Additive schwarz methods for indefinite hypersingular integral equations in R3- the p-version

DOI10.1080/00036819908840750zbMath1020.65100OpenAlexW1969246701MaRDI QIDQ4487789

Norbert Heuer

Publication date: 25 June 2000

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819908840750

zbMATH Keywords

numerical resultsboundary element methodSchwarz methodspreconditioning\(p\)-versionHelmholtz equationscalingGMRES methodgeneralized minimal residual methodindefinite hypersingular integral equations

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical methods for integral equations (65R20) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Integral equations with kernels of Cauchy type (45E05)

Related Items (6)

Anhp-adaptive refinement strategy for hypersingular operators on surfaces ⋮ Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D ⋮ A p‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen ⋮ Optimal additive Schwarz methods for the \(hp\)-BEM: the hypersingular integral operator in 3D on locally refined meshes ⋮ Approximation of Hypersingular Integral Operators With Cauchy Kernel ⋮ Multilevel methods for the \(h\)-, \(p\)-, and \(hp\)-versions of the boundary element method

Cites Work

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• Boundary integral equations for screen problems in \({\mathbb{R}}^ 3\)
• Duality estimates for the numerical solution of integral equations
• An iterative substructuring method for the \(p\)-version of the boundary element method for hypersingular integral operators in three dimensions
• A finite element method for some integral equations of the first kind
• Additive Schwarz methods for the \(p\)-version finite element method
• Schwarz methods with local refinement for the \(p\)-version finite element method
• Polynomial extensions of compatible polynomial traces in three dimensions
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Regularity of mixed boundary value problems in ℝ3 and boundary element methods on graded meshes
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• The Schwarz Algorithm for Spectral Methods
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Domain Decomposition Algorithms for Indefinite Elliptic Problems
• Domain Decomposition Algorithms for Indefinite Hypersingular Integral Equations: The h and p Versions
• A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions

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