Efficient mesh deformation using radial basis functions with a grouping-circular-based greedy algorithm

A grouping-circular-based (GCB) greedy algorithm is proposed to promote the efficiency of mesh deformation. By incorporating multigrid concept that computational errors on fine can be approximated with those coarse mesh, this stochastically divides all boundary nodes into $m$ groups and uses locally maximum radial basis functions (RBF) interpolation error each group as an approximation globally one in iterative procedure for reducing RBF support nodes. For reason, it avoids conducted at thus reduces corresponding complexity from $O\left({N_c^2{N_b}} \right)$ $O\left( {N_c^3} \right)$. Besides, after iterations, are computed once, allowing contribute control. Two canonical deformation problems ONERA M6 wing DLR-F6 Wing-Body-Nacelle-Pylon configuration validate GCB algorithm. The results show able remarkably computing data by dozens times. Because increase $N_c$, appropriate range $\left[ {{N_b}/{N_c},{\rm{ }}2{N_b}/{N_c}}\right]$ suggested prevent too much additional computations solving linear algebraic system displacements volume induced $N_c $. also tends generate a more significant improvement when larger-scale applied.