Radial basis functions appear in a wide field of applications in numerical mathematics and computer science. We present a fast algorithm for scattered data interpolation and approximation on the sphere with spherical radial basis functions of different spatial density. We discuss three settings, each leading to a special structure of the interpolation matrix allowing for an efficient implementa...

Approximation of the solution of an ill-posed spherical pseudo-differential equation at a given point Abstract This paper presents a method for approximating the solution of an ill-posed spherical pseudo-differential equation at a given point. The approximation is based on the regularized least-squares method of An et. al., We discuss an a posteriori parameter choice rule and illustrate our the...

in this research, the effect of the first order magnetic field on the ground-state of a centered hydrogenic donor impurity in a gaas/alas spherical quantum dot has been calculated. the perturbation method has been used within the framework of effective mass approximation for these calculations. overall, the analysis shows that a proper choice of quantum dot radius and magnetic field can signifi...

In this paper, we present a full wave method for determining the effective permittivity for random media in three dimensions. The type of media addressed is composed of spherical dielectric particles in a homogeneous dielectric background. The particle volume fraction ranges from 0 to 40% and dielectric contrast may be significantly different from the background medium. The method described rel...

The product-reactant Ornstein–Zernike approach, supplemented by the ideal network approximation, is formulated for the Yukawa sticky m-point ~YSmP! model of associating fluid. The model is represented by the multicomponent mixture of the Yukawa hard spheres with m sticky points randomly located on the surface of each hard sphere. Extensions of the regular integral equation closures, which inclu...

In this paper, the Lie group analysis method is applied to the geometric average Asian option pricing equation in financial problems. Firstly, the complete Lie symmetry group and infinitesimal generators of this equation are derived. Then the optimal system with one parameter for the Lie symmetry algebra are obtained, which gives the possibility to describe a complete set of invariant solutions...

The design and analysis ofradar systems that transmit over oceans or smooth terrain for example, airborne radars that spot distant incoming missiles, or coastal radars that fmd drug smugglers reqUires accurate evaluation of radar propagation over a smooth sphere. Analysis of smooth sphere diffraction is equally important for general radar applications; by combining several approximations, compo...

We discuss a Galerkin approximation scheme for the elliptic partial differential equation −∆u+ ω2u = f on Sn ⊂ Rn+1. Here ∆ is the Laplace-Beltrami operator on Sn, ω is a non-zero constant and f belongs to C2k−2(Sn), where k ≥ n/4 + 1, k is an integer. The shifts of a spherical basis function φ with φ ∈ H τ (Sn) and τ > 2k ≥ n/2 + 2 are used to construct an approximate solution. An H1(Sn)error ...

An adaptive multilevel wavelet solver for elliptic equations on an optimal spherical geodesic grid is developed. The method is based on second-generation spherical wavelets on almost uniform optimal spherical geodesic grids. It is an extension of the adaptive multilevel wavelet solver [O. V. Vasilyev and N. K.-R. Kevlahan, J. Comput. Phys., 206 (2005), pp. 412–431] to curved manifolds. Wavelet ...