Numerical integration over the spherical shell

Spherical Designs, Discrepancy and Numerical Integration

A spherical design is a point configuration on the sphere, which yields exact equal-weight quadrature formulae for polynomials up to a given degree. Until now only very specific constructions for spherical designs are known. We establish connections to spherical cap discrepancy and show some general discrepancy bounds. Furthermore, we reformulate the problem of constructing designs as an optimi...

Numerical Integration Over a Sphere*

Numerical Integration of the Primitive Equations on a Spherical Grid

A new spherical grid system whose grid density on the globe is almost homogeneous is proposed. The elementary rules of finite differencing on the grid system are defined so that a desirable condition for numerical area integration is satisfied. The integrations of primitive equations for a barotropic atmosphere with free surface are made. The patterns of initial fields are the same as Phillips ...

Numerical Integration over Simplexes and Cones

and fast rules for doing so. In the above example, for instance, if we substitute some other number, k say, for 2.507, the desired effect does not occur for all values of k. An integral power of ten will not work (since we are assuming rounding-off is done in the decimal system). Also one finds experimentally in this case that k = 1.001 and k = 2 are unsatisfactory choices. In our present study...

Adaptively weighted numerical integration over arbitrary domains

In adaptivelyweightednumerical integration, for a given set of quadrature nodes, order and domain of integration, the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense. The moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain, and then are corrected for the deviation fro...