Gauss-Jacobi quadratures for hypersingular integrals

Journal article

This paper introduces the use of finite part integration for hypersingular boundary integrals, with particular emphasis being placed on demonstrating the consistency between the underlying physical concept and the mathematical definition. Gaussian interpolative quadratures are then derived for the regular, Cauchy-singular, and hypersingular integrals. The resulting formulae depend on the Jacobi polynomials p_n^(α,β) and the associated functions q_n^(α,β), and the properties and numerical evaluation of these functions are discussed in the following section. The use of the hypersingular Gaussian quadrature technique is then demonstrated in application to the solution of boundary integral equations in fracture mechanics.

Authors: Korsunsky, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publication date: 2014-01-01
• Language: English
• Subjects: Engineering & allied sciences