Analytical study and numerical experiments for degenerate scale problems in boundary element method using degenerate kernels and circulants

For a potential problem, the boundary integral equation approach has been s hown to yield a nonunique solution when the geometry is equal to a degenera te scale. In this paper, the degenerate scale problem in boundary element m ethod (BEM) is analytically studied using the degenerate kernels and circul ants. For the circular domain problem, the singular problem of the degenera te scale with radius one can be overcome by using the hypersingular formula tion instead of the singular formulation. A simple example is shown to demo nstrate the failure using the singular integral equations. To deal with the problem with a degenerate scale, a constant term is added to the fundament al solution to obtain the unique solution and another numerical example wit h an annular region is also considered. (C) 2001 Elsevier Science Ltd. All rights reserved.