Spherical_Quadratur​e_RBF(Quadrature_No​des)

This function computes quadrature weights for evaluating the surface integral of a scalar function.

This zip file contains two Matlab functions:
1. Spherical_Quadrature_RBF.m:
This function computes quadrature weights for evaluating the surface integral of a scalar function f(x,y,z) over the sphere surface.
Inputs: Quadrature_Nodes - A set of points located exactly on the sphere surface (Number_of_Quadrature_Nodes X 3) Array
Output: Quadrature Weights - A set of quadrature weights- (Number_of_Quadrature_Nodes X 1) vector-corresponding to the set of points Quadrature_Nodes

This implementation uses the method and default settings discussed in:
J. A. Reeger and B. Fornberg, "Numerical Quadrature Over the Surface of the Sphere". submitted to Stud. Appl. Math.

NOTE: The main loop of this method (over each triangle) can be easily parallelized if you have access to the parallel toolbox. In such a case, change the for loop to a parfor loop.

2. Spherical_Quadrature_RBF_Test:

This function provides example calls to the function Spherical_Quadrature_RBF.m. The user can change the parameter Number_of_Quadrature_Nodes in this m-file to generate various sizes of node sets. The user can also change the parameters Poly_Order and Number_of_Nearest_Neighbors within the Spherical_Quadrature_RBF.m function.

This function approximates the surface integral of five test integrands over the surface of the sphere and prints the error in the approximation to the command window upon completion.

The function Spherical_Quadrature_RBF.m is the default implementation of the method described in:

J. A. Reeger and B. Fornberg, "Numerical Quadrature Over the Surface of the Sphere". submitted to Stud. Appl. Math