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

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.

On a connection between some classes of mapping on Riemannian manifolds

In this paper we study the connection between $\eta$-quasisymmetric homomorphisms and $K$-quasi\-con\-for\-mal mappings on $n$-dimensional smooth connected Riemannian manifolds. The main result of our research is the Theorem 3.1. For its proof we use a partition of unity method, which subordinate to the locally finite atlas of the manifold. Several results on the boundary behavior of $\eta$-quasisymmetric homomorphisms between two arbitrary domains, QED (uniform) domains and domains with weakly flat boundaries and compact closures on the Riemannian manifolds are also obtained in view of the above relations. The obtained results can be applied to Finsler manifolds with the addition of some conditions, which will take into account the specific of the initial manifold.

Calibration Method of Orthogonally Splitting Imaging Pose Sensor Based on KDFcmPUM

This paper proposes a partition of unity method (PUM) based on KDFCM (KDFcmPUM) that can be implemented to solve the dense matrix problem that occurs when the radial basis function (RBF) interpolation method deals with a large amount of scattered data. This method introduces a kernel fuzzy clustering algorithm to improve clustering accuracy and achieve the partition of unity. The local compact support RBF is used to construct the weight function, and local expression is obtained from the interpolation of the global RBF. Finally, the global expression is constructed by the weight function and local expression. In this paper, the method is applied to the orthogonally splitting imaging pose sensor to establish the mathematical model and the calibration and test experiments are carried out. The calibration and test accuracy both reached ±0.1 mm, and the number of operations was reduced by 4% at least. The experimental results show that KDFcmPUM is effective.