Analytical Evaluation of Weakly Singular Integrals for Helmholtz Equation

抄録

This paper presents analytical evaluation of weakly singular integrals arising in the boundary element analysis of Helmholtz and modified Helmholtz equations. Expressions for these boundary integrals are presented in terms of elementary integrals for straight line elements of arbitrary order, which are applicable not only to the singular integrals but also to the regular integrals when the collocation point is collinear with the integration element. Closed form analytical expressions have been derived for the elementary integrals for both the problems. The proposed finite term analytical formulae involving Bessel and Struve functions are very efficient compared to specialized numerical quadrature or the analytical formulae in terms of infinite series of some elementary integrals available in the literature.