Efficient Matrix-Free High-Order Finite Element Evaluation for Simplicial Elements
DOI10.1137/19M1246523zbMath1440.65223OpenAlexW3011811412WikidataQ114074261 ScholiaQ114074261MaRDI QIDQ5112634
Roman Amici, Mike Kirby, David Moxey
Publication date: 2 June 2020
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/19m1246523
high-performance computinghigh-order finite elementsspectral/\(hp\) element methodSIMD vectorization
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Parallel algorithms in computer science (68W10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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- To CG or to HDG: a comparative study in 3D
- PyFR: an open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach
- A new triangular spectral element method. I: Implementation and analysis on a triangle
- From h to p efficiently: strategy selection for operator evaluation on hexahedral and tetrahedral elements
- Dealiasing techniques for high-order spectral element methods on regular and irregular grids
- From \(h\) to \(p\) efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations
- High-order splitting methods for the incompressible Navier-Stokes equations
- Spectral methods on triangles and other domains
- An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
- De-aliasing on non-uniform grids: algorithms and applications.
- An isoparametric approach to high-order curvilinear boundary-layer meshing
- Nektar++: an open-source spectral/\(hp\) element framework
- Factorizing the factorization -- a spectral-element solver for elliptic equations with linear operation count
- A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
- Robust and efficient discontinuous Galerkin methods for under-resolved turbulent incompressible flows
- Optimising the performance of the spectral/\(hp\) element method with collective linear algebra operations
- Nonconforming Schwarz-spectral element methods for incompressible flow
- Fast simplicial finite element algorithms using Bernstein polynomials
- \textit{Nektar}++: enhancing the capability and application of high-fidelity spectral/\(hp\) element methods
- Algorithms and data structures for massively parallel generic adaptive finite element codes
- p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
- Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
- deal.II—A general-purpose object-oriented finite element library
- Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
- Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
- A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers
- A new triangular and tetrahedral basis for high‐order (hp) finite element methods
- Finite element assembly strategies on multi‐core and many‐core architectures
