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_(surface)~3, 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.
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