TITLE:
Quadrature Rules for Functions with a Mid-Point Logarithmic Singularity in the Boundary Element Method Based on the x = tp Substitution
AUTHORS:
Stephen M. Kirkup, Javad Yazdani, George Papazafeiropoulos
KEYWORDS:
Boundary Element Method, Singular Integral, Numerical Integration
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.9 No.4,
December
16,
2019
ABSTRACT: Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the numerical integration of the functions on the standard domain [-1, 1], with a logarithmic singularity at the centre. The substitution x = tp, where p (≥ 3) is an odd integer is given particular attention, as this returns a regular integral and the domain unchanged. Gauss-Legendre quadrature rules are applied to the transformed integrals for a number of values of p. It is shown that a high value for p typically gives more accurate results.