## 1 Introduction  
Simulation based on computational fluid dynamics (CFD) is an effective solution for various problems in aerospace engineering and ocean engineering [1], etc. Among methods adopted by CFD, the mesh deformation method plays a significant role. To promote the quality and precision of the grid after mesh deformation operation, researchers exploit two different mesh deformation strategies: connectivity methods and point-by-point methods. One typical instance of connectivity methods is the spring analogy [2]. It assumes that every edge has all the characteristics of a spring, shaping a mesh connected by springs and it is widely applied in aerodynamic field. Subsequently, [PERSON] et al. [3] improved its robustness by including the torsional condition. However, in large-scale mesh systems, the spring analogy method will produce an expensive cost due to its requirement for the whole mesh connectivity. The linear elastic analogy [4; 5; 6], in which the mesh cell is abstracted into an elastic solid, solves the mesh deformation based on the partial differential equation. This method has great robustness in large-scale mesh deformation but still produces a huge expensive cost. The point-by-point methods mean that each node displaced independently and has no relation with other nodes [7]. This means that the method could provide an identical solution for both structured and unstructured mesh. In the later period of time, [PERSON] et al. [8] proposed a method which propagates deformation from boundary points to internal points by interpolation of barycenter. [PERSON] [9] proposed a method that the boundary points could affect the deformation of the internal points by inverse distance weighted interpolation. In addition, [PERSON] et al. [10] decreased computational cost of aforementioned methodology via tree-code optimization. Although the point-by-point methods increase the efficiency of computation, it doesn't perform well in the complex mesh system and is not able to preserve the mesh orthogonality. Fortunately, one of the point-by-point methods, radial basis function interpolation, does not have these aforementioned problems. In 2007, [PERSON] et al. [11] put forward the application of radial basis function (RBF) interpolation in mesh deformation. It is a promotion of the original point-by-point methods that ensures the preservation of mesh orthogonality while still maintaining its good adaptability in all mesh types. The main idea is to calculate mesh motion by interpolating the displacements of the boundary points to the internal points. The research by [PERSON] et al. [11], [PERSON] et al. [12] and [PERSON] et al. [13] showed that different RBFs adopted in the mesh deformation could result in different results. [PERSON] and [PERSON] [14] proposed a point coarsening method for gradient-based aerodynamic shape optimization. By conducting a variety of testing cases, they finally gave some suggestions about how to choose these RBFs. However, it is demonstrated that, even using the best radial basis function, the computational cost will still grow rapidly as the mesh scale increases. This is due to the calculation redundancy caused by the interpolation from the unnecessary boundary points. To eliminate the calculation redundancy, [PERSON] et al. [15] proposed a greedy algorithm to reduce the boundary points for interpolation and the remaining boundary points are selected as a smaller set of control points. Based on the criterion of displacement error, the greedy algorithm could effectively remove the redundant boundary points that has a smaller impact on displacement interpolation. Meanwhile, it could also preserve the mesh quality as well as the conventional RBF mesh deformation. An important work done by [PERSON] [16] is that he directionalized the point selection by selecting a different set of points in each direction using a greedy selection method.