The \(hp\)-version of the boundary element method for Helmholtz screen problems

DOI10.1007/BF02276875zbMath0859.65122OpenAlexW1578357209MaRDI QIDQ1924481

H. Holm, Matthias Maischak, Ernst Peter Stephan

Publication date: 7 April 1997

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02276875

zbMATH Keywords

convergenceboundary element methodnumerical experimentsHelmholtz equationweakly singular\(hp\)-versionintegral equations of the first kindhypersingular

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (13)

Boundary elements with mesh refinements for the wave equation ⋮ \(hp\)-version time domain boundary elements for the wave equation on quasi-uniform meshes ⋮ A nonconforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator ⋮ Continuum limit of discrete Sommerfeld problems on square lattice ⋮ A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering ⋮ Exponential convergence of the h–p version BEM for mixed boundary value problems on polyhedrons ⋮ Boundary element methods for acoustic scattering by fractal screens ⋮ Adaptive multilevel BEM for acoustic scattering ⋮ Multilevel norms for \(H^{-1/2}\) ⋮ Acoustic waves scattered by elastic waveguides using a spectral approach with a 2.5D coupled boundary-finite element method ⋮ Application of the Trefftz method in an original variational formulation to the analysis of the current transformer field ⋮ Multilevel methods for the \(h\)-, \(p\)-, and \(hp\)-versions of the boundary element method ⋮ Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens

Cites Work

• A direct boundary integral equation method for transmission problems
• Boundary integral equations for screen problems in \({\mathbb{R}}^ 3\)
• Duality estimates for the numerical solution of integral equations
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Exponential convergence of the \(hp\)-version for the boundary element method on open surfaces
• A hypersingular boundary integral method for two-dimensional screen and crack problems
• Regularity of mixed boundary value problems in ℝ3 and boundary element methods on graded meshes
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron
• The Optimalp-Version Approximation of Singularities on Polyhedra in the Boundary Element Method
• A boundary element Galerkin method for a hypersingular integral equation on open surfaces
• An improved boundary element method for the charge density of a thin electrified plate in ℝ³
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