A combination of proper orthogonal decomposition–discrete empirical interpolation method (POD–DEIM) and meshless local RBF-DQ approach for prevention of groundwater contamination

Abstract

The main presented idea is to reduce the used CPU time for employing the local radial basis functions-differential quadrature (LRBF-DQ) method. To this end, the proper orthogonal decomposition–discrete empirical interpolation method (POD–DEIM) has been combined with the LRBF-DQ technique. For checking the ability of the new procedure, the groundwater equation is solved. This equation has been classified in category of system of advection–diffusion equations. The solutions of advection equations have some shock, thus, special numerical methods should be applied for example discontinuous Galerkin and finite volume methods. Moreover, several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes.