Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations
Mathematics of Computation
Analysis of multilevel methods for eddy current problems
Mathematics of Computation
Parallel multigrid smoothing: polynomial versus Gauss--Seidel
Journal of Computational Physics
Adaptive multigrid and domain decomposition methods in the computation of electromagnetic fields
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Journal of Computational Physics
An E-based splitting finite element method for time-dependent eddy current equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation
Computers & Mathematics with Applications
An efficient p-version multigrid solver for fast hierarchical vector finite element analysis
Finite Elements in Analysis and Design
A multigrid conjugate gradient method
Applied Numerical Mathematics
Applied Numerical Mathematics
Convergence analysis of an adaptive edge element method for Maxwell's equations
Applied Numerical Mathematics
Parallel SSOR preconditioning implemented on dynamic SMP clusters with communication on the fly
Future Generation Computer Systems
An efficient multigrid preconditioner for Maxwell's equations in micromagnetism
Mathematics and Computers in Simulation
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
A Second Order Discretization of Maxwell's Equations in the Quasi-Static Regime on OcTree Grids
SIAM Journal on Scientific Computing
Algebraic Multigrid for High-Order Hierarchical $H(curl)$ Finite Elements
SIAM Journal on Scientific Computing
Optimal control of Maxwell's equations with regularized state constraints
Computational Optimization and Applications
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Computers & Mathematics with Applications
Computers & Mathematics with Applications
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Journal of Computational Physics
Multigrid methods for two-dimensional Maxwell's equations on graded meshes
Journal of Computational and Applied Mathematics
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In this paper we are concerned with the efficient solution of discrete variational problems related to the bilinear form ({\bf curl}\! $\cdot$, {\bf curl}\! $\cdot)_{{\fontsize{6}{0pt}\selectfont\textbf{\textit{L}}}^2(\Omega)}$ + ($\cdot,\cdot)_{{\fontsize{6}{0pt}\selectfont\textbf{\textit{L}}}^2(\Omega)}$ defined on \textbf{\textit{H}}$_0$({\bf curl}; $\Omega$). This is a core task in the time-domain simulation of electromagnetic fields, if implicit timestepping is employed. We rely on Nédélec's \textbf{\textit{H}}({\bf curl}; $\Omega$)-conforming finite elements (edge elements) to discretize the problem. We construct a multigrid method for the fast iterative solution of the resulting linear system of equations. Since proper ellipticity of the bilinear form is confined to the complement of the kernel of the {\bf curl} operator, Helmholtz decompositions are the key to the design of the algorithm: ${\cal N}$({\bf curl}) and its complement ${\cal N}$({\bf curl})$^{\bot}$ require separate treatment. Both can be tackled by nodal multilevel decompositions, where for the former the splitting is set in the space of discrete scalar potentials.Under certain assumptions on the computational domain and the material functions, a rigorous proof of the asymptotic optimality of the multigrid method can be given, which shows that convergence does not deteriorate on very fine grids. The results of numerical experiments confirm the practical efficiency of the method.