A Scheme of Radial Basis Function Interpolation Based on Partition of Unity Method for FSI Boundary Data

Abstract For Fluid-Structure Interaction (FSI) analysis, Radial Basis Functions (RBF) interpolation is very effective for data transfer between fluids and structures because it can avoid interface mesh mismatches that make it difficult to transfer data. However, one of the main drawbacks of conventional RBF interpolation is the computational cost associated with solving linear equations, as well as the corresponding running times. In this paper, a scheme of RBF interpolation based on the Partition of Unity Method (RBF-PUM) is proposed to handle a large amount of FSI boundary data with the aim of striking a balance between computational accuracy and efficiency. And a cross-validation technique is coupled with RBF-PUM, for the purpose of searching for the optimal value of shape parameter related to RBF interpolation. The scheme basically focuses on two parts, one of which is how to partition the fluid domain of node points into a number of subdomains or patches, and the other is how to efficiently exploit the techniques that are applied to reduce the interpolation error locally and globally. Numerical experiments show that compared to the CSRBF method and the greedy algorithm-based RBF method, RBF-PUM significantly improves the computational efficiency of the interpolation and the computational accuracy is relatively competitive.