A convergence analysis of the performance of the DRM‐MD boundary integral approach

Abstract

AbstractIn this article, we study the performance of the dual reciprocity multi‐domains approach (DRM‐MD) when the shape functions of the boundary elements, for both the approximation of the geometry and the surface variables of the governing equations, are quadratic functions. A series of tests are carried out to study the consistency of the proposed boundary integral technique. For this purpose a limiting process of the subdivision of the domain is performed, reporting a comparison of the computed solutions for every refining scheme. Furthermore, the DRM‐MD is solved in its dual reciprocity approximation using two different radial basis interpolation functions, the conical function r plus a constant, i.e. (1+r), and the augmented thin plate spline. Special attention is paid to the contrast between numerical results yielded by the DRM‐MD approach using linear and quadratic boundary elements towards a full understanding of its convergence behaviour. Copyright © 2006 John Wiley & Sons, Ltd.