An Improved DRM Representation Of Partial Derivatives
Free (open access)
B Natalini & V Popov
The dual reciprocity method (DRM) is one of the most efficient boundary element (BEM) procedures to take the domain integrals to the boundary. The DRM when applied to advection-diffusion problems requires an algorithm to represent the partial derivatives introduced by the convective term. The classical procedure expresses them as a function of the potentials employing an approximation function. The Dual Reciprocity Method Multy-Domain (DRM-MD) is a technique which combines DRM and domain decomposition for a case when the domain is subdivided in a very large number of subregions and the resulting internal mesh pattern looks like a finite element grid. In the DRM-MD the partial derivatives can be represented either in the classical way or as functions of the normal derivatives. In this paper a set of examples of advection-diffusion problems which have been solved using DRM-MD codes with both formulations in first partial derivatives are presented. It is shown that the classical formulation produces large numerical errors when the approximation function is 1 + r, which can be removed with the new approach, and that the classical formulation provides suitable results when the approximation function is the augmented thin plate spline.