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.
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load_table(polygon,
family)
Return list of quadrature rules matching polygon and family. |
source code
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scale_table(rules)
Scales a set of quadrature rules from [-1,+1]^nsd to [0,1]^nsd. |
source code
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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
...
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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
...
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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
...
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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
...
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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
...
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newton_cotes_table
- Value:
"""\
2
1 1
-1 1
Closed Newton-Cotes quadrature constants order n=1
3
1 1/3
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chebyshev_table
- Value:
"""\
2
0.5773502691896257645091488 1
-0.5773502691896257645091488 1
Chebyshev quadrature constants order n+1=3
3
0.7071067811865475244008444 2/3
...
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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
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