Class TetrahedralElement
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An arbitrary-order tetrahedral finite element.
Coordinate systems used:
unit coordinates (r,s,t):
^ s
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C
/|\
/ | \
/ | \
/ | \
/ O| \
/ __A-----B---> r
/_--^ ___--^^
,D--^^^
t L
(squint, and it might start making sense...)
Points in unit coordinates:
O=( 0, 0, 0)
A=(-1,-1,-1)
B=(+1,-1,-1)
C=(-1,+1,-1)
D=(-1,-1,+1)
Points in equilateral coordinates (x,y,z):
O = (0,0)
A = (-1,-1/sqrt(3),-1/sqrt(6))
B = ( 1,-1/sqrt(3),-1/sqrt(6))
C = ( 0, 2/sqrt(3),-1/sqrt(6))
D = ( 0, 0, 3/sqrt(6))
When global vertices are passed in, they are mapped to the reference
vertices A, B, C, D in order.
Faces are always ordered ABC, ABD, ACD, BCD.
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__init__(self,
order)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature |
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faces_for_node_tuple(self,
node_tuple)
Return the list of face indices of faces on which the node
represented by node_tuple lies. |
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equilateral_nodes(self)
Generate warped nodes in equilateral coordinates (x,y). |
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| get_face_index_shuffle_to_match(self,
face_1_vertices,
face_2_vertices) |
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Inherited from SimplicialElement:
dt_non_geometric_factor,
equidistant_barycentric_nodes,
equidistant_equilateral_nodes,
equidistant_unit_nodes,
face_count,
face_indices,
face_node_count,
generate_mode_identifiers,
node_count,
unit_nodes,
vertex_indices
Inherited from Element:
differentiation_matrices,
find_diff_mat_permutation,
grad_vandermonde,
inverse_mass_matrix,
lifting_matrix,
mass_matrix,
multi_face_mass_matrix,
vandermonde
Inherited from object:
__delattr__,
__getattribute__,
__hash__,
__new__,
__reduce__,
__reduce_ex__,
__repr__,
__setattr__,
__str__
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barycentric_to_equilateral((lambda1, lambda2, lambda3, lambda4))
Return the equilateral (x,y) coordinate corresponding to the
barycentric coordinates (lambda1..lambdaN). |
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dimensions = 3
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has_local_jacobians = False
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equilateral_to_unit = AffineMap(numpy.array([[1,-1/ sqrt(3),-1...
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x.__init__(...) initializes x; see x.__class__.__doc__ for
signature
- Overrides:
object.__init__
- (inherited documentation)
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Generate tuples enumerating the node indices present in this element.
Each tuple has a length equal to the dimension of the element. The tuples
constituents are non-negative integers whose sum is less than or equal to
the order of the element.
The order in which these nodes are generated dictates the local node
numbering.
- Decorators:
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Return a list of tuples of indices into the node list that generate a
tesselation of the reference element.
- Decorators:
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Get a sequence of functions that form a basis of the approximation
space.
The approximation space is spanned by the polynomials:
r**i * s**j * t**k for i+j+k <= order
- Decorators:
- Overrides:
Element.basis_functions
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equilateral_to_unit
- Value:
AffineMap(numpy.array([[1,-1/ sqrt(3),-1/ sqrt(6)], [0, 2/ sqrt(3),-1/
sqrt(6)], [0, 0, sqrt(6)/ 2]]), numpy.array([-1/ 2,-1/ 2,-1/ 2]))
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