Refined RBF-FD Solution of Linear Elasticity Problem

Abstract

Solving PDEs with Radial Basis Functions, especially using local approaches, has become a promising alternative to the Finite Element Method. This paper describes one such approach, a local RBF-FD method, analogous to Finite Difference Method, that can handle irregular geometries, varying discretization densities and is easy to implement. RBF-FD method is analysed by solving basic linear elasticity problems using uniform and refined discretizations. Finally, a linear elasticity problem arising from analysis of fretting fatigue is solved and RBF-FD solution is compared to existing solutions, obtained using commercial software.