An efficient implementation of the radial basis integral equation method

An efficient and accurate implementation of the meshless radial basis integral equation method (RBIEM) is proposed. The proposed implementation does not involve discretization of the subdomains' boundaries. By avoiding the boundary discretization, it was hypothesised that a significant source of error in the numerical scheme is avoided. The proposed numerical scheme was tested on two problems governed by the Poisson and Helmholtz equations. The test problems were selected such that the spatial gradients of the solutions were high to examine the robustness of the numerical scheme. The dual reciprocity method (DRM) and the cell integration technique were used to treat the domain integrals arising from the source terms in the partial differential equations. The results showed that the proposed implementation is more accurate and more robust than the previously suggested implementation of the RBIEM. Though the CPU time usage of the proposed scheme is lower, the difference to the previously proposed scheme is not significant. The proposed scheme is easier to implement, since the task of keeping track of boundary elements and boundary nodes is not needed. The proposed implementation of the RBIEM is promising and opens up possibilities for efficient implementation in three-dimensional problems. This is currently under investigation.