Functions
	integrate_exact (f)

	duffy_quadrature (order)

	verify_duffy (max_order=8)

	verify_duffy_rational (max_p=4)

Variables
	max_order

	max_p

Function Documentation

◆ duffy_quadrature()

pyramid_duffy.duffy_quadrature ( order )

Build a pyramid quadrature rule via the Duffy transform:
    x = xi*(1-zeta), y = eta*(1-zeta), z = zeta
    J = (1-zeta)^2
A tensor product of n 1D Gauss-Legendre points (n = ceil((order+1)/2))
integrates the pulled-back polynomial stiffness integrand exactly for
pyramid basis degree p = order//2.

Returns (pts, weights) on the reference pyramid [0<=x,y<=1-z, 0<=z<=1].
Weights sum to 1/3.

Definition at line 13 of file pyramid_duffy.py.

Referenced by verify_duffy(), and verify_duffy_rational().

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◆ integrate_exact()

pyramid_duffy.integrate_exact ( f )

Exact integral of f over the reference pyramid: 0<=z<=1, 0<=x,y<=1-z.

Definition at line 4 of file pyramid_duffy.py.

Referenced by verify_duffy(), and verify_duffy_rational().

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◆ verify_duffy()

pyramid_duffy.verify_duffy ( max_order = 8 )

Verify that duffy_quadrature integrates all monomials x^i y^j z^k
(i+j+k <= order) exactly over the reference pyramid.

Definition at line 52 of file pyramid_duffy.py.

References duffy_quadrature(), and integrate_exact().

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◆ verify_duffy_rational()

pyramid_duffy.verify_duffy_rational ( max_p = 4 )

Verify Duffy integrates the actual pyramid rational basis products exactly.
Tests xy/(1-z), x^2*y/(1-z)^2, etc. that appear in stiffness integrals.

Definition at line 81 of file pyramid_duffy.py.

References duffy_quadrature(), and integrate_exact().

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Variable Documentation

◆ max_order

pyramid_duffy.max_order

Definition at line 116 of file pyramid_duffy.py.

◆ max_p

pyramid_duffy.max_p

Definition at line 119 of file pyramid_duffy.py.

Functions

Variables