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

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.

References in corpus (4)

• OCCA: A unified approach to multi-threading languages
• GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models
• Efficient discontinuous Galerkin finite element methods via Bernstein polynomials
• A short note on a Bernstein-Bezier basis for the pyramid

Cited by in corpus (4)

• GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models
• Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media
• Weight-adjusted discontinuous Galerkin methods: curvilinear meshes
• Reduced storage nodal discontinuous Galerkin methods on semi-structured prismatic meshes