Development and implementation of a parallel explicit multirate time stepping strategy for accelerating discontinuous Galerkin computations

This thesis is devoted to the development of robust and efficient time integration methods for ocean modeling which constitutes an important challenge. No singlerate time integration method works well for all physical processes in a complex model, as different subsystems have widely different time scales, dynamic behaviors, and accuracy requirements. If explicit singlerate schemes present attractive properties, such as their simple implementation and their efficient parallelization, they suffer from limiting time steps. The most constrained element, which may be much smaller than the average, determines the effective overall time step. Therefore, variable resolution is also recommended for the time integration. Multirate explicit methods have the vocation of reducing the computational cost by considering different time steps. Two multirate strategies, introduced by Constantinescu and Schlegel, have been adapted to the discontinuous Galerkin framework. The key idea is to gather mesh elements in groups which are stable for a certain range of time steps. The transition between them is accommodated by buffers which should preserve accuracy and conservation properties. The extension of the multirate approach to the parallel framework is challenging because classical mesh partitioning techniques are not adequate as the elements have different workloads. A multi-constraint partitioning strategy is employed to balance equitably the computational work on each processor at each stage of the algorithm. We propose an efficient parallel implementation of this multirate approach which minimizes the computational and communication overheads and maintains multirate speedups up to a significant number of processors.(FSA - Sciences de l) -- UCL, 201