GPU-accelerated discontinuous Galerkin methods on hybrid meshes

TL;DR

This paper introduces a GPU-accelerated discontinuous Galerkin solver for acoustic wave equations on hybrid meshes, combining stability, efficiency, and advanced element-specific techniques for improved computational performance.

Contribution

It develops a stable, efficient DG method for hybrid meshes with novel quadrature-free operators and multi-rate timestepping, optimized for GPU acceleration.

Findings

Achieved stable time stepping for hybrid meshes.

Implemented GPU acceleration with element-specific kernels.

Demonstrated computational efficiency improvements.

Abstract

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.