GPU-accelerated discontinuous Galerkin methods on hybrid meshes
arXiv:1507.02557 · doi:10.1016/j.jcp.2016.04.003
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.
Submitted to CMAME
References in corpus (5)
- Orientation Embedded High Order Shape Functions for the Exact Sequence Elements of All Shapes
- OCCA: A unified approach to multi-threading languages
- Nodal Discontinuous Galerkin Simulations for Reverse-Time Migration on GPU Clusters
- GPU accelerated spectral finite elements on all-hex meshes
- Orthogonal bases for vertex-mapped pyramids
Cited by in corpus (23)
- On discretely entropy conservative and entropy stable discontinuous Galerkin methods
- A Perspective on Machine Learning Methods in Turbulence Modelling
- Hex-Mesh Generation and Processing: a Survey
- GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models
- An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs
- Nodal Discontinuous Galerkin Simulations for Reverse-Time Migration on GPU Clusters
- Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion
- Solving the Discretised Neutron Diffusion Equations using Neural Networks
- A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities
- Weight-adjusted discontinuous Galerkin methods: matrix-valued weights and elastic wave propagation in heterogeneous media
- Robust Approaches to Handling Complex Geometries with Galerkin Difference Methods
- An Energy Stable Approach for Discretizing Hyperbolic Equations with Nonconforming Discontinuous Galerkin Methods
- An Improved Iterative HDG Approach for Partial Differential Equations
- A new discontinuous Galerkin spectral element method for elastic waves with physically motivated numerical fluxes
- High order weight-adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes
- Weight-adjusted discontinuous Galerkin methods: curvilinear meshes
- Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes
- A short note on a Bernstein-Bezier basis for the pyramid
- Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes
- Reduced storage nodal discontinuous Galerkin methods on semi-structured prismatic meshes
- Bernstein-Bezier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media
- GPU-accelerated discontinuous Galerkin methods on polytopic meshes
- Parallel Scaling of the Regionally-Implicit Discontinuous Galerkin Method with Quasi-Quadrature-Free Matrix Assembly