The boundary element method is a numerical computational method of solving partial differential equations which have been formulated as integral equations. It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics. The method can be seen as a weighted residual method for solving partial differential equations, characterized by choosing an appropriate fundamental solution as a weighting function and by using the generalized Green's formula for complete transfer of one or more partial differential operators on the weighting function.
In this work, the dual reciprocity method has been used, where the right-hand side of the given partial differential equation is replaced by a set of radial basis functions, which are polynomials of order 1 and 2. The fundamental solution used in this formulation is that of the Laplace operator. Three test problems have been used to implement the solution, where each represents a given traffic flow situation.
Analysis was done basing on approximation functions of order 2, as these gave more accurate results compared to order 1. The root-mean-square errors were computed and these were found to be reducing with the increasing CFL number. The formulation took advantage of the matrix manipulation feature of MATLAB, where boundary conditions were computed in only two steps and did not involve loops for space nodes.
Keywords: Boundary element method, advection-diffusion equation, radial basis functions