Meshfree approximation methods are a relatively new area of research, and there are only a
few books covering it at present. Whereas other works focus almost entirely on theoretical …

Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

In this popular text for an Numerical Analysis course, the authors introduce several major
methods of solving various partial differential equations (PDEs) including elliptic, parabolic …

Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

Abstract Background/Objectives: The approximation using radial basis function (RBF) is an
extremely powerful method to solve partial differential equations (PDEs). This paper …

Meshless methods are a promising new field in computational electromagnetics. Instead of
relying on an explicit mesh topology, a numerical solution is computed on an unstructured …

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the
kernels so they are 'flat'leads to smaller discretization errors. However, the direct numerical …

Meshfree methods are the topic of recent research in many areas of computational science
and approximation theory. These methods come in various flavors, most of which can be …

In our previous work, an effective preconditioning scheme that is based upon constructing
least-squares approximation cardinal basis functions (ACBFs) from linear combinations of …

Although meshless radial basis function (RBF) methods applied to partial differential
equations (PDEs) are not only simple to implement and enjoy exponential convergence …