tetrahedron01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate the integral of a function F(X,Y,Z) over the interior of the unit tetrahedron in 3D.
The interior of the unit tetrahedron in 3D is defined by the constraints:
0 <= X
0 <= Y
0 <= Z
X + Y + Z <= 1
The functions F(X,Y,Z) are monomials, having the form
F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3)
where the exponents are nonnegative integers.
The computer code and data files described and made available on this web page are distributed under the MIT license
tetrahedron01_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.
tetrahedron01_monte_carlo_test
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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;
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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;
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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_arbq_rule, an Octave code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3d, by Hong Xiao and Zydrunas Gimbutas.
tetrahedron_exactness, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.
tetrahedron_felippa_rule, an Octave code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3d.
tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
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tetrahedron_ncc_rule, an Octave code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3d.
tetrahedron_nco_rule, an Octave code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3d.
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triangle01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2d.
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