An efficient and accurate implementation of the Localized Regular Dual Reciprocity Method

Abstract

In this work we present an efficient and accurate implementation of the LRDRM. This integral domain decomposition method exploits two advantages: first, it imposes the boundary conditions at the Local RBF interpolation. Second, the integrals to compute are always regular. The approximation of the derivative of the field variable is computed in a posteriori way, directly differentiating the Local RBF interpolation or the local integral equation. The efficient and accurate behaviour of this method are demonstrated by performing numerical examples, with special emphasis on a 1D benchmark convective-diffusion equation. Results for 2D convection–diffusion, 2D Helmholtz and 2D Poisson equations are also presented.