Task-based parallelization of an implicit kinetic scheme

TL;DR

This paper introduces a parallel implementation of the Palindromic Discontinuous Galerkin method for high-order implicit approximation of conservation laws in multiple dimensions, leveraging the StarPU runtime for efficiency.

Contribution

It extends the PDG method to higher dimensions and provides a parallel implementation using StarPU, demonstrating its applicability to complex systems.

Findings

Successful implementation of PDG in higher dimensions

Parallelization with StarPU improves computational efficiency

Preliminary tests validate the method's effectiveness

Abstract

In this paper we present and implement the Palindromic Discontinuous Galerkin (PDG) method in dimensions higher than one. The method has already been exposed and tested in [4] in the one-dimensional context. The PDG method is a general implicit high order method for approximating systems of conservation laws. It relies on a kinetic interpretation of the conservation laws containing stiff relaxation terms. The kinetic system is approximated with an asymptotic-preserving high order DG method. We describe the parallel implementation of the method, based on the StarPU runtime library. Then we apply it on preliminary test cases.