A GPU-accelerated nodal discontinuous Galerkin method with high-order absorbing boundary conditions and corner/edge compatibility

TL;DR

This paper introduces a GPU-accelerated nodal discontinuous Galerkin method with high-order absorbing boundary conditions, ensuring accurate wave simulations with efficient boundary handling on modern parallel hardware.

Contribution

It develops a novel combination of a nodal discontinuous Galerkin scheme with high-order absorbing boundary conditions and corner/edge compatibility, optimized for GPU implementation.

Findings

Demonstrates high accuracy in wave-propagation simulations.

Achieves significant computational efficiency on GPU architectures.

Provides compatibility conditions for boundary intersections.

Abstract

Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective boundary treatments to limit the size of the computational domain without losing accuracy or computational efficiency, which remains a challenging task. In this paper, we present a combination of a nodal discontinuous Galerkin method with high-order absorbing boundary conditions (HABCs) for cuboidal computational domains. Compatibility conditions are derived for HABCs intersecting at the edges and the corners of a cuboidal domain. We propose a GPU implementation of the computational procedure, which results in a multidimensional solver with equations to be solved on 0D, 1D, 2D and 3D spatial regions. Numerical results demonstrate both the accuracy and the computational efficiency of our approach.