Package sfc :: Package quadrature :: Module quad_tables
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Module quad_tables

source code


This module contains quadrature rule tables copied from
    P. Solin, K Segeth, and I Dolezel. Higher–Order Finite Element Methods.
    Studies in Advanced Mathematics. Chapman and Hall/CRC, 2004.

Use the function load_table(polygon, family) to get a list of QuadRule objects.
The family can be one of {"composite_gauss", "economical_gauss"}, the polygon name one of the UFC polygon names.

Functions [hide private]
 
load_rule(polygon, order, family) source code
 
load_table(polygon, family)
Return list of quadrature rules matching polygon and family.
source code
 
parse_table_string(polygon, family) source code
 
scale_table(rules)
Scales a set of quadrature rules from [-1,+1]^nsd to [0,1]^nsd.
source code
Variables [hide private]
  gauss_interval_table = "...
  economical_gauss_quadrilateral_table = "...
  economical_gauss_hexahedron_table = "...
  economical_gauss_triangle_table = "...
  economical_gauss_tetrahedron_table = "...
  newton_cotes_table = "...
  chebyshev_table = "...
  lobatto_table = "...
Variables Details [hide private]

gauss_interval_table

Value:
"""\
1
0.0000000000000000000000000  2.0000000000000000000000000
  Gauss  quadrature  points  and  weights  order  2n-1=1

2
-0.5773502691896257645091488  1.0000000000000000000000000
0.5773502691896257645091488  1.0000000000000000000000000
...

economical_gauss_quadrilateral_table

Value:
"""\
1
0.000000000000000  0.000000000000000  4.000000000000000
  Gauss  quadrature  points  and  weights  on  the  reference  quadril\
ateral  order  p=0  1

4
0.577350269189626  0.577350269189626  1.000000000000000
...

economical_gauss_hexahedron_table

Value:
"""\
1
0.000000000000000  0.000000000000000  0.000000000000000  8.00000000000\
0000
  Gauss  quadrature  points  and  weights  on  the  reference  cube  o\
rder  p=0  1

6
...

economical_gauss_triangle_table

Value:
"""\
1
-0.333333333333333  -0.333333333333333  2.000000000000000
  Gauss  quadrature  points  and  weights  on  the  reference  triangl\
e  order  p=1

3
-0.666666666666667  -0.666666666666667  0.666666666666667
...

economical_gauss_tetrahedron_table

Value:
"""\
1
-0.500000000000000  -0.500000000000000  -0.500000000000000  1.33333333\
3333333
  Gauss  quadrature  constants  for  the  reference  tetrahedron  orde\
r  p=1

4
...

newton_cotes_table

Value:
"""\
2
1  1
-1  1
  Closed  Newton-Cotes  quadrature  constants  order  n=1

3
1  1/3
...

chebyshev_table

Value:
"""\
2
0.5773502691896257645091488  1
-0.5773502691896257645091488  1
  Chebyshev  quadrature  constants  order  n+1=3

3
0.7071067811865475244008444  2/3
...

lobatto_table

Value:
"""\
3
1.0000000000000000000000000  0.3333333333333333333333333
0.0000000000000000000000000  1.3333333333333333333333333
-1.0000000000000000000000000  0.3333333333333333333333333
  Lobatto  (Radau)  quadrature  constants  order  2n-3=3

4
...