Wavenumber-explicit analysis for the Helmholtz \(h\)-BEM: error estimates and iteration counts for the Dirichlet problem
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Publication:1740636
DOI10.1007/s00211-019-01032-yzbMath1414.35054arXiv1608.01035OpenAlexW2963438872WikidataQ128265013 ScholiaQ128265013MaRDI QIDQ1740636
Eike H. Müller, Jeffrey Galkowski, Euan A. Spence
Publication date: 2 May 2019
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1608.01035
Numerical methods for integral equations (65R20) Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Related Items (15)
Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems ⋮ Frequency-robust preconditioning of boundary integral equations for acoustic transmission ⋮ A Burton-Miller boundary element-free method for Helmholtz problems ⋮ Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators ⋮ Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency? ⋮ Does the Helmholtz Boundary Element Method Suffer from the Pollution Effect? ⋮ Recent Advances in Acoustic Boundary Element Methods ⋮ A Parameter Study of the Burton–Miller Formulation in the BEM Analysis of Acoustic Resonances in Exterior Configurations ⋮ Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation ⋮ Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification ⋮ Bi-parametric operator preconditioning ⋮ Pollution and accuracy of solutions of the Helmholtz equation: a novel perspective from the eigenvalues ⋮ High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis ⋮ A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency ⋮ High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem
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