Multiple reciprocity singular boundary method for 3D inhomogeneous problems. (August 2020)

• Record Type: Journal Article
• Authors: Wei, Xing; Huang, Ai; Sun, Linlin; Chen, Bin
• Is Part Of: Engineering analysis with boundary elements. Volume 117(2020)
• Page Start: 212
• Page End: 220
• Publication Date: 2020-08
• Subjects: Singular boundary method -- Multiple reciprocity method -- Origin intensity factor -- Inhomogeneous elliptic problem -- Method of fundamental solutions -- Meshless method; 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.2020.04.015
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this study, the singular boundary method (SBM) is extended to solve 3D inhomogeneous elliptic boundary value problems. Before applying the SBM, the multiple reciprocity method (MRM) removes the inhomogeneous terms and establishes an equivalent high-order homogeneous problem, which is then solved by the SBM, a boundary-only fundamental-solution based collocation method. It is worth-noting that the conventional MRM is not applicable in most cases because polyharmonic operators cannot deal with most of the source terms. Thus, in this study a recursive multiple reciprocity method is developed via different operators. The high-order fundamental solutions are involved as kernel functions in solving a high-order homogeneous problem by the SBM. It is of great importance to remove the source singularity of the kernels when the collocation points coincide with the source points. In this study, simple formulas are analytically derived to desingularize the source singularity of kernel functions. The accuracy and efficiency of the proposed method are illustrated via several numerical examples governed by different partial differential equations.