Efficient and Exact Mesh Deformation using Multi-Scale RBF Interpolation

Abstract

Mesh deformation schemes are vital in many areas of numerical simulation, and radial basis function(RBF)-based interpolation schemes are popular due to their excellent quality preservation properties. However, the system solution cost scales with moving surface points as N 3 surf ace , and so there have been numerous works investigating efficient methods of reducing the data set. However, reduced data methods require the addition of a secondary 'correction vector field' to ensure surface points not included in the primary deformation are moved to the correct location, and the volume mesh moved accordingly. A new method is presented here, which captures global and local motions at multiple scales using all the surface points, and so there is no need for a correction stage. The multiscale formulation developed means that although all surface points are used and a single interpolation built, the cost and conditioning issues associated with RBF methods are eliminated while still retaining exact recovery of the surface. Moreover, the sparsity introduced can be exploited, using an existing wall distance function, to further reduce the cost. The method is compared with a conventional greedy method on two-and three-dimensional meshes with large deformations. It is shown that mesh quality is always comparable with or better than with the greedy method, and cost and complexity is also comparable or cheaper for all stages. The most expensive stage of reduced point methods is surface mesh preprocessing, and the cost is reduced significantly here; a three or four orders of magnitude reduction in cost is demonstrated compared to greedy-type methods.

A large‐scale parallel hybrid grid generation technique for realistic complex geometry

“…In recent years, RBF interpolation is becoming increasingly popular as a method to provide a solution for mesh deformation . Mesh deformation is achieved by point movement interpolated from boundary displacement to the volume field mesh points.…”

Challenges and Opportunities in Geometric Modeling of Complex Bio-Inspired Three-Dimensional Objects Designed for Additive Manufacturing

“…This requires extra calculations made which slows the mesh generation and the modelling process corresponding to it. The interpolation based on radial basis functions (RBFs) attempts to improve the performance of this operations significantly [46]. However, this approach was initially designed for 2D mesh generation and still requires certain improvements to be widely used in 3D.…”