Non-Overlapping Domain Decomposition Algorithm for the Hermite Radial Basis Function Meshless Collocation Approach: Applications to Convection Diffusion Problems

Abstract

In the particular case of solving large-scale boundary value problems, the computational cost derived as a result of the application of any numerical scheme represent a determinant factor in the determination of its computational efficiency. The present work studies the influence of the non-overlapping domain decomposition and higher order interpolation functions on the Hermite radial basis collocation method, as a way to improve its efficiency under high demanding numerical conditions. A series of high Péclet convection diffusion and multi-zone problems are tested. Comparison between the numerical results and its analytical solution is carried out for each of them.