A grouping-circular-based (GCB) greedy algorithm is proposed to improve the efficiency of mesh deformation. By incorporating the multigrid concept that the computational errors on the fine mesh can be approximated with those on the coarse mesh, this algorithm stochastically divides all boundary nodes into m groups and uses the locally maximum radial basis functions (RBF) interpolation error of the active group as an approximation to the globally maximum one of all boundary nodes for reducing the RBF support nodes. For this reason, it avoids the interpolation conducted at all boundary nodes in each iterative procedure. After m iterations, the interpolation errors of all boundary nodes are computed once, thus allowing all boundary nodes can contribute to error control. A theoretical analysis reveals that this algorithm can make the computational complexity for computing the interpolation errors reduced from $O(N_c^2{N}_b)$ to $O(N_c^3)$, where $N_b$ and $N_c$ denote the numbers of boundary nodes and support nodes, respectively. Two deformation problems of the ONERA M6 wing and the DLR-F6 Wing-Body-Nacelle-Pylon configuration are computed to validate the GCB greedy algorithm. It is shown that this algorithm is able to remarkably promote the efficiency of computing the interpolation errors by dozens of times. It is also shown that the convergence indicated by the variation of the globally interpolation error of this algorithm is consistent with that of the traditional greedy algorithm. It is indicated by the Kullback-Leibler (KL) divergence that it can generate a reasonable set of support nodes. Besides, it ensures similar statistical property to the traditional greedy algorithm. The theoretical analysis also reveals that if $m>2.25N_b/N_c$, the amount of computation for computing the interpolation errors will be lower than that for solving the linear algebraic system. However, it is found that an increase of m results in an increase of $N_c$, indicating that m cannot be too large, otherwise it will generate too much additional computations for solving the linear algebraic system and computing the displacements of volume nodes since the amounts of computation for these two processes increase as functions of $N_c^3$ and $N_c$, respectively. For this reason, there is an appropriate value for m. It is also found that this algorithm tends to generate a more significant efficiency improvement for mesh deformation when a larger-scale mesh is applied. Furthermore, it can produce a deformed mesh with a comparable quality to the undeformed one for both structured and unstructured meshes.

为了提高网格变形的效率，提出了一种基于分组圆的贪心算法。通过结合多网格概念，可以将细网格上的计算误差近似于粗网格上的计算误差，该算法随机地将所有边界节点划分为m个组，并使用活动组的局部最大径向基函数（RBF）插值误差作为所有边界节点的全局最大值之一的近似值，以减少RBF支持节点。因此，它避免了在每个迭代过程中在所有边界节点上进行的插值。m之后迭代中，所有边界节点的插值误差均被计算一次，因此使所有边界节点都可以有助于误差控制。理论分析表明，该算法可以降低插值误差的计算复杂度。$Ø（{ñ}_C^2{ñ}_b）$ 到 $Ø（{ñ}_C^3）$， 在哪里 ${ñ}_b$ 和 ${ñ}_C$分别表示边界节点和支持节点的数量。计算了ONERA M6机翼和DLR-F6机翼-纳赛尔-皮尔龙构型的两个变形问题，以验证GCB贪婪算法。结果表明，该算法可以显着提高内插误差的计算效率数十倍。还表明，该算法的全局插值误差变化所指示的收敛性与传统贪婪算法的收敛性是一致的。Kullback-Leibler（KL）散度表明它可以生成一组合理的支持节点。此外，它确保了与传统贪婪算法相似的统计特性。理论分析还表明，如果$米>2.25{ñ}_b/{ñ}_C$，用于计算插值误差的计算量将小于用于求解线性代数系统的计算量。然而，发现m的增加导致m的增加。${ñ}_C$，表明m不能太大，否则它将生成过多的额外计算来求解线性代数系统和计算体积节点的位移，因为这两个过程的计算量随函数的增加而增加${ñ}_C^3$ 和 ${ñ}_C$， 分别。因此，有一个合适的m值。还发现，当应用较大规模的网格时，该算法倾向于对网格变形产生更显着的效率提高。此外，对于结构化和非结构化网格，它都可以产生与未变形质量相当的变形网格。