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Add a higher order quadrature rule (exact up to p=10) #73

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Dec 3, 2023
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Add a higher order quadrature rule (exact up to p=10) #73

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54 changes: 54 additions & 0 deletions optimism/QuadratureRule.py
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Original file line number Diff line number Diff line change
Expand Up @@ -131,6 +131,60 @@ def create_quadrature_rule_on_triangle(degree):
4.14255378091870E-02,
4.14255378091870E-02,
4.14255378091870E-02])
elif degree <= 10:
xi = onp.array([[0.33333333333333333E+00, 0.33333333333333333E+00],
[0.4269134091050342E-02, 0.49786543295447483E+00],
[0.49786543295447483E+00, 0.4269134091050342E-02],
[0.49786543295447483E+00, 0.49786543295447483E+00],
[0.14397510054188759E+00, 0.42801244972905617E+00],
[0.42801244972905617E+00, 0.14397510054188759E+00],
[0.42801244972905617E+00, 0.42801244972905617E+00],
[0.6304871745135507E+00, 0.18475641274322457E+00],
[0.18475641274322457E+00, 0.6304871745135507E+00],
[0.18475641274322457E+00, 0.18475641274322457E+00],
[0.9590375628566448E+00, 0.20481218571677562E-01],
[0.20481218571677562E-01, 0.9590375628566448E+00],
[0.20481218571677562E-01, 0.20481218571677562E-01],
[0.3500298989727196E-01, 0.1365735762560334E+00],
[0.1365735762560334E+00, 0.8284234338466947E+00],
[0.8284234338466947E+00, 0.3500298989727196E-01],
[0.1365735762560334E+00, 0.3500298989727196E-01],
[0.8284234338466947E+00, 0.1365735762560334E+00],
[0.3500298989727196E-01, 0.8284234338466947E+00],
[0.37549070258442674E-01, 0.3327436005886386E+00],
[0.3327436005886386E+00, 0.6297073291529187E+00],
[0.6297073291529187E+00, 0.37549070258442674E-01],
[0.3327436005886386E+00, 0.37549070258442674E-01],
[0.6297073291529187E+00, 0.3327436005886386E+00],
[0.37549070258442674E-01, 0.6297073291529187E+00]])

w = onp.array([0.4176169990259819E-01,
0.36149252960283717E-02,
0.36149252960283717E-02,
0.36149252960283717E-02,
0.3724608896049025E-01,
0.3724608896049025E-01,
0.3724608896049025E-01,
0.39323236701554264E-01,
0.39323236701554264E-01,
0.39323236701554264E-01,
0.3464161543553752E-02,
0.3464161543553752E-02,
0.3464161543553752E-02,
0.147591601673897E-01,
0.147591601673897E-01,
0.147591601673897E-01,
0.147591601673897E-01,
0.147591601673897E-01,
0.147591601673897E-01,
0.1978968359803062E-01,
0.1978968359803062E-01,
0.1978968359803062E-01,
0.1978968359803062E-01,
0.1978968359803062E-01,
0.1978968359803062E-01])
else:
raise ValueError("Quadrature of precision this high is not implemented.")

return QuadratureRule(xi, w)

Expand Down
17 changes: 9 additions & 8 deletions optimism/test/test_QuadratureRule.py
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Original file line number Diff line number Diff line change
Expand Up @@ -43,7 +43,7 @@ def are_positive_weights(QuadratureRuleFactory, degree):

class TestQuadratureRules(TestFixture.TestFixture):
endpoints = (0.0, 1.0) # better if the quadrature rule module provided this
max_degree_2D = 6
max_degree_2D = 10
max_degree_1D = 25


Expand Down Expand Up @@ -87,13 +87,14 @@ def test_triangle_quadrature_points_in_domain(self):

def test_triangle_quadrature_exactness(self):
for degree in range(self.max_degree_2D + 1):
qr = QuadratureRule.create_quadrature_rule_on_triangle(degree)
for i in range(degree + 1):
for j in range(degree + 1 - i):
monomial = qr.xigauss[:,0]**i * qr.xigauss[:,1]**j
quadratureAnswer = np.sum(monomial * qr.wgauss)
exactAnswer = integrate_2D_monomial_on_triangle(i, j)
self.assertNear(quadratureAnswer, exactAnswer, 14)
with self.subTest(i=degree):
qr = QuadratureRule.create_quadrature_rule_on_triangle(degree)
for i in range(degree + 1):
for j in range(degree + 1 - i):
monomial = qr.xigauss[:,0]**i * qr.xigauss[:,1]**j
quadratureAnswer = np.sum(monomial * qr.wgauss)
exactAnswer = integrate_2D_monomial_on_triangle(i, j)
self.assertNear(quadratureAnswer, exactAnswer, 14)

if __name__ == '__main__':
unittest.main()