On the singularities of Green's formula and its normal derivative, with an application to surface-wave-body interaction problems

Abstract

The paper presents the non-singular forms of Green's formula and its normal derivative of exterior problems for three-dimensional Laplace's equation. The main advantage of these modified formulations is that they are amenable to solution by directly using quadrature formulas. Thus, the conventional boundary element approximation, which locally regularizes the singularities in each element, is not required. The weak singularities are treated by both the Gauss flux theorem and the property of the associated equipotential body. The hypersingularities are treated by further using the boundary formula for the associated interior problems. The efficacy of the modified formulations is examined by a sphere, in an infinite domain, subject to Neumann and Dirichlet conditions, respectively. The modified integral formulations are further applied to a practical problem, i.e. surface-wave–body interactions. Using the conventional boundary integral equation formulation is known to break down at certain discrete frequencies for such a problem. Removing the ‘irregular’ frequencies is performed by linearly combining the standard integral equation with its normal derivative. Computations are presented of the added-mass and damping coefficients and wave exciting forces on a floating hemisphere. Comparing the numerical results with that by other approaches demonstrates the effectiveness of the method. Copyright © 2000 John Wiley & Sons, Ltd.