Three-dimensional solution for acoustic and transport problems using the radial basis integral equation method

The radial basis integral equations method (RBIEM) has been applied for solution of three-dimensional (3D) acoustic and transport problems. The acoustic problem is often described using the Helmholtz equation, while the transport problems are usually described using the Laplace equation (diffusion only), the Poisson equation (diffusion with sources/sinks) and the convection–diffusion equation. The accuracy of the numerical scheme employing the first and second order Duchon splines augmented by first and second order polynomials, respectively, was examined. The effect of the number of interpolation points used in the radial basis function approximation on the condition number of the system was investigated. Numerical results obtained for the convection–diffusion equation were compared with the solutions obtained using the multi-domain dual reciprocity boundary element method (DRM-MD). The RBIEM formulation was found to be more accurate than the DRM-MD formulation. The implementation does not involve discretization over the boundaries of the subdomains used in the RBIEM formulation when evaluating the integrals.