Meshfree Full Approximation Scheme-Full multilevel algorithm for Convection-dominated problems

Abstract

This paper presents an efficient full approximation scheme-full multilevel (FAS-FML) algorithm for the radial basis function-based finite difference (RBF-FD) method. The algorithm produces an accurate solution by solving the discretized equations from the coarsest level to the coarser level and then to the finer level to desire the finest level node points. Convection-dominated problems are taken to demonstrate the validity of the algorithm. The proposed algorithm saves a minimum 66% of computation time for the convection-dominated problems than the general RBF-FD method. The convergence conditions of the method were verified numerically. Outcomes prove that the developed algorithm concurs with exact solutions in the measure of accuracy and efficiency.