Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example, the direct evaluation at M locations of a radial b...

Abstract. We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initialboundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the inter...

This paper presents a novel formulation for static limit analysis of structures, which the Airy stress function is approximated using stabilized Radial Point Interpolation Mesh-free method (RPIM). The field determined as second-order derivatives function, and equilibrium equations are automatically satisfied priori. so-called Stabilized Conforming Nodal Integration (SCNI) employed to ensure pre...

This paper adopts an efficient meshless approach for approximating the nonlinear fractional fourth-order diffusion model described in Riemann–Liouville sense. A second-order difference technique is applied to discretize temporal derivatives, while radial basis function generated finite scheme approximates spatial derivatives. One key advantage of local collocation method approximation derivativ...

We propose a novel meshless deformable model for in vivo Left Ventricle (LV) 3D motion estimation and analysis based on tagged MRI (tMRI). The meshless deformable model can capture global deformations such as contraction and torsion with a few parameters, while track local deformations with Laplacian representation. In particular, the model performs well even when the control points (tag inters...

A truly meshless Galerkin method is formulated in the present study, as a special case of the general Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. The Galerkin method is implemented as a truly meshless method, for solving elasto-static problems. In the present Galerkin method, the test function is chosen to be the same as the trial function, as a special case of the MLPG approach. Ho...

This article describes an approach based on hierarchical radial basis functions to reconstruction and modification of motion / image data, which are formulated as problems of scattered data interpolation. Assuming little about the data and choosing highly scalable / well adjustable basis functions, the approach can handle both the reconstruction and the manipulation in a unified and widely appl...