LINE_FELIPPA_RULE
Quadrature Rules for a Line Segment in 1D

LINE_FELIPPA_RULE, a MATLAB library which generates the points and weights of a quadrature rule over the interior of a line segment in 1D.

Licensing:

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

Languages:

LINE_FELIPPA_RULE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CCN_RULE, a MATLAB program which defines a nested Clenshaw Curtis quadrature rule.

CHEBYSHEV1_RULE, a MATLAB program which computes and prints a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a MATLAB program which computes and prints a Gauss-Chebyshev type 2 quadrature rule.

CLENSHAW_CURTIS_RULE, a MATLAB program which defines a Clenshaw Curtis quadrature rule.

LEGENDRE_RULE, a MATLAB program which computes a 1D Gauss-Legendre quadrature rule.

LINE_CVT_LLOYD, a MATLAB library which applies Lloyd's iteration repeatedly to a set of N points, to compute a Centroidal Voronoi Tessellation (CVT) over the interior of a line segment in 1D.

LINE_FEKETE_RULE, a MATLAB library which estimates the location of N Fekete points, for polynomial interpolation or quadrature, over the interior of a line segment in 1D.

line_felippa_rule_test

LINE_GRID, a MATLAB library which computes a grid of points over the interior of a line segment in 1D.

LINE_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

LINE_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

LINE_NCC_RULE, a MATLAB library which defines a Newton Cotes Closed (NCC) rule using equally spaced points over the interior of a line segment in 1D.

LINE_NCO_RULE, a MATLAB library which defines a Newton Cotes Open (NCO) rule using equally spaced points over the interior of a line segment in 1D.

PATTERSON_RULE, a MATLAB program which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.

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:

• line_monomial.m, returns the exact integral of a monomial over a line segment in 1D.
• line_rule.m, returns a quadrature rule for a line segment in 1D.
• line_unit_o01.m, returns a 1 point quadrature rule for the unit line.
• line_unit_o02.m, returns a 2 point quadrature rule for the unit line.
• line_unit_o03.m, returns a 3 point quadrature rule for the unit line.
• line_unit_o04.m, returns a 4 point quadrature rule for the unit line.
• line_unit_o05.m, returns a 5 point quadrature rule for the unit line.
• line_volume.m, returns the volume of line segment in 1D;
• timestamp.m, prints the YMDHMS date as a timestamp;