Author(s)

Stephen M. Kirkup^1*, Javad Yazdani¹, George Papazafeiropoulos²

¹School of Engineering, University of Central Lancashire, Preston, UK.
²Hellenic Ministry of National Defence, Athens, Greece.

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 = t^p, 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.

Boundary Element Method, Singular Integral, Numerical Integration

Kirkup, S. , Yazdani, J. and Papazafeiropoulos, G. (2019) Quadrature Rules for Functions with a Mid-Point Logarithmic Singularity in the Boundary Element Method Based on the x = t^p Substitution. American Journal of Computational Mathematics, 9, 282-301. doi: 10.4236/ajcm.2019.94021.