Analytical derivation and numerical experiment of degenerate scale by using the degenerate kernel of the bipolar coordinates. (December 2017)

• Record Type: Journal Article
• Authors: Chen, Jeng-Tzong; Kao, Shing-Kai; Lee, Jia-Wei
• Is Part Of: Engineering analysis with boundary elements. Volume 85(2017)
• Page Start: 70
• Page End: 86
• Publication Date: 2017-12
• Subjects: Degenerate scale -- Degenerate kernel -- Bipolar coordinates -- Eccentric annulus; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2017.08.006
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Degenerate scales of an eccentric annulus and an infinite plane with two identical circular holes in the boundary integral equation method (BIEM) are analytically derived and numerically implemented in this paper. To analytically study the degenerate scale of the BIE, the closed-form fundamental solution of the two-dimensional Laplace equation, ln r, is expanded by a degenerate (separate) kernel in terms of the bipolar coordinates. It is proved that unit radius of the outer circle dominates the degenerate scale of eccentric annulus. An analytical formula of degenerate scale for the infinite plane with two identical circular boundaries was also derived at the first time. In addition, null fields of the domain and complementary domain for the ordinary and degenerate scales are both shown, respectively. Finally, comparison with available results and the BEM data are well done.