Hybrid multigrid methods for high-order discontinuous Galerkin discretizations
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Publication:2194349
DOI10.1016/j.jcp.2020.109538zbMath1440.65135arXiv1910.01900OpenAlexW2978939434MaRDI QIDQ2194349
Peter Munch, Wolfgang A. Wall, Martin Kronbichler, Niklas Fehn
Publication date: 25 August 2020
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.01900
discontinuous Galerkin methodmultigridinterior penalty methodhigh-order discretizationsmatrix-free algorithmstime-to-solution
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)
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Cites Work
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- To CG or to HDG: a comparative study in 3D
- An implicit discontinuous Galerkin method for the unsteady compressible Navier-Stokes equations
- To CG or to HDG: A comparative study
- A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems
- GPU accelerated spectral finite elements on all-hex meshes
- From h to p efficiently: strategy selection for operator evaluation on hexahedral and tetrahedral elements
- \(p\)-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
- Efficient nonlinear solvers for nodal high-order finite elements in 3D
- Smoothed aggregation multigrid solvers for high-order discontinuous Galerkin methods for elliptic problems
- Scale separation in fast hierarchical solvers for discontinuous Galerkin methods
- Algebraic multigrid techniques for discontinuous Galerkin methods with varying polynomial order
- A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
- Multigrid algorithms for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
- Spectral element multigrid. II: Theoretical justification
- Robust smoothers for high-order discontinuous Galerkin discretizations of advection-diffusion problems
- Coupling \(p\)-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection-diffusion equation
- From \(h\) to \(p\) efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations
- Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
- Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
- Spectral element multigrid. I: Formulation and numerical results
- Spectral methods for problems in complex geometries
- A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations
- An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
- Parallel multigrid smoothing: Polynomial versus Gauss--Seidel
- A multilevel discontinuous Galerkin method
- Robust multigrid for high-order discontinuous Galerkin methods: a fast Poisson solver suitable for high-aspect ratio Cartesian grids
- A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
- Robust multigrid for Cartesian interior penalty DG formulations of the Poisson equation in 3D
- Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods
- The deal.II library, version 9.0
- Algebraic multigrid for higher-order finite elements
- Spectral-element preconditioners for the Uzawa pressure operator applied to incompressible flows
- Matrix-free multigrid block-preconditioners for higher order discontinuous Galerkin discretisations
- Scaling to the stars -- a linearly scaling elliptic solver for \(p\)-multigrid
- A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods
- A generic interface for parallel cell-based finite element operator application
- Direct solution of partial difference equations by tensor product methods
- Nonuniformly weighted Schwarz smoothers for spectral element multigrid
- High-order discontinuous Galerkin methods using an \(hp\)-multigrid approach
- A \(p\)-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
- Hybrid multigrid/Schwarz algorithms for the spectral element method
- FFT, FMM, or Multigrid? A comparative Study of State-Of-the-Art Poisson Solvers for Uniform and Nonuniform Grids in the Unit Cube
- Spectral p-multigrid discontinuous Galerkin solution of the Navier-Stokes equations
- Multigrid methods for the symmetric interior penalty method on graded meshes
- p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
- Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods
- Smoothed Aggregation Multigrid for the Discontinuous Galerkin Method
- Towards Textbook Efficiency for Parallel Multigrid
- Comparison of multigrid algorithms for high‐order continuous finite element discretizations
- Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems
- Implementing Spectral Methods for Partial Differential Equations
- Two‐level preconditioning of discontinuous Galerkin approximations of second‐order elliptic equations
- High‐order accuratep‐multigrid discontinuous Galerkin solution of the Euler equations
- Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier–Stokes Equations
- An Interior Penalty Finite Element Method with Discontinuous Elements
- Two-Level Fourier Analysis of a Multigrid Approach for Discontinuous Galerkin Discretization
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- High-Order Methods for Incompressible Fluid Flow
- Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method
- Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes
- Numerical Solution of the Euler Equations with a Multiorder Discontinuous Finite Element Method
- Convergence of Multigrid Algorithms for Interior Penalty Methods
- A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers
- Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems
- Fast Matrix-Free Evaluation of Discontinuous Galerkin Finite Element Operators
- Multigrid Algorithms for $hp$-Discontinuous Galerkin Discretizations of Elliptic Problems
- Performance and Scalability of Hierarchical Hybrid Multigrid Solvers for Stokes Systems
- Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations
- A hybrid geometric + algebraic multigrid method with semi‐iterative smoothers
- Investigation of Near-Wall Grid Spacing Effect in High-Order Discontinuous Galerkin RANS Computations of Turbomachinery Flows
- Methods of conjugate gradients for solving linear systems
- An efficient implicit discontinuous spectral Galerkin method
- A two-fluid spectral-element method
