Numerical integration over simplexes and cones

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...

Numerical Integration Over a Sphere*

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...

High-Order Numerical Integration over Discrete Surfaces

We consider the problem of numerical integration of a function over a discrete surface to high-order accuracy. Surface integration is a common operation in numerical computations for scientific and engineering problems. Integration over discrete surfaces (such as a surface triangulation) is typically limited to only first or second-order accuracy due to the piecewise linear approximations of th...

Numerical Integration of Fluid Flow over Triangular Grids

Discrete approximations to hyperbolic partial differential equations governing frictionless two-dimensional fluid flow are developed in Cartesian geometry for use over arbitrary triangular grids. A class of schemes is developed that conserves mass, momentum, and total energy. The terms of the governing equations are also approximated individually and their truncation error is examined. For test...