PDE centres enhancement in the Localized Regular Dual Reciprocity Method

Abstract

In this work we present an improvement of the Localized Regular Dual Reciprocity Method (LRDRM). LRDRM is an integral domain decomposition method with two distinguishing features, the boundary conditions are imposed at the local interpolation level and all the calculated integrals are regular. In this work we present an enhancement of this method where the interpolation functions themselves satisfy the partial differential equation to be solved. Results for 1D and 2D convection‐diffusion, 2D Helmholtz and 2D Poisson equations are presented, attaining accuracies two to three orders of magnitude higher than the original version of the LRDRM.