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

• Published in: Engineering analysis with boundary elements Vol. 25; no. 9; pp. 819 - 828
• Main Authors: Chen, J.T., Lin, J.H., Kuo, S.R., Chiu, Y.P.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2001; Elsevier
• Subjects: Boundary elements; Boundary-integral methods; Circulant; Computational techniques; Degenerate kernel; Degenerate scale; Exact sciences and technology; Mathematical methods in physics; Physics; Degenerate kernel; Degenerate scale; Boundary elements; Circulant; Singularity; Mathematical analysis; Integral equations; Singular equation; Numerical method; Experimental study; Analytical solution; Boundary element method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(01)00064-9

For a potential problem, the boundary integral equation approach has been shown to yield a nonunique solution when the geometry is equal to a degenerate scale. In this paper, the degenerate scale problem in boundary element method (BEM) is analytically studied using the degenerate kernels and circulants. For the circular domain problem, the singular problem of the degenerate scale with radius one can be overcome by using the hypersingular formulation instead of the singular formulation. A simple example is shown to demonstrate the failure using the singular integral equations. To deal with the problem with a degenerate scale, a constant term is added to the fundamental solution to obtain the unique solution and another numerical example with an annular region is also considered.