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

Abstract

This work presents a multi-domain decomposition integral equation method for the numerical solution of domain dominant problems, for which it is known that the standard Boundary Element Method (BEM) is in disadvantage in comparison with classical domain schemes, such as Finite Difference (FDM) and Finite Element (FEM) methods. As in the recently developed Green Element Method (GEM), in the present approach the original domain is divided into several subdomains. In each of them the corresponding Green's integral representational formula is applied, and on the interfaces of the adjacent subregions 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 transformed into surface integrals at the contour of each subregion via the Dual Reciprocity Method (DRM), using some of the most efficient radial basis functions 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 FEM and GEM the obtained global matrix system possesses a banded structure. However 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 interpolation. Finally, some examples showing the accuracy, the efficiency, and the flexibility of the method for the solution of the linear and non-linear convection–diffusion equation are presented. Copyright © 1999 John Wiley & Sons, Ltd.