Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: The singular complement method.

DOI10.1016/S0021-9991(03)00309-7zbMath1033.65086OpenAlexW2151558909MaRDI QIDQ1413125

J. Segré, Franck Assous, Simon Labrunie, Patrick~jun. Ciarlet

Publication date: 16 November 2003

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-9991(03)00309-7

zbMATH Keywords

numerical examplesMaxwell equationsSingularitiesAxisymmetryConforming finite element methodsingular complement methodsingular doamins

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Electromagnetic theory (general) (78A25)

Related Items (22)

The Fourier singular complement method for the Poisson problem. II: Axisymmetric domains ⋮ Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field ⋮ Nonlinear thermo-electromagnetic analysis of inductive heating processes ⋮ A NUMERICAL METHOD FOR 3D TIME-DEPENDENT MAXWELL’S EQUATIONS IN AXISYMMETRIC SINGULAR DOMAINS WITH ARBITRARY DATA ⋮ New numerical method for solving time-harmonic Maxwell equations with strong singularity ⋮ A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem ⋮ The singular complement method for 2d scalar problems ⋮ Axi symmetric 2D simulation and numerical heat transfer characteristics for the calibration furnace in a rectangular enclosure ⋮ Exact boundary controllability of the second-order Maxwell system: theory and numerical simulation ⋮ Numerical solution to the 3D static Maxwell equations in axisymmetric singular domains with arbitrary data ⋮ Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries ⋮ A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem ⋮ A generalization of \(Mv\) integral to axisymmetric problems for viscoelastic materials ⋮ Time-dependent Maxwell's equations with charges in singular geometries ⋮ Augmented formulations for solving Maxwell equations ⋮ Approximation of the axisymmetric elasticity equations ⋮ Time-dependent electromagnetic waves in a cavity ⋮ Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in nonsmooth axisymmetric domains ⋮ Solving Vlasov-Maxwell equations in singular geometries ⋮ A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL–CURL PROBLEM ⋮ NUMERICAL ANALYSIS OF THE GENERALIZED MAXWELL EQUATIONS (WITH AN ELLIPTIC CORRECTION) FOR CHARGED PARTICLE SIMULATIONS ⋮ Stabilized mixed approximation of axisymmetric Brinkman flows

Cites Work

• Unnamed Item
• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
• Mixed finite elements in \(\mathbb{R}^3\)
• On finite element methods for elliptic equations on domains with corners
• Elliptic problems in domains with piecewise smooth boundaries
• On a finite-element method for solving the three-dimensional Maxwell equations
• The singular complement method for 2d scalar problems
• Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: The singular complement method
• Numerical approximation of the Maxwell equations in inhomogeneous media by a \(P^ 1\) conforming finite element method
• Inf-sup condition for the 3-D \(P_2\)-iso-\(P_1\) Taylor-Hood finite element; application to Maxwell equations
• Two coupled particle-finite volume methods using Delaunay-Voronoï meshes for the approximation of Vlasov-Poisson and Vlasov-Maxwell equations
• On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra
• Updating the Inverse of a Matrix
• Maxwell and Lamé eigenvalues on polyhedra
• Analyse spectrale et singularités d'un problème de transmission non coercif
• Theoretical tools to solve the axisymmetric Maxwell equations
• Éléments finis d'arête et condensation de masse pour les équations de Maxwell: le cas de dimension 3
• Solution of axisymmetric Maxwell equations
• A Singular Field Method for Maxwell's Equations: Numerical Aspects for 2D Magnetostatics
• Résolution des équations de Maxwell instationnaires avec charges dans un domaine singulier bidimensionnel

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