Efficient mesh motion using radial basis functions with volume grid points reduction algorithm

As one of the most robust mesh deformation technique available, the radial basis function (RBF) mesh deformation has been accepted widely. However, for volume mesh deformation driven by surface motion, the RBF system may become impractical for large meshes due to the large number of both surface (control) points and volume points. Surface points selection procedure based on the greedy algorithm results in an efficient implementation of the RBF-based mesh deformation procedure. The greedy algorithm could reduce the number of surface points involved in the RBF interpolation while acquire an acceptable accuracy as shown in literature. To improve the efficiency of the RBF method furthermore, an issue that how to reduce the number of the volume points needed to be moved is addressed. In this paper, we propose an algorithm for volume points reduction based on a wall distance based restricting function which is added to the formulation of the RBF based interpolation. This restricting function is firstly introduced by the current article. To support large deformation, a multi-level subspace interpolation is essentially needed, although this technique was used to improve the efficiency of the surface points selection procedure in the existed literature. The key point of this technique is setting the error of previous interpolation step as the object of current step, and restricting interpolation region gradually. Because the tolerance of the error is decreased hierarchically, the number of the surface points is increased but the number of the volume points needed to be moved is reduced gradually. Therefore, the CPU cost of updating the mesh motion could be reduced eventually since it scales with the product of these two numbers. The computational requirement of the proposed procedure is reduced evidently compared with the standard procedure as proved by some examples.