  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.
