Integration by Rbf over the Sphere

نویسندگان

  • ALVISE SOMMARIVA
  • ROBERT S. WOMERSLEY
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Vector Field Rbf Interpolation on a Sphere

This paper presents a new approach for Radial Basis Function (RBF) interpolation on a sphere. Standard approaches use the Euclidian metrics for the distance calculation of two points. However, for interpolation on a sphere, more naturally is computation of the distance as the shortest distance over the surface on a sphere, i.e. spherical distance of two points is more natural for interpolation ...

متن کامل

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...

متن کامل

A Stable Algorithm for Flat Radial Basis Functions on a Sphere

When radial basis functions (RBFs) are made increasingly flat, the interpolation error typically decreases steadily until some point when Runge-type oscillations either halt or reverse this trend. Because the most obvious method to calculate an RBF interpolant becomes a numerically unstable algorithm for a stable problem in case of near-flat basis functions, there will typically also be a separ...

متن کامل

A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

The current paper establishes the computational efficiency and accuracy of the RBFFD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as...

متن کامل

On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere

Radial basis function (RBF) approximations have been used for some time to interpolate data on a sphere (as well as on many other types of domains). Their ability to solve, to spectral accuracy, convection-type PDEs over a sphere has been demonstrated only very recently. In such applications, there are two main choices that have to be made: (i) which type of radial function to use, and (ii) wha...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005