Imposing the boundary conditions in the LBIE/RBF method: a simplified approach

A simple approach for imposing the boundary conditions in the local boundary integral equation (LBIE) method is proposed. The proposed approach maintains the weak formulation on the boundary by enforcing the integral equation derived from the Green's second identity and the fundamental solution of the Laplace equation. Unlike in the LBIE, the subdomains at the boundary in the proposed method preserve their circular shapes, such that difficulties associated with the evaluation of near-singular and singular integrals and the determination of intersection between the global and local boundaries can be avoided. The proposed approach is compared with the conventional LBIE by solving the convection-diffusion equation. The unknown field variables were approximated with the RBF approximations. Numerical results showed that the proposed method, despite its simplicity, yielded results of comparable accuracy with the LBIE when third order RBF was used.