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High order quadratures for triangles, squares, cubes, and tetrahedra

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Quadratures for triangles, squares, cubes and tetrahedra

Copyright (C) 2009-2012: Zydrunas Gimbutas and Hong Xiao

Contact: Zydrunas Gimbutas [email protected], Hong Xiao [email protected]

Date: June 18, 2020

Version 1.10

Contents

triasymq.f - fully symmetric (D_3) quadrature for triangle
triarotq.f - rotationally symmetric quadrature for triangle
triaarbq.f - arbitrary symmetric (or asymmetric) quadrature for triangle
triaintq.f - interpolation nodes/quadrature for smooth functions on triangle
squaresymq.f - fully symmetric (D_4) quadrature for a unit square
squaresymvq.f - centro/rotationally symmetric quadrature for a unit square
squarearbq.f - arbitrary symmetric (or asymmetric) quadrature for a unit square
squareintq.f - interpolation nodes/quadrature for smooth functions on a square
tetraarbq.f - arbitrary symmetric (or asymmetric) quadrature for tetrahedron
tetraintq.f - interpolation nodes/quadrature for smooth functions on tetrahedron
cubearbq.f - arbitrary symmetric (or asymmetric) quadrature for a unit cube

Quadratures for triangles

makefile - run a simple test (triasymq)
triasymq.f - construct (or rather retrieve) a fully symmetric (D_3) 
quadrature formula on the user-defined triangle in the plane.

triasymq_dr.f - driver routines for triasymq.f

makefile.triasymq - makefile for triasymq.f
                       ( make -f makefile.triasymq )
c
c   n       1     2     3     4     5     6     7     8     9    10
c  -----------------------------------------------------------------
c nodes     1     3     6     6     7    12    15    16    19    25
c
c
c   n      11    12    13    14    15    16    17    18    19    20
c  -----------------------------------------------------------------
c nodes    28    33    37    42    49    55    60    67    73    79
c
c
c   n      21    22    23    24    25    26    27    28    29    30
c  -----------------------------------------------------------------
c nodes    87    96   103   112   120   130   141   150   159   171
c
c
c   n      31    32    33    34    35    36    37    38    39    40
c  -----------------------------------------------------------------
c nodes   181   193   204   214   228   243   252   267   282   295
c
c
c   n      41    42    43    44    45    46    47    48    49    50
c  -----------------------------------------------------------------
c nodes   309   324   339   354   370   385   399   423   435   453
triarotq.f - construct (or rather retrieve) a rotationally symmetric
quadrature formula on the user-defined triangle in the plane.

triarotq_dr.f - driver routines for triarotq.f

makefile.triarotq - makefile for triarotq.f
                       ( make -f makefile.triarotq )
c   n       1     2     3     4     5     6     7     8     9    10
c  -----------------------------------------------------------------
c nodes     1     3     6     6     7    12    12    16    19    24
c
c
c   n      11    12    13    14    15    16    17    18    19    20
c  -----------------------------------------------------------------
c nodes    27    33    36    42    48    54    60    66    70    78
c
c
c   n      21    22    23    24    25    26    27    28    29    30
c  -----------------------------------------------------------------
c nodes    85    93   102   111   117   129   138   147   156   168
c
c
c   n      31    32    33    34    35    36    37    38    39    40
c  -----------------------------------------------------------------
c nodes   177   189   201   213   225   237   249   262   277   291
c
c
c   n      41    42    43    44    45    46    47    48    49    50
c  -----------------------------------------------------------------
c nodes   303   318   333   348   363   378   393   414   429   444
triaarbq.f - construct (or rather retrieve) an asymmetric
quadrature formula on the user-defined triangle in the plane.

triaarbq_dr.f - driver routines for triaarbq.f

makefile.triaarbq - makefile for triaarbq.f
                       ( make -f makefile.triaarbq )
c
c   n       1     2     3     4     5     6     7     8     9    10
c  -----------------------------------------------------------------
c nodes     1     3     4     6     7    11    12    16    19    24
c
c
c   n      11    12    13    14    15    16    17    18    19    20
c  -----------------------------------------------------------------
c nodes    27    32    36    41    46    53    58    65    70    78
c
c
c   n      21    22    23    24    25    26    27    28    29    30
c  -----------------------------------------------------------------
c nodes    85    93   101   109   117   128   136   147   156   168
c
c
c   n      31    32    33    34    35    36    37    38    39    40
c  -----------------------------------------------------------------
c nodes   177   189   201   212   225   236   249   262   274   290
c
c
c   n      41    42    43    44    45    46    47    48    49    50
c  -----------------------------------------------------------------
c nodes   302   318   332   348   363   378   393   412   429   444
c
triaintq.f - construct (or rather retrieve) fully symmetric (D_3) 
interpolation nodes on the user-defined triangle in the plane.

triaintq_dr.f - driver routines for triaintq.f

makefile.triaintq - makefile for triaintq.f
                       ( make -f makefile.triaintq )
c interp    0     1     2     3     4     5     6     7     8     9    10
c  -----------------------