The aim of this work is to introduce the physics community to the high performance of radial basis functions (RBFs) compared to other spectral methods for modeling transport (pure advection) and to provide the first known application of the RBF methodology to hyperbolic partial differential equations on a sphere. First, it is shown that even when the advective operator is posed in spherical coo...

0045-7930/$ see front matter 2010 Elsevier Ltd. A doi:10.1016/j.compfluid.2010.08.005 * Corresponding author. E-mail addresses: [email protected] (N. Flyer), fornber Radial basis functions (RBFs) can be seen as a major generalization of pseudospectral (PS) methods, abandoning the orthogonality of the basis functions and in return obtaining much improved simplicity and geometric flexibility. Spectr...

Aiming at a complex multi-block structured grid, an efficient dynamic mesh generation method is presented in this paper, which is based on radial basis functions (RBFs) and transfinite interpolation (TFI). When the object is moving, the multi-block structured grid would be changed. The fast mesh deformation is critical for numerical simulation. In this work, the dynamic mesh deformation is comp...

Infinitesimal deformations of a homogeneous and isotropic thick elastic plate have been analyzed by using a meshless local Petrov– Galerkin (MLPG) method and a higher-order shear and normal deformable plate theory (HONSDPT). Radial basis functions (RBF) are employed for constructing trial solutions, while a spline function is used as the weight function over a local subdomain. The present metho...

A subdomain variational inequality and its meshless linear complementary formulation are developed in the present paper for solving two-dimensional contact problems. The subdomain variational inequality will be defined in detail. The meshless method is based on a local weighted residual method with the Heaviside step function as the weighting function over a local subdomain and radial basis fun...

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) – w...

Volumetric Subdivision (VS) is a powerful paradigm that enables volumetric sculpting and realistic volume deformations that give rise to the concept of “virtual clay”. In VS, volumes are commonly represented as a space-filling set of deformed polyhedra, which can be further decomposed into a mesh of tetrahedra for rendering. Images can then be generated via tetrahedral projection or raycasting....

In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aim to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image regi...

Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together . . . through fractals. First, we iden...