Boundary element methods for Maxwell transmission problems in Lipschitz domains

DOI10.1007/s00211-002-0407-zzbMath1071.65160OpenAlexW1999052490WikidataQ58841947 ScholiaQ58841947MaRDI QIDQ1412174

Christoph Schwab, Tobias von Petersdorff, Ralf Hiptmair, Annalisa Buffa

Publication date: 9 November 2003

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

Full work available at URL: https://doi.org/10.1007/s00211-002-0407-z

zbMATH Keywords

convergenceGalerkin methodMaxwell equationsHodge decompositionboundary element methodsRaviart-Thomas spacesexterior scattering problem

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items

The BEM with graded meshes for the electric field integral equation on polyhedral surfaces, Stabilized boundary element methods for low-frequency electromagnetic scattering, A posteriori error estimation for acoustic wave propagation problems, Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems, M-dissipative boundary conditions and boundary tuples for Maxwell operators, Natural hp-BEM for the electric field integral equation with singular solutions, Time Domain Integral Equation Methods in Computational Electromagnetism, A hybrid formulation of eddy current problems, Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions, ACA accelerated high order BEM for Maxwell problems, Wavenumber-explicit \textit{hp}-FEM analysis for Maxwell's equations with transparent boundary conditions, Stable and convergent fully discrete interior-exterior coupling of Maxwell's equations, The fluid-solid interaction scattering problem with unknown buried objects, Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media, Second-kind boundary integral equations for electromagnetic scattering at composite objects, Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains, Coupled-Cluster theory revisited, Ap-hierarchical error estimator for a fe–be coupling formulation applied to electromagnetic scattering problems in ℝ³, De Rham compatible deep neural network FEM, An Interface Formulation of the Laplace–Beltrami Problem on Piecewise Smooth Surfaces, Nanophotonic resonators in stratified media with the \textsc{nanobem} toolbox, Eddy-current asymptotics of the Maxwell PMCHWT formulation for multiple bodies and conductivity levels, ReLU neural network Galerkin BEM, Multilevel domain uncertainty quantification in computational electromagnetics, Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem, A well-conditioned boundary integral equation for transmission problems of electromagnetism, The eddy current model as a low-frequency, high-conductivity asymptotic form of the Maxwell transmission problem, Single and double layer potentials on domains with conical points. I: Straight cones, First-Kind Boundary Integral Equations for the Hodge--Helmholtz Operator, Shape derivatives of boundary integral operators in electromagnetic scattering. II: Application to scattering by a homogeneous dielectric obstacle, Matrix valued adaptive cross approximation, A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell's equations in unbounded domains, Analytical investigation of an integral equation method for electromagnetic scattering by biperiodic structures, Explicit time integration with lumped mass matrix for enriched finite elements solution of time domain wave problems, A multiscale approach and a hybrid FE-BE algorithm for heterogeneous scattering of Maxwell's equations, Integral equations for acoustic scattering by partially impenetrable composite objects, Multiple traces boundary integral formulation for Helmholtz transmission problems, A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces, Algebraic convergence for anisotropic edge elements in polyhedral domains, Coupled boundary-element scheme for eddy-current computation, Time dependent electromagnetic scattering by a penetrable obstacle, A dual finite element complex on the barycentric refinement, The effect of quadrature rules on finite element solutions of Maxwell variational problems. Consistency estimates on meshes with straight and curved elements, A FE/BE coupling for the 3D time-dependent eddy current problem. I: A priori error estimates, Interior penalty method for the indefinite time-harmonic Maxwell equations, Topological Sensitivity for Solving Inverse Multiple Scattering Problems in Three-Dimensional Electromagnetism. Part II: Iterative Method, Adaptive FE-BE coupling for an electromagnetic problem in ℝ3-A residual error estimator, A Posteriori Error Estimates for the Electric Field Integral Equation on Polyhedra, Solving inverse electromagnetic scattering problems via domain derivatives^†, Versatile and accurate schemes of discretization for the electromagnetic scattering analysis of arbitrarily shaped piecewise homogeneous objects, WELL-POSEDNESS AND FINITE ELEMENT APPROXIMABILITY OF TIME-HARMONIC ELECTROMAGNETIC BOUNDARY VALUE PROBLEMS INVOLVING BIANISOTROPIC MATERIALS AND METAMATERIALS, Error analysis of fully discrete mixed finite element schemes for 3-D Maxwell's equations in dispersive media, Multi-Trace Boundary Integral Formulation for Acoustic Scattering by Composite Structures, Variational formulations for transmission problems of the electromagnetic field, Spurious resonances in coupled domain-boundary variational formulations of transmission problems in electromagnetism and acoustics, Topological Sensitivity for Solving Inverse Multiple Scattering Problems in Three-dimensional Electromagnetism. Part I: One Step Method