square_minimal_rule

square_minimal_rule, a MATLAB code which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric unit square in 2D, by Mattia Festa and Alvise Sommariva.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

square_minimal_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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Reference:

1. Mattia Festa, Alvise Sommariva,
   Computing almost minimal formulas on the square,
   Journal of Computational and Applied Mathematics,
   Volume 17, Number 236, November 2012, pages 4296-4302.

Source Code:

• set_amr_square.m, the original code by Festa and Sommariva.
• square_minimal_rule.m, the original code by Festa and Sommariva.
• square_minimal_rule_degree_max.m, returns the maximum degree for which a rule is available.
• square_minimal_rule_error_max.m, returns the maximum error made by a rule over all the monomials it should integrate exactly.
• square_minimal_rule_order.m, returns the order (number of points used) for the rule of given degree.
• square_minimal_rule_print.m, prints a minimal rule for the symmetric unit square.
• squaresym_monomial_integral.m, returns the exact integral of a momomial over the symmetric unit square.