The method of two-point angular basis function for solving Laplace equation. (September 2019)

• Record Type: Journal Article
• Authors: Kuo, Chung-Lun; Yeih, Weichung; Ku, Cheng-Yu; Fan, Chia-Ming
• Is Part Of: Engineering analysis with boundary elements. Volume 106(2019)
• Page Start: 264
• Page End: 274
• Publication Date: 2019-09
• Subjects: Two-point angular basis function -- Cracklets -- Logarithm singularity -- Multiply connected domain; 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.2019.05.018
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper, an approach to improve the method of angular basis function (MABF) proposed by Young et al. (2015) is proposed. Instead of using ln r in the method of fundamental solution (MFS), the MABF adopts θ to construct the solution. However, since the nature of θ introduces multiple values along the branch cut such that to avoid the branch cut passing through the domain is an important issue (Li et al., 2018). Noticing this difficulty, Alves et al. (2018) first proposed a remedy which used a pair of two points to restrict the discontinuity appearing only along the line segment between two points, and they named this approach as cracklets. In this article, the two-point angular basis function (cracklets) is investigated deeply. We explain why for a multiply connected domain with a logarithm singular solution the cracklets will encounter failure. To resolve this difficulty, one can adopt the proposed method (cracklets) with the MFS or one can use domain decomposition method to separate the domain into several singly connected domains. Seven numerical examples are provided to show the validity of this method, and examples for dealing with the multiply connected domain are focused to support our claims.