A simplified approach for imposing the boundary conditions in the local boundary integral equation method. (English) Zbl 1308.74159

Ooi, Ean Hin; Popov, Viktor

Comput. Mech. 51, No. 5, 717-729 (2013).

Summary: A simplified approach for imposing the boundary conditions in the local boundary integral equation (LBIE) method is presented. The proposed approach employs an integral equation derived using the fundamental solution and the Green’s second identity when the collocation node is at the boundary of the solution domain (global boundary). The subdomains for the nodes placed at the global boundary preserve their circular shapes; avoiding in this way any integration over the global boundary. Consequently, the difficulties related to evaluation of singular integrals and determination of intersection points between the global and local circular boundaries are avoided. So far, attempts to avoid these issues have focused on using schemes based on meshless approximations. The downside of such schemes is that the weak formulation is abandoned. In this study the interpolation of field variables over the boundaries of the subdomains is carried out using the radial basis function approximation. Numerical examples show that the proposed approach despite its simplicity, achieves comparable accuracy to the classical treatment of the boundary conditions in the LBIE.

MSC:

74S15	Boundary element methods applied to problems in solid mechanics
65N38	Boundary element methods for boundary value problems involving PDEs

Keywords:

LBIE; radial basis functions; meshless methods; cell integration; weak formulation

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