New complex Fourier shape functions for the analysis of two-dimensional potential problems using boundary element method

In this paper, boundary element analysis for two-dimensional potential problems is investigated. In this study, the boundary element method (BEM) is reconsidered by proposing new shape functions to approximate the potentials and fluxes. These new shape functions, called complex Fourier shape function, are derived from complex Fourier radial basis function (RBF) in the form of exp(iωr). The proposed shape functions may easily satisfy various functions such as trigonometric, exponential, and polynomial functions. In order to illustrate the validity and accuracy of the present study, several numerical examples are examined and compared to the results of analytical and with those obtained by classic real Lagrange shape functions. Compared to the classic real Lagrange shape functions, the proposed complex Fourier shape functions show much more accurate results.