PRODUCT_RULE_GL
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.

Licensing:

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

Related Data and Programs:

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.

Sample Files:

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.