GPU-accelerated Bernstein-Bezier discontinuous Galerkin methods for wave problems
Provides a more efficient basis for high-order DG simulations on GPUs, benefiting computational scientists solving wave propagation problems.
The paper evaluates Bernstein-Bezier basis for DG methods, showing up to 2x speedup over nodal DG at high polynomial orders on GPUs for wave problems.
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.