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 2418-2436, 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.