Analytical integration of weakly singular integrals in boundary element analysis of Helmholtz and advection-diffusion equations

This paper presents analytical evaluation of weakly singular integrals aris ing in the boundary element analysis of Helmholtz, modified Helmholtz and a dvection-diffusion equations. Expressions for these boundary integrals are presented in terms of elementary integrals for straight line elements of ar bitrary 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. Analytical expressions have been derived for the e lementary integrals using integrals of Bessel functions. Analytical approxi mations of the zeroth order elementary integrals for the modified Helmholtz and advection-diffusion equations suitable for single as well as double pr ecision computations have been proposed, which would be specially useful fo r large wave numbers or Peclet numbers for the respective problems. (C) 200 0 Elsevier Science S.A. All rights reserved.