GPU-accelerated Bernstein-Bezier discontinuous Galerkin methods for wave problems

TL;DR

This paper demonstrates that Bernstein-Bezier basis functions, when GPU-accelerated, offer superior efficiency and stability for high-order discontinuous Galerkin methods in wave simulations, outperforming nodal kernels.

Contribution

It introduces an optimized, quadrature-free evaluation method for Bernstein-Bezier DG discretizations on GPUs, improving computational performance and stability for wave problems.

Findings

Bernstein-Bezier kernels outperform nodal kernels at high approximation orders.

The proposed method achieves optimal complexity in DG evaluations.

GPU implementation enhances the efficiency of Bernstein-Bezier DG methods.

Abstract

We evaluate the computational performance of the Bernstein-Bezier basis for discontinuous Galerkin (DG) discretizations and show how to exploit properties of derivative and lift operators specific to Bernstein polynomials for an optimal complexity quadrature-free evaluation of the DG formulation. Issues of efficiency and numerical stability are discussed in the context of a model wave propagation problem. We compare the performance of Bernstein-Bezier kernels to both a straightforward and a block-partitioned implementation of nodal DG kernels in a time-explicit GPU-accelerated DG solver. Computational experiments confirm the advantage of Bernstein-Bezier DG kernels over both straightforward and block-partitioned nodal DG kernels at high orders of approximation.