New preconditioners with two variable relaxation parameters for the discretized time-harmonic Maxwell equations in mixed form
type: Item
instance of: scholarly article
title: New preconditioners with two variable relaxation parameters for the discretized time-harmonic Maxwell equations in mixed form
zbMATH Open document ID: 1264.65201
DOI: 10.1155/2012/617390
author: Yuping Zeng
author: Chenliang Li
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We provide new preconditioners with two variable relaxation parameters for the saddle point linear systems arising from finite element discretization of time-harmonic Maxwell equations in mixed form. The new preconditioners are of block-triangular forms and Schur complement-free. They are extensions of the results in [\textit{G. Cheng} et al., Comput. Phys. Commun. 180, No. 2, 192--196 (2009; Zbl 1198.65219); \textit{C. Greif} and \textit{D. Schötzau}, ETNA, Electron. Trans. Numer. Anal. 22, 114--121 (2006; Zbl 1112.65042)] and [\textit{T. Huang} et. al., Comput. Phys. Commun. 180, No. 10, 1853--1859 (2009; Zbl 1197.78068)]. Theoretical analysis shows that all eigenvalues of the preconditioned matrices are tightly clustered, and numerical tests confirm our analysis.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 6173427
MaRDI profile type: Publication
Wikidata QID: Q58912312
full work available at URL: https://doi.org/10.1155/2012/617390
OpenAlex ID: W1987199740
cites work: Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients
cites work: Block triangular preconditioners for the discretized time-harmonic Maxwell equations in mixed form
cites work: Preconditioners for the discretized time-harmonic Maxwell equations in mixed form
cites work: Substructuring preconditioners for saddle-point problems arising from Maxwell’s equations in three dimensions
cites work: Stabilized interior penalty methods for the time-harmonic Maxwell equations.
cites work: Multigrid in H(div) and H(curl)
cites work: Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations
cites work: Multigrid Method for Maxwell's Equations
cites work: An algebraic multigrid method for finite element discretizations with edge elements
cites work: An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
cites work: A Nonoverlapping Domain Decomposition Method for Maxwell's Equations in Three Dimensions
cites work: Overlapping Schwarz methods for Maxwell's equations in three dimensions
cites work: An iterative substructuring method for Maxwell's equations in two dimensions
cites work: Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
cites work: New block triangular preconditioner for linear systems arising from the discretized time-harmonic Maxwell equations
cites work: On generalized successive overrelaxation methods for augmented linear systems
cites work: On parameterized inexact Uzawa methods for generalized saddle point problems
cites work: Structured preconditioners for nonsingular matrices of block two-by-two structures
cites work: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems
cites work: Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices
cites work: Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
cites work: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems
cites work: Constraint Preconditioners for Symmetric Indefinite Matrices
cites work: Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems
cites work: A Mixed Method for Approximating Maxwell’s Equations
cites work: Finite Element Methods for Maxwell's Equations
cites work: Mixed finite elements in \(\mathbb{R}^3\)
cites work: Preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks
cites work: Parallel numerical solution of the time‐harmonic Maxwell equations in mixed form
cites work: Q4348514
description: scientific article; zbMATH DE number 6173427