Product Rules formed from 1D Gauss-Legendre Rules

**PRODUCT_RULE_GL**
is a dataset directory which
contains some examples of multidimensional quadrature rules formed
as a product rule from 1D Gauss-Legendre rules.

For this directory, a quadrature rule is stored as three files, containing the weights, the points, and a file containing two points defining the endpoints of the region.

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

INT_EXACTNESS_LEGENDRE, a FORTRAN90 program which can read a set of files defining a Gauss-Legendre quadrature rule, and test it for exactness against monomial integrands.

LEGENDRE_RULE, a FORTRAN90 program which generates a Gauss-Legendre rule of the desired order.

PRODUCT_RULE, a FORTRAN90 program which creates a multidimensional product rule whose factors are 1D quadrature rules.

Gauss-Legendre product rule, dimension 2, 1x1 rule, 1 point:

- gl_d2_1x1_x.txt, the abscissas.
- gl_d2_1x1_w.txt, the weights.
- gl_d2_1x1_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 2, 2x2 rule, 4 points:

- gl_d2_2x2_x.txt, the abscissas.
- gl_d2_2x2_w.txt, the weights.
- gl_d2_2x2_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 2, 4x4, 16 points:

- gl_d2_4x4_x.txt, the abscissas.
- gl_d2_4x4_w.txt, the weights.
- gl_d2_4x4_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 2, 8x8, 64 points:

- gl_d2_8x8_x.txt, the abscissas.
- gl_d2_8x8_w.txt, the weights.
- gl_d2_8x8_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 2, 16x16, 256 points:

- gl_d2_16x16_x.txt, the abscissas.
- gl_d2_16x16_w.txt, the weights.
- gl_d2_16x16_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 2, 32x32, 1024 points:

- gl_d2_32x32_x.txt, the abscissas.
- gl_d2_32x32_w.txt, the weights.
- gl_d2_32x32_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 6, sixth power of order 1 rule, 1 point:

- gl_d6_l1_x.txt, the abscissas.
- gl_d6_l1_w.txt, the weights.
- gl_d6_l1_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 6, sixth power of order 2 rule, 64 points:

- gl_d6_l2_x.txt, the abscissas.
- gl_d6_l2_w.txt, the weights.
- gl_d6_l2_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 6, sixth power of order 3 rule, 729 points:

- gl_d6_l3_x.txt, the abscissas.
- gl_d6_l3_w.txt, the weights.
- gl_d6_l3_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 6, sixth power of order 4 rule, 4096 points:

- gl_d6_l4_x.txt, the abscissas.
- gl_d6_l4_w.txt, the weights.
- gl_d6_l4_r.txt, the range of the integration region.

Gauss-Legendre product rule, dimension 6, sixth power of order 5 rule, 15,625 points:

- gl_d6_l5_x.txt, the abscissas.
- gl_d6_l5_w.txt, the weights.
- gl_d6_l5_r.txt, the range of the integration region.

You can go up one level to the DATASETS page.