Improving the Accuracy of DRBEM Wave Model by Using Radial Basis Function

Since 1982 the dual reciprocity boundary element method was published by Nardini & Brebbia, it was used to solve many engineering problems successfully. However, how to choose the radial basis function is an important issue, which was discussed recently and many researches were published. M.A. Golberg & C.S Chen (1994) provided a mathematical foundation for ad-hoc ‘1+r’ and suggested that thin plate splines was the better choice for two-dimensional approximation than the ad-hoc ‘1+r’ distance functions. However, Agnantiaris et al. (1996) indicated that TPS showed little or no improvement of accuracy over the conventional ad-hoc ‘1+r’. In their study, Agnantiaris et al. examined how the RBF affected the accuracy in the numerical model. Although RBF became a great concern in this field of computation techniques, it still remains unsettled equation so far. According to the reasons mentioned above, we investigated the influence in the change of RBF and evaluated the relative errors of all numerical results. The numerical model of this paper, based on mildslope equation and solving by DRBEM, was developed to study the wave’s distribution around Homma’s island. By replacing the ad-hoc ‘1+r’ with TPS, all numerical results were compared with analytical solutions and all relative errors of TPS were below 6%. The present results demonstrated that TPS have significant improvement of DRBEM accuracy.