The DRM-MD integral equation method for the numerical solution of convection-diffusion equation

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 at a 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 sub-domains. 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 sub-region the domain integrals are computed by the use of cell integration, here those integrals are transformed into surface integrals at the contour of each sub-region via the dual reciprocity method (DRM), using some of the most efficient interpolation functions in the literature on mathematical interpolation. 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, ie 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 convection-diffusion equation are presented.