An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions

DOI10.1007/s002110000134zbMath0953.65084OpenAlexW2126897161MaRDI QIDQ1572931

Publication date: 10 January 2001

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

Full work available at URL: https://doi.org/10.1007/s002110000134

zbMATH Keywords

boundary element method condition number hypersingular integral equations additive Schwarz preconditioners wirebasket space

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Boundary element methods for boundary value problems involving PDEs (65N38) Higher-order parabolic equations (35K25)

Related Items (20)

Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals ⋮ Superconvergence of Newton-Cotes rule for computing hypersingular integral on a circle ⋮ Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. III: Inverse approximation theorems ⋮ On uniform approximations to hypersingular finite-part integrals ⋮ Two-level preconditioning for \(h\)-version boundary element approximation of hypersingular operator with GenEO ⋮ Stress computations on perforated polygonal domains. ⋮ Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles ⋮ Sparse shape functions for tetrahedral \(p\)-FEM using integrated Jacobi polynomials ⋮ The extrapolation methods based on Simpson's rule for computing supersingular integral on interval ⋮ Remarks on Sobolev norms of fractional orders ⋮ The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval ⋮ Optimal additive Schwarz methods for the \(hp\)-BEM: the hypersingular integral operator in 3D on locally refined meshes ⋮ Optimal extensions on tensor-product meshes ⋮ A domain decomposition preconditioner for \(p\)-FEM discretizations of two-dimensional elliptic problems ⋮ Additive Schwarz preconditioners for theh-pversion boundary-element approximation to the hypersingular operator in three dimensions ⋮ New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials ⋮ An extension theorem for polynomials on triangles ⋮ Explicit polynomial preserving trace liftings on a triangle ⋮ Superconvergence of Hermite rule for hypersingular integrals on interval ⋮ Optimal error estimate of a projection based interpolation for the \(p\)-version approximation in three dimensions

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