In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in ℝ d . Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scatt...

Volume morphing is a technique used for generating smooth 3D image transformations and deformations. In this paper, several algorithms are developed for morphing transformations that create new forms and simulate shape deformation and growth in biomedical applications. 3D biological point landmarks and their movements are deened to guide the morphing transformation using a scattered data interp...

This paper presents a normed G1 space and a weakened weak (W2) formulation of a cellbased smoothed point interpolation method (CS-PIM) for 2D solid mechanics problems using three-node triangular cells. Displacement fields in the CS-PIM are constructed using the point interpolation method (polynomial PIM or radial PIM) and hence the shape functions possess the Kronecker delta property facilitati...

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...

Interpolation by analytic radial basis functions like the Gaussian and inverse multiquadrics can degenerate in two ways: the radial basis functions can be scaled to become “increasingly flat”, or the data points “coalesce” in the limit while the radial basis functions stays fixed. Both cases call for a careful regularization. If carried out explicitly, this yields a preconditioning technique fo...

Error estimation and adaptive applications help to control the discretization errors in finite element analysis. The study implements radial point interpolation (RPI)-based error-recovery approaches displacement/pressure-based mixed approach is used formulation. RPI considers basis functions (RBF) polynomials together interpolate solutions, i.e., displacement over influence zones recover soluti...

A novel approach, radial basis function (RBF) mixed with domain decomposition method (DDM) based on Galerkin finite element method (FEM) has been introduced in our previous work. The proposed method divides the computational domain into a series of rectangular sub-domains, and each sub-domain is taken as a separate calculation area to get the solution expression and shape function by using the ...

This paper presents a provably convergent multifidelity optimization algorithm for unconstrained problems that does not require high-fidelity gradients. The method uses a radial basis function interpolation to capture the error between a high-fidelity function and a low-fidelity function. The error interpolation is added to the low-fidelity function to create a surrogate model of the high-fidel...

This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. Th...