A modified Gauss quadrature formula with special integration points for evaluation of Quasi-singular integrals

It is well known in the boundary element method that integration rules fail when the integrand presents a nearby singularity. This drawback arises when the field point is near the source point, i.e. in the case of a domain with very narrow boundaries or when the field point where we try to calculate stresses or any other field variables, is near the boundaries.In the present paper a quadrature formulas for ℓ isolated singularities near the integration interval, based on ordinary or special Langrange interpolatory polynomials, is obtained. This interpolatory formulas present similarities with known formulas for the numerical evaluation of singular integrals. Quadrature formulas for regular and singular integrals with conjugate poles are also derived. Numerical examples are given and the proposed quadrature rules present the expected polynomial accuracy.