Hierarchical quadrature for singular integrals

DOI10.1007/s00607-004-0076-0zbMath1068.65038OpenAlexW2050124308MaRDI QIDQ1776516

Steffen Börm, Wolfgang Hackbusch

Publication date: 12 May 2005

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-004-0076-0

zbMATH Keywords

numerical examplessingular integralsalgorithmic complexityhypersingular integralsNumerical quadraturediscretization of integral equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical quadrature and cubature formulas (65D32) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Complexity and performance of numerical algorithms (65Y20)

Related Items (6)

Computing the Hilbert transform using biorthogonal spline wavelets ⋮ Analytic integration of the Newton potential over cuboids and an application to fast multipole methods ⋮ Tensor structured evaluation of singular volume integrals ⋮ Efficient convolution with the Newton potential in \(d\) dimensions ⋮ Hierarchical quadrature for multidimensional singular integrals ⋮ Fast multipole preconditioners for sparse matrices arising from elliptic equations

Cites Work

• Multidimensional weakly singular integral equations
• A remark on the numerical computation of improper integrals
• On numerical cubatures of singular surface integrals in boundary element methods
• Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation
• On numerical cubatures of nearly singular surface integrals arising in BEM collocation
• Variable order composite quadrature of singular and nearly singular integrals
• Quadrature for \(hp\)-Galerkin BEM in \(\mathbb{R}^3\)
• Low-rank approximation of integral operators by interpolation
• Efficient automatic quadrature in 3-D Galerkin BEM
• Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
• Boundary Elements: Implementation and Analysis of Advanced Algorithms
• On a Class of Winkler‐Type Contact Problems
• Transformation of hypersingular integrals and black-box cubature
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