wedge_monte_carlo

wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit wedge in 3D

The interior of the unit wedge in 3D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
       -1 <= Z <= +1
      

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

wedge_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

wedge_monte_carlo_test

matlab_monte_carlo, a MATLAB code which uses Monte Carlo sampling to estimate areas and integrals.

wedge_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

wedge_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of the unit wedge in 3D.

wedge_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

Reference:

1. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Source Code:

• monomial_value.m, evaluates a monomial.
• wedge01_integral.m, returns the integral of a monomial in the unit wedge in 3D.
• wedge01_sample.m, samples points uniformly from the unit wedge in 3D.
• wedge01_volume.m, returns the volume of the unit wedge in 3D.