Base Point Reduction Methods

The number of base points ns has a major influence on the performance of the radial basis function interpolation algorithm. The needed (direct) matrix inversion depends on the third power of ns and the interpolation of the grid points depends linearly on the base point number. If the tool is used for the coupling of a structural finite elements (FEM) grid to a computational fluid dynamics grid, the number of input base points will be equal to the number of surface grid nodes of the FEM-grid. The common number of surface nodes of these grids is way too large to use them all for the RBF grid deformation and still having satisfactory runtime results. So the reduction of the base points is indispensable for the mesh deformation module.

The reduction of the base points is not the only way to increase the efficiency of radial basis function interpolation methods. Other possibilities are, for example, multilevel approaches combined with base point reduction [9] or partition of unity approaches like in [12]. The multilevel approach uses a base point set hierarchy to start the interpolation at a coarse level and then refining it progressively. The partition of unity approach breaks the large problem down to several small ones by partitioning the base points into neighbor sets.

A useful attribute of the radial basis function interpolation approach is that no connectivity information of the input base points is needed. To conserve this char­acteristic the reduction algorithms do not use connectivity information as well.

Fig. 4