Class TriangularElement
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An arbitrary-order triangular finite element.
Coordinate systems used:
unit coordinates (r,s):
C |\ | \ | O | \ | \ A-----B
Points in unit coordinates:
O = (0,0)
A = (-1,-1)
B = (1,-1)
C = (-1,1)
equilateral coordinates (x,y):
C
/ \
/ \
/ \
/ O \
/ \
A-----------B
Points in equilateral coordinates:
O = (0,0)
A = (-1,-1/sqrt(3))
B = (1,-1/sqrt(3))
C = (0,2/sqrt(3))
When global vertices are passed in, they are mapped to the reference
vertices A, B, C in order.
Faces are always ordered AB, BC, AC.
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__init__(self,
order,
fancy_node_ordering=True)
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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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))
Return the equilateral (x,y) coordinate corresponding to the
barycentric coordinates (lambda1..lambdaN). |
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| get_face_index_shuffle_to_match(face_1_vertices,
face_2_vertices) |
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dimensions = 2
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has_local_jacobians = False
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equilateral_to_unit = AffineMap(numpy.array([[1,-1/ sqrt(3)], ...
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__init__(self,
order,
fancy_node_ordering=True)
(Constructor)
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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 for i+j <= N
- Decorators:
- Overrides:
Element.basis_functions
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equilateral_to_unit
- Value:
AffineMap(numpy.array([[1,-1/ sqrt(3)], [0, 2/ sqrt(3)]]), numpy.array
([-1/ 3,-1/ 3]))
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