论文标题
使用径向基函数具有基于分组圆形的贪婪算法的有效网格变形
Efficient mesh deformation using radial basis functions with a grouping-circular-based greedy algorithm
论文作者
论文摘要
提出了一种基于分组圆形（GCB）贪婪算法，以促进网格变形的效率。 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 each group as an approximation to the globally maximum one of all boundary nodes in each iterative procedure for reducing the RBF support nodes.因此，它避免了在所有边界节点进行的插值，因此将相应的计算复杂性从$ o \ left（{n_c^2 {n_b}} \ right）$降低到$ o \ left（{n_c^3} \ right）$。此外，在$ m $迭代后，一次计算所有边界节点的插值误差，因此允许所有边界节点都可以导致误差控制。 ONERA M6机翼和DLR-F6机翼 - 奈瑟尔 - 奈瑟尔杆孔构型的两个规范变形问题被计算以验证GCB贪婪算法。计算结果表明，GCB贪婪算法能够显着提高计算数据减少数十个时间中数据插值误差的效率。因为增加$ n_c $的增加会导致$ \左[{{{n_b}/{n_c}，{\ rm {}} 2 {\ rm {}} 2 {n_b}/{n_b}/{n_c}}} \ right]对于$ m $的求解，以防止更大的计算。由$ N_C $的增加引起的。结果还表明，当应用较大的网格时，GCB贪婪算法倾向于对网格变形产生更大的效率提高。
A grouping-circular-based (GCB) greedy algorithm is proposed to promote 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 each group as an approximation to the globally maximum one of all boundary nodes in each iterative procedure for reducing the RBF support nodes. For this reason, it avoids the interpolation conducted at all boundary nodes and thus reduces the corresponding computational complexity from $O\left({N_c^2{N_b}} \right)$ to $O\left( {N_c^3} \right)$. Besides, after $m$ iterations, the interpolation errors of all boundary nodes are computed once, thus allowing all boundary nodes can contribute to error control. Two canonical deformation problems of the ONERA M6 wing and the DLR-F6 Wing-Body-Nacelle-Pylon configuration are computed to validate the GCB greedy algorithm. The computational results show that the GCB greedy algorithm is able to remarkably promote the efficiency of computing the interpolation errors in the data reducing procedure by dozens of times. Because an increase of $m$ results in an increase of $N_c$, an appropriate range of $\left[ {{N_b}/{N_c},{\rm{ }}2{N_b}/{N_c}}\right]$ for $m$ is suggested to prevent too much additional computations for solving the linear algebraic system and computing the displacements of volume nodes induced by the increase of $N_c $. The results also show that the GCB greedy algorithm tends to generate a more significant efficiency improvement for mesh deformation when a larger-scale mesh is applied.
