line_felippa_rule

line_felippa_rule, a MATLAB code 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 MIT 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 code which defines a nested clenshaw curtis quadrature rule.

chebyshev1_rule, a MATLAB code which computes and prints a gauss-chebyshev type 1 quadrature rule.

chebyshev2_rule, a MATLAB code which computes and prints a gauss-chebyshev type 2 quadrature rule.

clenshaw_curtis_rule, a MATLAB code which defines a clenshaw curtis quadrature rule.

legendre_rule, a MATLAB code which computes a 1d gauss-legendre quadrature rule.

line_cvt_lloyd, a MATLAB code 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 code 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 code which computes a grid of points over the interior of a line segment in 1d.

line_integrals, a MATLAB code 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 code 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 code 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 code 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 code 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;