Numerical integration over a sphere

Numerical Integration Over a Sphere*

Local numerical integration on the sphere

Many applications in geomathematics as well as bio–medical applications require the analysis of an unknown target function of a large amount of data, which can be modeled as data on a subset of the surface of a sphere. An important ingredient of this analysis is to develop numerical integration schemes (quadrature formulas) to integrate spherical polynomials of as high a degree as possible exac...

Integration by Rbf over the Sphere

In this paper we consider numerical integration over the sphere by radial basis functions (RBF). After a brief introduction on RBF and spherical radial basis functions (SRBF), we show how to compute integrals of functions whose values are known at scattered data points. Numerical examples are given.

Numerical quadrature over the surface of a sphere

Large-scale simulations in spherical geometries require associated quadrature formulas. Classical approaches based on tabulated weights are limited to specific quasi-uniform distributions of relatively low numbers of nodes. By using a radial basis function-generated finite differences (RBF-FD) based approach, the proposed algorithm creates quadrature weights for N arbitrarily scattered nodes in...

Extremal Systems of Points and Numerical Integration on the Sphere

This paper considers extremal systems of points on the unit sphere Sr ⊆ Rr+1, related problems of numerical integration and geometrical properties of extremal systems. Extremal systems are systems of dn = dim Pn points, where Pn is the space of spherical polynomials of degree at most n, which maximize the determinant of an interpolation matrix. Extremal systems for S2 of degrees up to 191 (36, ...