A Cauchy integral element for power-type singularities (Q1208749)

The paper deals with the complex variable boundary element method in the context of power-type boundary singularities of plane harmonic functions. The singular behaviour is such as may be observed at corner points of polygonal domains and at boundary points where a change in the boundary conditions occurs. The element is composed of two straight line segments, and the function is expressed through its power series expansion about the vertex point, and a truncation is adopted as the complex density distribution in a Cauchy integral over the element. The integral is evaluated and the element formulation is expressed in closed form. With proper adjustment of the coefficients of the truncation, the element formulation can represent a regular or singular behaviour of the analytic function. The method is used for potential flow problems involving equipotential and streamline boundary conditions.