Gauss Integration Singular Integrals of BEM for Geometrically Linear ElementsLimits in Nearly


1 Department of Civil Engineering,Sharif University of Technology

2 Department of Mechanical Engineering,Sharif University of Technology


The most suitable and widely used numerical integration method for boundary integrals
in the BEM method is Gauss-Legendre integration. But, this integration method is not appropriate
for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for
recognizing nearly singular integrals in the integral form of the Laplace equation. At the rst stage,
a criterion is obtained for the constant element and, at the later stages, higher order elements are
investigated. In the present research, the Romberg integration method is used for nearly singular
integrals. The results of this numerical method have good agreement with analytical integration. The
singular integrals are solved by composing the Romberg method and midpoint rule. Constant, linear
and other interpolation functions of potentials over an element are a category of BEM elements. In
those elements, the Gauss-Legendre integration will be accurate if the source point is placed out of
the circle with a diameter equal to element length, and its center matched to the midpoint of the