Numerical solution of the degenerate scale problem with arbitrary hole configuration in 2D Laplace equation

Abstract

This paper provides a numerical solution for the degenerate scale of arbitrary hole configuration in 2D Laplace equation. The problem can be first formulated in the degenerate scale. After making a coordinate transform, we can obtain the relevant boundary integral equation (BIE) in the ordinary scale. The formulated BIE in the ordinary scale represents a weaker singular equation. After solving the weaker singular equation, the degenerate scale can be evaluated immediately.