Quadrature of Integrands with a Logarithmic Singularity

DOI10.2307/2153167zbMath0795.65010OpenAlexW4251989254MaRDI QIDQ4293969

J.A.Crow

Publication date: 10 July 1994

Full work available at URL: https://doi.org/10.2307/2153167

zbMATH Keywords

Galerkin methodfinite element methodsquadrature rulelogarithmic singularitycubic B-splineboundary integral equations method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (6)

Fast non-polynomial interpolation and integration for functions with logarithmic singularities ⋮ On the singularity of the axially symmetric Helmholtz Green's function, with application to BEM ⋮ Generalized quadrature rules of Gaussian type for numerical evaluation of singular integrals ⋮ A contour dynamics algorithm for axisymmetric flow ⋮ Isogeometric boundary element analysis of liquid nonlinear sloshing in two dimensional rectangular tanks ⋮ Direct Gauss quadrature formulae for logarithmic singularities on isoparametric elements

Uses Software

• Algorithm 693

Cites Work

• Unnamed Item
• Unnamed Item
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• Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature
• Wilf-quadrature
• On a certain quadrature formula
• Quadrature formulas obtained by variable transformation
• Exactness conditions in numerical quadrature
• The tanh transformation for singular integrals
• Extension of numerical quadrature formulae to cater for end point singular behaviours over finite intervals
• Algorithm 693: a FORTRAN package for floating-point multiple-precision arithmetic

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