The DRM-MD integral equation method: An efficient approach for the numerical solution of domain dominant problems

This work presents a multi-domain decomposition integral equation method fo r the numerical solution of domain dominant problems, for which it is known that the standard Boundary Element Method (BEM) is in disadvantage in comp arison with classical domain schemes, such as Finite Difference (FDM) and F inite Element (FEM) methods. As in the recently developed Green Element Met hod (GEM), in the present approach the original domain is divided into seve ral subdomains. In each of them the corresponding Green's integral represen tational formula is applied, and on the interfaces of the adjacent subregio ns the full matching conditions are imposed. In contrast with the GEM, where in each subregion the domain integrals are computed by the use of cell integration, here those integrals are transform ed into surface integrals at the contour of each subregion via the Dual Rec iprocity Method (DRM), using some of the most efficient radial basis functi ons known in the literature on mathematical interpolation. In the numerical examples presented in the paper, the contour elements are defined in terms of isoparametric linear elements, for which the analytical integrations of the kernels of the integral representation formula are known. As in the FE M and GEM the obtained global matrix system possesses a banded structure. H owever in contrast with these two methods (GEM and non-Hermitian FEM), here one is able to solve the system for the complete internal nodal variables, i.e. the field variables and their derivatives, without any additional int erpolation. Finally, some examples showing the accuracy, the efficiency, and the flexib ility of the method for the solution of the linear and non-linear convectio n-diffusion equation are presented. Copyright (C) 1999 John Wiley & Sons, L td.