A discrete weighted Helmholtz decomposition and its application

DOI10.1007/s00211-013-0536-6zbMath1277.65098OpenAlexW2152892406MaRDI QIDQ368580

Qiya Hu, Shi Shu, Jun Zou

Publication date: 23 September 2013

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-013-0536-6

zbMATH Keywords

convergencefinite element methodcondition numberMaxwell's equationspreconditionersaddle-point problemdiscontinuity of the coefficientsdiscrete weighted Helmholtz decompositionedge element

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with low regular coefficients and/or low regular data (35R05) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Electromagnetic theory (general) (78A25) Preconditioners for iterative methods (65F08) Maxwell equations (35Q61)

Related Items

A recovery-based a posteriori error estimator for \(H\)(curl) interface problems, Convergence of the Hiptmair–Xu Preconditioner for \(\boldsymbol{H}\textbf{(curl)}\)-Elliptic Problems with Jump Coefficients (ii): Main Results, Convergence of the Hiptmair--Xu Preconditioner for Maxwell's Equations with Jump Coefficients (i): Extensions of the Regular Decomposition, A BDDC Algorithm with Deluxe Scaling for Three-Dimensional H (curl) Problems, Domain decomposition preconditioners for mixed finite-element discretization of high-contrast elliptic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On electric and magnetic problems for vector fields in anisotropic nonhomogeneous media
• Fully discrete finite element approaches for time-dependent Maxwell's equations
• Overlapping Schwarz methods for Maxwell's equations in three dimensions
• Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems
• Some remarks on the characterization of the space of tangential traces of \(H(\text{rot}; \Omega)\) and the construction of an extension operator
• An iterative substructuring method for Maxwell's equations in two dimensions
• An Iterative Method with Variable Relaxation Parameters for Saddle-Point Problems
• Finite element convergence for the Darwin model to Maxwell's equations
• Magnetostatic field computations in terms of two-component vector potentials
• Dual-primal FETI algorithms for edge finite-element approximations in 3D
• Finite elements in computational electromagnetism
• A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
• The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
• An analysis of the Darwin model of approximation to Maxwell’s equations
• Mixed and Hybrid Finite Element Methods
• A Preconditioned Iterative Method for Saddlepoint Problems
• Some Nonoverlapping Domain Decomposition Methods
• An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
• Multigrid Method for Maxwell's Equations
• Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
• Substructuring preconditioners for saddle-point problems arising from Maxwell’s equations in three dimensions
• A Nonoverlapping Domain Decomposition Method for Maxwell's Equations in Three Dimensions
• Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
• Preconditioning Poincare-Steklov operators arising from domain decompositions with mortar multipliers
• Finite Element Methods for Maxwell's Equations