An iterative substructuring method for Maxwell's equations in two dimensions

DOI10.1090/S0025-5718-00-01244-8zbMath1017.78008OpenAlexW1966937669MaRDI QIDQ2719060

Andrea Toselli, Olof B. Widlund, Barbara I. Wohlmuth

Publication date: 14 May 2001

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01244-8

zbMATH Keywords

domain decompositionMaxwell's equationsNédélec finite elementsiterative substructuring methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10)

Related Items (13)

Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations ⋮ Nonoverlapping domain decomposition methods with a simple coarse space for elliptic problems ⋮ Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell's equations ⋮ A discrete weighted Helmholtz decomposition and its application ⋮ BDDC Deluxe Algorithms for Two-Dimensional H($curl$) Isogeometric Analysis ⋮ A three-level BDDC algorithm for a saddle point problem ⋮ New preconditioners with two variable relaxation parameters for the discretized time-harmonic Maxwell equations in mixed form ⋮ A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell's equations in unbounded domains ⋮ A BDDC algorithm with deluxe scaling for $H(curl)$ in two dimensions with irregular subdomains ⋮ Substructuring preconditioners for saddle-point problems arising from Maxwell’s equations in three dimensions ⋮ A new coarse space for overlapping Schwarz algorithms for H(curl) problems in three dimensions with irregular subdomains ⋮ An effective preconditioner for a PML system for electromagnetic scattering problem ⋮ An optimal Robin-type domain decomposition method for the Well-posed Maxwell's equations in two dimensions

Cites Work

• Mixed finite elements in \(\mathbb{R}^3\)
• Multigrid method for \(H\text{(div)}\) in three dimensions
• Neumann-Neumann methods for vector field problems
• Overlapping Schwarz methods for Maxwell's equations in three dimensions
• Multigrid in H(div) and H(curl)
• Finite Element Methods for Navier-Stokes Equations
• An Iterative Method for Elliptic Problems on Regions Partitioned into Substructures
• Mixed and Hybrid Finite Element Methods
• An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
• Multigrid Method for Maxwell's Equations
• Schwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions
• Preconditioning in H(𝑑𝑖𝑣) and applications
• An Iterative Substructuring Method for Raviart--Thomas Vector Fields in Three Dimensions
• A FETI Domain Decomposition Method for Edge Element Approximations in Two Dimensions with Discontinuous Coefficients
• Time-discrete finite element schemes for Maxwell's equations
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