Application of radial basis functions augmented by polynomials in the boundary element method to solve problems governed by the Laplace equation

Purpose Radial basis function interpolation is a highly valuable tool in the field of numerical methods, and its polynomially augmented version holds promise in addressing some limitations of the traditional formulation. In this article, we aim to analyze the performance of the boundary element method, which employs an alternative approach to traditional boundary discretization with the aid of radial basis functions. Design/methodology/approach This work presents the complete mathematical formulation along with the associated theory, as well as a comparison of errors between the proposed formulation and the traditional formulation, which uses polynomial interpolation. Additionally, a processing time analysis was conducted and is presented. Findings The proposed method yielded the lowest error across all examples with straight geometries. However, its performance was less effective in the problem involving a circular section, likely due to challenges in accurately representing this type of geometry. Originality/value The study presents an interpolation technique that can aid in mesh generation and can be extended to three-dimensional applications. Moreover, the lower errors observed in certain easily identifiable geometries suggest that this approach could be a good option for problems requiring higher accuracy.