TRIANGLE_WANDZURA_RULE
High Order Quadrature in a Triangle.

TRIANGLE_WANDZURA_RULE is a C++ library which can return any of six Wandzura rules for high order quadrature over the interior of a triangle in 2D.

There are six rules, which have polynomial degree of exactness of 5, 10, 15, 20, 25, and 30.

Licensing:

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

Languages:

TRIANGLE_WANDZURA_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

ANNULUS_RULE, a C++ library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

CUBE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

PYRAMID_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

SIMPLEX_GM_RULE, a C++ library which defines Grundmann-Moeller quadrature rules over the interior of the simplex in M dimensions.

SQUARE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

STROUD, a C++ library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TETRAHEDRON_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TRIANGLE_ANALYZE, a C++ program which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.

TRIANGLE_DUNAVANT_RULE, a C++ library which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

TRIANGLE_EXACTNESS, a C++ program which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.

TRIANGLE_FEKETE_RULE, a C++ library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

TRIANGLE_LYNESS_RULE, a C++ library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a C++ library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a C++ library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_SYMQ_RULE, a C++ library which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.

WEDGE_FELIPPA_RULE, a C++ library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

1. James Lyness, Dennis Jespersen,
   Moderate Degree Symmetric Quadrature Rules for the Triangle,
   Journal of the Institute of Mathematics and its Applications,
   Volume 15, Number 1, February 1975, pages 19-32.
2. Stephen Wandzura, Hong Xiao,
   Symmetric Quadrature Rules on a Triangle,
   Computers and Mathematics with Applications,
   Volume 45, Number 12, June 2003, pages 1829-1840.

Source Code:

• triangle_wandzura_rule.cpp, the source code.
• triangle_wandzura_rule.hpp, the include file.

Examples and Tests:

• triangle_wandzura_rule_test.cpp, a sample calling program.
• triangle_wandzura_rule_test.txt, the output file.

List of Routines:

• FILE_NAME_INC increments a partially numeric file name.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the smaller of two I4's.
• I4_MODP returns the nonnegative remainder of I4 division.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• R8_HUGE returns a "huge" R8.
• R8_NINT returns the nearest integer to an R8.
• REFERENCE_TO_PHYSICAL_T3 maps T3 reference points to physical points.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_AREA computes the area of a triangle.
• WANDZURA_DEGREE returns the degree of a given Wandzura rule for the triangle.
• WANDZURA_ORDER_NUM returns the order of a given Wandzura rule for the triangle.
• WANDZURA_RULE returns the points and weights of a Wandzura rule.
• WANDZURA_RULE_NUM returns the number of Wandzura rules available.
• WANDZURA_SUBORDER returns the suborders for a Wandzura rule.
• WANDZURA_SUBORDER_NUM returns the number of suborders for a Wandzura rule.
• WANDZURA_SUBRULE returns a compressed Wandzura rule.
• WANDZURA_SUBRULE_1 returns a compressed Wandzura rule 1.
• WANDZURA_SUBRULE_2 returns a compressed Wandzura rule 2.
• WANDZURA_SUBRULE_3 returns a compressed Wandzura rule 3.
• WANDZURA_SUBRULE_4 returns a compressed Wandzura rule 4.
• WANDZURA_SUBRULE_5 returns a compressed Wandzura rule 5.
• WANDZURA_SUBRULE_6 returns a compressed Wandzura rule 6.
• WANDZURA_SUBRULE2_1 returns a compressed Wandzura rule 1.
• WANDZURA_SUBRULE2_2 returns a compressed Wandzura rule 2.
• WANDZURA_SUBRULE2_3 returns a compressed Wandzura rule 3.
• WANDZURA_SUBRULE2_4 returns a compressed Wandzura rule 4.
• WANDZURA_SUBRULE2_5 returns a compressed Wandzura rule 5.
• WANDZURA_SUBRULE2_6 returns a compressed Wandzura rule 6.

You can go up one level to the C++ source codes.