Efficient algorithms for the \(p\)-version of the boundary element method

DOI10.1216/jiea/1181075956zbMath0872.65102OpenAlexW1994843419MaRDI QIDQ1353460

Norbert Heuer

Publication date: 20 October 1997

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jiea/1181075956

zbMATH Keywords

Galerkin methodnumerical examplesboundary element methoddomain decompositionerror bounds\(p\)-versionpreconditionersLegendre polynomialsadditive Schwarz methoddegree decompositionsimple layer potential operator

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Numerical computation of matrix norms, conditioning, scaling (65F35) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (5)

Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods ⋮ Remarks on Sobolev norms of fractional orders ⋮ Stable multilevel splittings of boundary edge element spaces ⋮ Multiplicative Schwarz algorithms for the \(p\)-version Galerkin boundary element method in 3D ⋮ Multilevel methods for the \(h\)-, \(p\)-, and \(hp\)-versions of the boundary element method

Cites Work

• Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem
• Schwarz iterations for the efficient solution of screen problems with boundary elements
• On the \(h\)-\(p\) version of the boundary element method for Symm's integral equation on polygons
• The problem of selecting the shape functions for ap-type finite element
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• The $h-p$ version of the boundary element method on polygonal domains with quasiuniform meshes
• Additive schwarz methods for the H-version boundary element method
• Multiwavelets for Second-Kind Integral Equations
• Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
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