DeepAI AI Chat
Log In Sign Up

Multigrid Reduction in Time for non-linear hyperbolic equations

by   Federico Danieli, et al.

Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computation of its solution. While parallelisation in time has allowed remarkable speed-ups in applications involving parabolic equations, its effectiveness in the hyperbolic framework remains debatable: growth of instabilities and slow convergence are both strong issues in this case, which often negate most of the advantages from time-parallelisation. Here, we focus on the Multigrid Reduction in Time (MGRIT) algorithm, investigating in detail its performance when applied to non-linear conservation laws with a variety of discretisation schemes. Specific attention is given to high-accuracy Weighted Essentially Non-Oscillatory (WENO) reconstructions, coupled with Strong Stability Preserving (SSP) integrators, which are often the discretisations of choice for such PDEs. A technique to improve the performance of MGRIT when applied to a low-order, more dissipative scheme is also outlined. This study aims at identifying the main causes for degradation in the convergence speed of the algorithm, and finds the Courant-Friedrichs-Lewy (CFL) limit to be the principal determining factor.


page 1

page 2

page 3

page 4


ExaHyPE: An Engine for Parallel Dynamically Adaptive Simulations of Wave Problems

ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for s...

Lax-Wendroff flux reconstruction method for hyperbolic conservation laws

The Lax-Wendroff method is a single step method for evolving time depend...

A new non-linear instability for scalar fields

In this letter we introduce the non-linear partial differential equation...

Well-posedness study of a non-linear hyperbolic-parabolic coupled system applied to image speckle reduction

In this article, we consider a non-linear hyperbolic-parabolic coupled s...

Model Reduction of Time-Dependent Hyperbolic Equations using Collocated Residual Minimisation and Shifted Snapshots

We develop a non-linear approximation for solution manifolds of parametr...

CUDACLAW: A high-performance programmable GPU framework for the solution of hyperbolic PDEs

We present cudaclaw, a CUDA-based high performance data-parallel framewo...