GPU-Accelerated Bernstein--Bézier Discontinuous Galerkin Methods for Wave Problems

DOI10.1137/15M1053542zbMath1365.65219arXiv1512.06025OpenAlexW2964304017MaRDI QIDQ5738171

Jesse Chan, Timothy Warburton

Publication date: 31 May 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06025

zbMATH Keywords

stabilitynumerical examplewave propagationBernstein polynomialsdiscontinuous GalerkinBernstein-Bézier basis

Mathematics Subject Classification ID

Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (13)

A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media ⋮ Reduced storage nodal discontinuous Galerkin methods on semi-structured prismatic meshes ⋮ Recent advances in numerical methods for solving the wave equation in the context of seismic depth imaging ⋮ Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes ⋮ Weight-Adjusted Discontinuous Galerkin Methods: Wave Propagation in Heterogeneous Media ⋮ Adaptive mesh refinement on graphics processing units for applications in gas dynamics ⋮ Bernstein-Bézier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media ⋮ A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities ⋮ High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration ⋮ An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs ⋮ A Short Note on a Bernstein--Bezier Basis for the Pyramid ⋮ Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains ⋮ GPU-Accelerated Discontinuous Galerkin Methods on Polytopic Meshes

Uses Software

• CUBLAS
• OCCA
• GiMMiK

Cites Work

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• The Bernstein polynomial basis: a centennial retrospective
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• On multivariate approximation by Bernstein-type polynomials
• On the constants in \(hp\)-finite element trace inverse inequalities.
• Legendre-Bernstein basis transformations
• Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains
• Recursive de Casteljau bisection and rounding errors
• Fast simplicial finite element algorithms using Bernstein polynomials
• New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials
• Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension
• Pyramid Algorithms for Bernstein--Bézier Finite Elements of High, Nonuniform Order in Any Dimension
• Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
• Basis Functions for Triangular and Quadrilateral High-Order Elements
• A Short Note on a Bernstein--Bezier Basis for the Pyramid

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