## 1 Introduction
However, it is found that, with the increasing quantity of control points, the computational complexity of most greedy point selection processes is approximately \(O(n^{4})\), which significantly influences the computational efficiency of the whole process [17]. To solve this problem, in the last decade, researchers have achieved some effective methods by analysing the concrete process of each separated step in the greedy algorithm. [PERSON] et al. [18] adopted an adaptive method to reduce the frequency of greedy point selection. [PERSON] et al. [19] proposed an incremental approach to effectively accelerate the step of matrix inversion. Based on it, [PERSON] et al. [20] presented an improvement method of lower-upper (LU) decomposition. Afterwards, [PERSON] et al. [21] provided an effective method based on recurrence Cholesky decomposition. In addition, in 2017, [PERSON] et al. [22] proposed a form of data reduction that still includes all the points. In addition, researchers also consider the feasibility of parallel computation in the greedy algorithm. [PERSON] et al. [23] parallelized RBF mesh deformation. Then, [PERSON] et al. [24] proposed a parallel approach applied in multi-bladed rotors. In addition, [PERSON] et al. [17] and [PERSON] et al. [21] proposed parallel computation methods based on the master-slave architecture. Nevertheless, all of the aforementioned methods could just focus on some specific steps without an overall optimization for the greedy algorithm. Meanwhile, considering the continuity of all steps, only some parts could be well parallelized. Therefore, this paper proposes a method combining block iteration with parallel computing. This method provides an optimization scheme for each step in the point selection procedure and could significantly reduce the time cost for the whole RBF mesh deformation. Specifically, the main dedications are summarized as follows:  
* A block iteration method is developed by analyzing the mathematical characters of the greedy algorithm. With the application of the block iteration, some specific steps that have the feasibility of iteration could be greatly optimized. The computational complexity could be reduced from \(O(n^{3})\) to \(O(n^{2})\). * The parallelization is accomplished by analyzing the data dependency of the whole procedure. Steps that have the parallel feasibility could have good speedups because of the low communication cost. * Our block iteration with parallelization method is firstly validated by three-dimensional undulating fish and ONERA M6 wing which are both \(10^{6}\) cells mesh models. To validate the method efficiency of large-scale mesh, we adopt a three-dimensional Super-cavitating Hydrofoil model with 11 million cells. All three of the models could obtain an effective improvement via the proposed method. The rest of this paper is allocated as follows. Section 2 recalls the methodology of RBF mesh deformation and the conventional greedy algorithm. Section 3 demonstrates the fundamental theory of block iteration and the implementation of parallel computing in detail. In Section 4, it exhibits the experimental results and discusses how the results could be explained by the previous studies. Finally, conclusions are described in Section 5.