichs–Lewy condition that limits the global time step. Multirate schemes present a way to partly circumvent these restrictions by gathering the mesh elements in groups that have a specific stable time step. However, the transitions between these multirate groups have to be accommodated in a clever way. In particular, global consistency and conservation properties are significantly linked with the way groups communicate with each other. Moreover, applications like the GBR require the use of parallel computers. Since elements have different costs depending on their belonging to a specific multirate group, a load balancing strategy has to be supplied. This problem can be posed as a graph partitioning problem with multiple objectives