Name
Title | ||
|---|---|---|
An efficient parallel implementation of explicit multirate Runge-Kutta schemes for discontinuous Galerkin computations |
Abstract | ||
|---|---|---|
Although explicit time integration schemes require small computational efforts per time step, their efficiency is severely restricted by their stability limits. Indeed, the multi-scale nature of some physical processes combined with highly unstructured meshes can lead some elements to impose a severely small stable time step for a global problem. Multirate methods offer a way to increase the global efficiency by gathering grid cells in appropriate groups under local stability conditions. These methods are well suited to the discontinuous Galerkin framework. The parallelization of the multirate strategy is challenging because grid cells have different workloads. The computational cost is different for each sub-time step depending on the elements involved and a classical partitioning strategy is not adequate any more. In this paper, we propose a solution that makes use of multi-constraint mesh partitioning. It tends to minimize the inter-processor communications, while ensuring that the workload is almost equally shared by every computer core at every stage of the algorithm. Particular attention is given to the simplicity of the parallel multirate algorithm while minimizing computational and communication overheads. Our implementation makes use of the MeTiS library for mesh partitioning and the Message Passing Interface for inter-processor communication. Performance analyses for two and three-dimensional practical applications confirm that multirate methods preserve important computational advantages of explicit methods up to a significant number of processors. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jcp.2013.07.041 | J. Comput. Physics |
Keywords | Field | DocType |
small computational effort,computational cost,grid cell,multi-constraint mesh partitioning,mesh partitioning,explicit time integration scheme,classical partitioning strategy,inter-processor communication,important computational advantage,efficient parallel implementation,explicit multirate runge-kutta scheme,discontinuous galerkin computation,multirate method,discontinuous galerkin,parallelization,high performance computing | Discontinuous Galerkin method,Runge–Kutta methods,Mathematical optimization,Polygon mesh,Supercomputer,Workload,Computer science,Stability conditions,Message Passing Interface,Computation | Journal |
Volume | Issue | ISSN |
256 | C | 0021-9991 |
Citations | PageRank | References |
5 | 0.53 | 16 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bruno Seny | 1 | 5 | 0.53 |
| Jonathan Lambrechts | 2 | 28 | 4.26 |
| Thomas Toulorge | 3 | 27 | 2.54 |
| Vincent Legat | 4 | 5 | 0.53 |
| Jean-François Remacle | 5 | 247 | 37.52 |