Low-Order Preconditioning for the High-Order Finite Element de Rham Complex

Clark R. Dohrmann, Will Pazner, Tzanio V. Kolev

Publication date: 20 April 2023

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

Full work available at URL: https://arxiv.org/abs/2203.02465

zbMATH Keywords

finite elements preconditioning de Rham complex algebraic multigrid high-order

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Preconditioners for iterative methods (65F08)

Related Items (1)

High-Order Mixed Finite Element Variable Eddington Factor Methods

Uses Software

hypre
MFEM

Cites Work

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A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems
Efficient nonlinear solvers for nodal high-order finite elements in 3D
Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation
Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
Differencing of the diffusion equation in Lagrangian hydrodynamic codes
Spectral methods for problems in complex geometries
On a BPX-preconditioner for P1 elements
An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
Preconditioned minimal residual methods for Chebyshev spectral calculations
Algebraic multigrid theory: The symmetric case
Stabilization of spectral methods by finite element bubble functions
Condition number and diagonal preconditioning: Comparison of the $p$-version and the spectral element methods
Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa
Uniform subspace correction preconditioners for discontinuous Galerkin methods with $hp$-refinement
MFEM: a modular finite element methods library
Matrix-free multigrid block-preconditioners for higher order discontinuous Galerkin discretisations
Hybrid multigrid/Schwarz algorithms for the spectral element method
Edge Functions for Spectral Element Methods
Finite-Element Preconditioning of G-NI Spectral Methods
Finite element exterior calculus, homological techniques, and applications
Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems
Algebraic Multigrid Preconditioning of High-Order Spectral Elements for Elliptic Problems on a Simplicial Mesh
Parallel Auxiliary Space AMG for H(Curl) Problems
Algebraic multigrid for k‐form Laplacians
Two‐level preconditioning of discontinuous Galerkin approximations of second‐order elliptic equations
Approximation Results for Orthogonal Polynomials in Sobolev Spaces
Multigrid Methods for Variational Problems: General Theory for the V-Cycle
An Interior Penalty Finite Element Method with Discontinuous Elements
Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
Low-Order Preconditioning of High-Order Triangular Finite Elements
Domain Decomposition Preconditioners for Spectral Nédélec Elements in Two and Three Dimensions
Finite Element Methods for Maxwell's Equations
Preconditioning Legendre Spectral Collocation Approximations to Elliptic Problems
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces
Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces
Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods
Diffusion Synthetic Acceleration Preconditioning for Discontinuous Galerkin Discretizations of $S_N$ Transport on High-Order Curved Meshes
An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations
Scalable Low-Order Finite Element Preconditioners for High-Order Spectral Element Poisson Solvers
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
An algebraic multigrid method for finite element discretizations with edge elements
Toward an h-Independent Algebraic Multigrid Method for Maxwell's Equations
Fully discrete $hp$-finite elements: Fast quadrature
Implicit Monte Carlo diffusion -- an acceleration method for Monte Carlo time-dependent radiative transfer simulations
On condition numbers in $hp$-FEM with Gauss-Lobatto-based shape functions

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