wedge_monte_carlo

wedge_monte_carlo, an Octave 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 computer code and data files described and made available on this web page are 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

annulus_monte_carlo an Octave code which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

ball_monte_carlo, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3D;

circle_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

cube_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

disk_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

disk01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

disk01_quarter_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2D;

ellipse_monte_carlo an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ellipsoid_monte_carlo an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.

hyperball_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

hypercube_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions;

hypersphere_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

line_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

polygon_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

pyramid_monte_carlo, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

sphere_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the surface of the unit sphere in 3D.

sphere_triangle_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D;

square_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

tetrahedron_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of a general tetrahedron in 3D.

tetrahedron01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

triangle_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of a general triangle in 2D.

triangle01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

wedge_integrals, an Octave 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.