pyramid_jaskowiec_rule
pyramid_jaskowiec_rule,
an Octave code which
returns quadrature rules, with exactness up to total degree 20,
over the interior of a pyramid in 3D,
by Jan Jaskowiec, Natarajan Sukumar.
The integration region is:
 ( 1  Z ) <= X <= 1  Z
 ( 1  Z ) <= Y <= 1  Z
0 <= Z <= 1.
When Z is zero, the integration region is a square lying in the (X,Y)
plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the
radius of the square diminishes, and when Z reaches 1, the square has
contracted to the single point (0,0,1).
Licensing:
The computer code and data files made available on this
web page are distributed under
the MIT license
Languages:
pyramid_jaskowiec_rule 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:
pyramid_jaskowiec_rule_test
pyramid_exactness,
an Octave code which
computes the monomial exactness of a quadrature rule
over the interior of a pyramid in 3D.
pyramid_felippa_rule,
an Octave code which
returns a Felippa quadrature rule for approximating integrals
over the interior of a pyramid in 3D.
pyramid_grid,
an Octave code which
computes a grid of points
over the interior of the unit pyramid in 3D;
pyramid_integrals,
an Octave code which
returns the exact value of the integral of any monomial
over the interior of the unit pyramid in 3d.
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;
pyramid_rule,
an Octave code which
computes a conical product quadrature rule
over the interior of the unit pyramid in 3d.
pyramid_witherden_rule,
an Octave code which
returns a Witherden quadrature rule, with exactness up to total
degree 10, over the interior of a pyramid in 3D.
quadrature_rules_pyramid,
a dataset directory which
contains quadrature rules
over the interior of the unit pyramid in 3d.
Reference:

Jan Jaskowiec, Natarajan Sukumar,
High order cubature rules for tetrahedra and pyramids,
International Journal of Numerical Methods in Engineering,
Volume 121, Number 11, pages 24182436, 15 June 2020.
Source Code:

comp_next.m,
returns the next composition of an integer.

monomial_value.m,
evaluates a multidimensional monomial.

pyramid_jaskowiec_rule.m,
returns a quadrature rule of given precision for the unit
pyramid.

pyramid_unit_monomial_integral.m,
returns the exact integral of a given monomial over the unit pyramid.

pyramid_unit_volume.m,
returns the volume of the unit pyramid.

pyramid_volume.m,
returns the volume of a pyramid.

rule_order.m,
returns the number of quadrature points used in a rule
of given degree.

rule00.m,
returns the rule of degree 0.

rule01.m,
returns the rule of degree 1.

rule02.m,
returns the rule of degree 2.

rule03.m,
returns the rule of degree 3.

rule04.m,
returns the rule of degree 4.

rule05.m,
returns the rule of degree 5.

rule06.m,
returns the rule of degree 6.

rule07.m,
returns the rule of degree 7.

rule08.m,
returns the rule of degree 8.

rule09.m,
returns the rule of degree 9.

rule10.m,
returns the rule of degree 10.

rule11.m,
returns the rule of degree 11.

rule12.m,
returns the rule of degree 12.

rule13.m,
returns the rule of degree 13.

rule14.m,
returns the rule of degree 14.

rule15.m,
returns the rule of degree 15.

rule16.m,
returns the rule of degree 16.

rule17.m,
returns the rule of degree 17.

rule18.m,
returns the rule of degree 18.

rule19.m,
returns the rule of degree 19.

rule20.m,
returns the rule of degree 20.

pyramid_jaskowiec_rule_to_matlab.m,
a MATLAB code which reads a data file describing one of
the rules (with 128 digits) and writes a function
to return points and weights.
Last revised on 15 May 2023.