Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1289.65048
published in: Numerical Linear Algebra with Applications
publication date: 2013-12-06T00:00:00Z
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6236479
zbMATH Keywords: splitting iteration method
zbMATH Keywords: preconditioning
zbMATH Keywords: saddle-point problem
zbMATH Keywords: time-harmonic eddy current problem
zbMATH Keywords: hybrid formulation
zbMATH Keywords: finite element approximation
zbMATH Keywords: numerical examples
zbMATH Keywords: convergence
zbMATH Keywords: Krylov subspace methods
zbMATH Keywords: GMRES
zbMATH Keywords: BiCGSTAB
author: Zhong-Zhi Bai
MaRDI profile type: Publication
full work available at URL: nla.810
OpenAlex ID: W2107722226
cites work: Mixed and Hybrid Finite Element Methods
cites work: Iterative Methods for the Saddle-Point Problem Arising from the ${\bfH}_C/{\bfE}_I$ Formulation of the Eddy Current Problem
cites work: Eddy current approximation of Maxwell equations. Theory, algorithms and applications
cites work: On the condition ‘h normal to the wall’ in magnetic field problems
cites work: Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
cites work: SOR-like methods for augmented systems
cites work: On generalized successive overrelaxation methods for augmented linear systems
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: A Preconditioner for Generalized Saddle Point Problems
cites work: Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
cites work: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems
cites work: Splitting iteration methods for non-Hermitian positive definite systems of linear equations
cites work: An Iteration for Indefinite Systems and Its Application to the Navier--Stokes Equations
cites work: Minimum residual methods for augmented systems
cites work: Constraint Preconditioning for Indefinite Linear Systems
cites work: Numerical solution of saddle point problems
cites work: Eigenvalue estimates for preconditioned saddle point matrices
cites work: Constraint Preconditioners for Symmetric Indefinite Matrices
cites work: A domain decomposition approach for heterogeneous time-harmonic Maxwell equations
cites work: Optimal Parameter in Hermitian and Skew-Hermitian Splitting Method for Certain Two-by-Two Block Matrices
cites work: Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices
cites work: A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations
cites work: Q4414854
cites work: Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation
DOI: 10.1002/NLA.810
title: Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models.
review text: The time-harmonic eddy current model is often used to simulate the electromagnetic phenomena concerning alternating currents at low frequencies. This paper studies the solution for the saddle-point systems that arise from the finite element discretizations of the hybrid formulations of the time-harmonic eddy current problems. By sufficiently utilizing the algebraic properties and the sparse structures of the coefficient matrix, they establish a class of block alternating splitting implicit iteration methods and demonstrate its unconditional convergence. Experimental results shown the feasibility and effectiveness of this class of iterative methods when they are employed as preconditioners for Krylov subspace methods such as GMRES and BiCGSTAB.
description: scientific article; zbMATH DE number 6236479