Numerical solution of three-dimensional Laplacian problems using the multiple scale Trefftz method. (January 2015)

• Record Type: Journal Article
• Authors: Ku, Cheng-Yu; Kuo, Chung-Lun; Fan, Chia-Ming; Liu, Chein-Shan; Guan, Pai-Chen
• Is Part Of: Engineering analysis with boundary elements. Volume 50(2015:Jan.)
• Page Start: 157
• Page End: 168
• Publication Date: 2015-01
• Subjects: Trefftz method -- Ill-conditioned -- The dynamical Jacobian-inverse free method -- The multiple scale -- Three-dimensional; 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.2014.08.007
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper proposes the numerical solution of three-dimensional Laplacian problems based on the multiple scale Trefftz method with the incorporation of the dynamical Jacobian-inverse free method. A numerical solution for three-dimensional Laplacian problems was approximated by superpositioning T-complete functions formulated from 18 independent functions satisfying the governing equation in the cylindrical coordinate system. To mitigate a severely ill-conditioned system of linear equations, this study adopted the newly developed multiple scale Trefftz method and the dynamical Jacobian-inverse free method. Numerical solutions were conducted for problems involving three-dimensional groundwater flow problems enclosed by a cuboid-type domain, a peanut-type domain, a sphere domain, and a cylindrical domain. The results revealed that the proposed method can obtain accurate numerical solutions for three-dimensional Laplacian problems, yielding a superior convergence in numerical stability to that of the conventional Trefftz method.