PRODUCT_RULE_TANH_SINH
Product Rules formed from 1D Tanh-Sinh Rules

PRODUCT_RULE_TANH_SINH is a dataset directory which contains examples of multidimensional quadrature rules formed as a product rule from 1D tanh-sinh 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.

TANH_SINH_RULE, a FORTRAN90 program which generates a tanh-sinh rule of the desired order.

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

Sample Files:

Tanh-sinh product rule, dimension 2, 1x1 rule, 1 point:

• ts_d2_1x1_x.txt, the abscissas.
• ts_d2_1x1_w.txt, the weights.
• ts_d2_1x1_r.txt, the range of the integration region.

Tanh-sinh product rule, dimension 2, 3x3 rule, 9 points:

• ts_d2_3x3_x.txt, the abscissas.
• ts_d2_3x3_w.txt, the weights.
• ts_d2_3x3_r.txt, the range of the integration region.

Tanh-sinh product rule, dimension 2, 7x7, 49 points:

• ts_d2_7x7_x.txt, the abscissas.
• ts_d2_7x7_w.txt, the weights.
• ts_d2_7x7_r.txt, the range of the integration region.

Tanh-sinh product rule, dimension 2, 15x15, 225 points:

• ts_d2_15x15_x.txt, the abscissas.
• ts_d2_15x15_w.txt, the weights.
• ts_d2_15x15_r.txt, the range of the integration region.

Tanh-sinh product rule, dimension 2, 31x31, 961 points:

• ts_d2_31x31_x.txt, the abscissas.
• ts_d2_31x31_w.txt, the weights.
• ts_d2_31x31_r.txt, the range of the integration region.

Tanh-sinh product rule, dimension 2, 63x63, 3969 points:

• ts_d2_63x63_x.txt, the abscissas.
• ts_d2_63x63_w.txt, the weights.
• ts_d2_63x63_r.txt, the range of the integration region.

Tanh-sinh product rule, dimension 2, 127x127, 16129 points:

• ts_d2_127x127_x.txt, the abscissas.
• ts_d2_127x127_w.txt, the weights.
• ts_d2_127x127_r.txt, the range of the integration region.

You can go up one level to the DATASETS page.