Master of Science (Hons.)
Department of Mathematics
Zhang, Yinglong, On the dual reciprocity boundary element method, Master of Science (Hons.) thesis, Department of Mathematics, University of Wollongong, 1993. https://ro.uow.edu.au/theses/2846
The Dual Reciprocity Boundary Element Method (DRBEM) is thus far the most powerful numerical technique to tackle elliptic, parabolic, or hyperbolic type differential equations, while maintaining the elegance of the Boundary Element Method. In this thesis, the details of DRBEM are examined and discussed, with respect to the two-dimensional versions of partial differential equations of type V^w = b(X, y, u, u^, Uy, uj, posed in a bounded (interior) or unbounded (exterior) region. For interior problems, the problem associated with the traditional DRBEM, i.e., the singularities created by differentiating the interpolation functions sometimes leading to large numerical errors, is first pointed out. Then two remedies for this problem are given, supported by a number of numerical experiments. As to exterior problems, heretofore little effort has been made and the only approach available by now is far from completeness and satisfaction. Therefore an endeavour is made to extend DRBEM from interior problems to exterior problems. The robustness and reliability of the newly proposed approach are supported by the numerical tests so far completed.