QUADRATURE_RULES_PYRAMID
Quadrature Rules for a Pyramid

QUADRATURE_RULES_PYRAMID is a dataset directory which contains definitions of quadrature rules over a pyramid.

The integration region is:

     - ( 1 - Z ) <= X <= 1 - Z
     - ( 1 - Z ) <= Y <= 1 - Z
               0 <= Z <= 1.
      

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:

FELIPPA, a C++ library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.

PYRAMID_EXACTNESS, a C++ program which investigates the polynomial exactness of a quadrature rule for the pyramid.

PYRAMID_RULE, a C++ program which computes a quadrature rule for a pyramid.

QUADRATURE_RULES_TET, a dataset directory which contains quadrature rules for tetrahedrons, stored as a file of abscissas, a file of weights, and a file of vertices.

QUADRATURE_RULES_TRI, a dataset directory which contains quadrature rules for triangles, stored as a file of abscissas, a file of weights, and a file of vertices.

QUADRATURE_RULES_WEDGE, a dataset directory which contains quadrature rules for a wedge ( triangle x a line ).

Reference:

1. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Data Files:

PYRA_FELIPPA_O01 is a rule of order 1 due to Felippa.

• pyra_felippa_o01_w.txt, the weights.
• pyra_felippa_o01_x.txt, the abscissas.

PYRA_FELIPPA_O05 is a rule of order 5 due to Felippa.

• pyra_felippa_o05_w.txt, the weights.
• pyra_felippa_o05_x.txt, the abscissas.

PYRA_FELIPPA_O06 is a rule of order 6 due to Felippa.

• pyra_felippa_o06_w.txt, the weights.
• pyra_felippa_o06_x.txt, the abscissas.

PYRA_FELIPPA_O08 is a rule of order 8 due to Felippa.

• pyra_felippa_o08_w.txt, the weights.
• pyra_felippa_o08_x.txt, the abscissas.

PYRA_FELIPPA_O08b is a rule of order 8 due to Felippa.

• pyra_felippa_o08b_w.txt, the weights.
• pyra_felippa_o08b_x.txt, the abscissas.

PYRA_FELIPPA_O09 is a rule of order 9 due to Felippa.

• pyra_felippa_o09_w.txt, the weights.
• pyra_felippa_o09_x.txt, the abscissas.

PYRA_FELIPPA_O13 is a rule of order 13 due to Felippa.

• pyra_felippa_o13_w.txt, the weights.
• pyra_felippa_o13_x.txt, the abscissas.

PYRA_FELIPPA_O18 is a rule of order 18 due to Felippa.

• pyra_felippa_o18_w.txt, the weights.
• pyra_felippa_o18_x.txt, the abscissas.

PYRA_FELIPPA_O27 is a rule of order 27 due to Felippa.

• pyra_felippa_o27_w.txt, the weights.
• pyra_felippa_o27_x.txt, the abscissas.

PYRA_FELIPPA_O48 is a rule of order 48 due to Felippa.

• pyra_felippa_o48_w.txt, the weights.
• pyra_felippa_o48_x.txt, the abscissas.

PYRAMID_L1X1_J1 is a conical product rule 1x1 Legendre and 1 Jacobi, with precision 1.

• pyramid_l1x1_j1_w.txt, the weights.
• pyramid_l1x1_j1_x.txt, the abscissas.
• pyramid_l1x1_j1_r.txt, the region.

PYRAMID_L2X2_J2 is a conical product rule 2x2 Legendre and 2 Jacobi, with precision 3.

• pyramid_l2x2_j2_w.txt, the weights.
• pyramid_l2x2_j2_x.txt, the abscissas.
• pyramid_l2x2_j2_r.txt, the region.

PYRAMID_L3X3_J3 is a conical product rule 3x3 Legendre and 3 Jacobi, with precision 5.

• pyramid_l3x3_j3_w.txt, the weights.
• pyramid_l3x3_j3_x.txt, the abscissas.
• pyramid_l3x3_j3_r.txt, the region.

PYRAMID_L4X4_J4 is a conical product rule 4x4 Legendre and 4 Jacobi, with precision 7.

• pyramid_l4x4_j4_w.txt, the weights.
• pyramid_l4x4_j4_x.txt, the abscissas.
• pyramid_l4x4_j4_r.txt, the region.

PYRAMID_L5X5_J5 is a conical product rule 5x5 Legendre and 5 Jacobi, with precision 9.

• pyramid_l5x5_j5_w.txt, the weights.
• pyramid_l5x5_j5_x.txt, the abscissas.
• pyramid_l5x5_j5_r.txt, the region.

PYRAMID_L6X6_J6 is a conical product rule 6x6 Legendre and 6 Jacobi, with precision 11.

• pyramid_l6x6_j6_w.txt, the weights.
• pyramid_l6x6_j6_x.txt, the abscissas.
• pyramid_l6x6_j6_r.txt, the region.

PYRAMID_L7X7_J2 is a conical product rule 7x7 Legendre and 7 Jacobi, with precision 13.

• pyramid_l7x7_j7_w.txt, the weights.
• pyramid_l7x7_j7_x.txt, the abscissas.
• pyramid_l7x7_j7_r.txt, the region.

PYRAMID_L8X8_J8 is a conical product rule 8x8 Legendre and 8 Jacobi, with precision 15.

• pyramid_l8x8_j8_w.txt, the weights.
• pyramid_l8x8_j8_x.txt, the abscissas.
• pyramid_l8x8_j8_r.txt, the region.

PYRAMID_L9X9_J9 is a conical product rule 9x9 Legendre and 9 Jacobi, with precision 17.

• pyramid_l9x9_j9_w.txt, the weights.
• pyramid_l9x9_j9_x.txt, the abscissas.
• pyramid_l9x9_j9_r.txt, the region.

PYRAMID_L10X10_J10 is a conical product rule 10x10 Legendre and 10 Jacobi, with precision 19.

• pyramid_l10x10_j10_w.txt, the weights.
• pyramid_l10x10_j10_x.txt, the abscissas.
• pyramid_l10x10_j10_r.txt, the region.

PYRAMID_L11X11_J11 is a conical product rule 11x11 Legendre and 11 Jacobi, with precision 21.

• pyramid_l11x11_j11_w.txt, the weights.
• pyramid_l11x11_j11_x.txt, the abscissas.
• pyramid_l11x11_j11_r.txt, the region.

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