A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Numerical methods for ordinary differential equations in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Multilevel algorithms for multi-constraint graph partitioning
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
High Resolution Schemes for Conservation Laws with Locally Varying Time Steps
SIAM Journal on Scientific Computing
A quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes
Journal of Scientific Computing
Journal of Scientific Computing
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
Journal of Scientific Computing
Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes
SIAM Journal on Numerical Analysis
Validity of the single processor approach to achieving large scale computing capabilities
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
Multirate Runge-Kutta schemes for advection equations
Journal of Computational and Applied Mathematics
Nonuniform time-step Runge-Kutta discontinuous Galerkin method for Computational Aeroacoustics
Journal of Computational Physics
Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
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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.