Volume 15 (2020)

Abstract :

The present work concerns the derivation of a well-balanced scheme to approximate the weak solutions of the shallow-water model. Here, the numerical scheme exactly captures all the smooth steady solutions with nonvanishing velocities. To address such an issue, a Godunov-type scheme is adopted. A particular attention is paid on the derivation of the intermediate states within the approximate Riemann solver. Indeed, because of the moving steady states, the intermediate states may be ill-defined. Here, we introduce a suitable correction in order to get a fully well-defined finite volume scheme. In addition, the numerical method is established to be positive preserving and to satisfy a discrete entropy inequality up to small perturbations. Several numerical experiments, including wet/dry transition, illustrate the relevance of the designed scheme.

Abstract:

Since the recent advance in microprocessor design, the optimization of computing software becomes more and more technical. One of the difficulties is to transform sequential algorithms into parallel ones. A possible solution is the task-based design. In this approach, it is possible to describe the parallelization possibilities of the algorithm automatically. The task-based design is also a good strategy to optimize software in an incremental way. The objective of this paper is to describe a practical experience of a task-based parallelization of a Discontinuous Galerkin method in the context of electromagnetic simulations. The task-based description is managed by the StarPU runtime. Additional acceleration is obtained by OpenCL.

Key words : Discontinuous Galerkin, StarPU, OpenCL, hybrid parallelism.