# annulus_rule

annulus_rule, an Octave code which computes a quadrature rule over the interior of the annulus in 2D, with center (XC,YC), inner radius R1 and outer radius R2.

The user specifies values NT and NR, where NT is the number of equally spaced angles, and NR controls the number of radial points.

To use a rule that is equally powerful in R and T, typically, set NT = 4 * NR.

### Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

### Languages:

annulus_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:

alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

annulus_distance, an Octave code which estimates the typical distance between a pair of points randomly selected inside a circular annulus.

annulus_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of an annulus centered at the origin.

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.

circle_rule, an Octave code which computes quadrature rules over the circumference of the unit circle in 2D.

cube_felippa_rule, an Octave code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

disk_rule, an Octave code which computes quadrature rules over the interior of the general disk in 2D.

disk01_quarter_rule, an Octave code which computes a quadrature rule over the interior of the unit quarter disk in 2D, with radius 1 and center (0,0).

disk01_rule, an Octave code which computes quadrature rules over the interior of the unit disk in 2D.

pyramid_felippa_rule, an Octave code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

pyramid_rule, an Octave code which computes a quadrature rule over the interior of a pyramid in 3D.

sphere_lebedev_rule, an Octave code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

square_felippa_rule, an Octave code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

tetrahedron_felippa_rule, an Octave code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

triangle_fekete_rule, an Octave code which defines Fekete rules for quadrature or interpolation over the interior of a triangle in 2D.

triangle_felippa_rule, an Octave code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

### Reference:

1. Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
2. Sylvan Elhay, Jaroslav Kautsky,
Algorithm 655: IQPACK, FORTRAN Subroutines for the Weights of Interpolatory Quadrature,
ACM Transactions on Mathematical Software,
Volume 13, Number 4, December 1987, pages 399-415.

### S-ource Code:

Last revised on 04 November 2018.