Analytical integration in the 2D boundary element method

The integrals required in the computation of influence coefficient matrices of the boundary element method (BEM) depend on the distance r(x, x') from the collocation point or field point x to the source or load point x'. As a consequence, a distinction must be made between the case where the collocation point does not belong to the integration domain (proper integrals) and the case where the collocation point does belong to the integration domain (improper integrals), Moreover, situations arise where x comes close to x' and the integrals, albeit of a regular character, behave almost as improper, this case being referred to as nearly singular integration. Analytical integration captures best the singular or nearly singular kernel behavior, but this technique can only be carried out in very simple situations as, for instance, boundary integrals over straight elements. In the present paper a set of useful analytical integration formulas for the 2D BEM with curved elements is deduced, employing a symbolic computational algebra system. (C) 1997 John Wiley & Sons, Ltd.