Cell classes

This document summarizes the classes denoted to store and handle data about polygonal cells in 1, 2 or 3 dimensions.

class sigmaepsilon.mesh.cells.H27(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

27-node isoparametric triquadratic hexahedron.

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class Geometry

classmethod master_center() → ndarray

Returns the local coordinates of the center of the cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

class sigmaepsilon.mesh.cells.H8(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

8-node hexahedron.

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class Geometry

classmethod master_center() → ndarray

Returns the local coordinates of the center of the cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod tetmap() → ndarray

Returns a mapper to transform topology and other data to a collection of tetrahedral simplices.

sigmaepsilon.mesh.cells.Hex

alias of H8

class sigmaepsilon.mesh.cells.L2(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

2-Node line element.

class Geometry

class sigmaepsilon.mesh.cells.L3(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

3-Node line element.

class Geometry

sigmaepsilon.mesh.cells.Line

alias of L2

class sigmaepsilon.mesh.cells.Q4(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

Polygon class for 4-noded bilinear quadrilaterals.

class Geometry

classmethod master_center() → ndarray

Returns the local coordinates of the center of the cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod trimap() → ndarray

Returns a mapper to transform topology and other data to a collection of triangular simplices.

to_triangles() → ndarray

Returns the topology as a collection of T3 triangles, represented as a 2d NumPy integer array, where the first axis runs along the triangles, and the second along the nodes.

Only for 2d cells.

class sigmaepsilon.mesh.cells.Q8(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

Polygon class for 8-noded quadratic quadrilaterals.

class Geometry

classmethod master_center() → ndarray

Returns the local coordinates of the center of the cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

shape_function_derivative_evaluator() → ndarray

Returns the first orderderivatives of the shape functions, evaluated at multiple points, according to ‘pcoords’.

— (nP, nNE, 2)

classmethod trimap() → ndarray

Returns a mapper to transform topology and other data to a collection of triangular simplices.

to_triangles() → ndarray

Returns the topology as a collection of T3 triangles, represented as a 2d NumPy integer array, where the first axis runs along the triangles, and the second along the nodes.

Only for 2d cells.

class sigmaepsilon.mesh.cells.Q9(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

Polygon class for 9-noded biquadratic quadrilaterals.

class Geometry

classmethod master_center() → ndarray

Returns the local coordinates of the center of the cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

shape_function_derivative_evaluator()

Returns the first orderderivatives of the shape functions, evaluated at multiple points, according to ‘pcoords’.

— (nP, nNE, 2)

classmethod trimap() → ndarray

Returns a mapper to transform topology and other data to a collection of triangular simplices.

to_triangles() → ndarray

Returns the topology as a collection of T3 triangles, represented as a 2d NumPy integer array, where the first axis runs along the triangles, and the second along the nodes.

Only for 2d cells.

sigmaepsilon.mesh.cells.Quad

alias of Q4

sigmaepsilon.mesh.cells.QuadraticLine

alias of L3

class sigmaepsilon.mesh.cells.T3(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

A class to handle 3-noded triangles.

Example

>>> from sigmaepsilon.mesh import TriMesh, CartesianFrame, PointData, triangulate
>>> from sigmaepsilon.mesh.cells import T3 as CellData
>>> A = CartesianFrame(dim=3)
>>> coords, topo = triangulate(size=(800, 600), shape=(10, 10))
>>> pd = PointData(coords=coords, frame=A)
>>> cd = CellData(topo=topo)
>>> trimesh = TriMesh(pd, cd)
>>> trimesh.area()
480000.0

class Geometry

classmethod master_center() → ndarray

Returns the center of the master cell relative to the origo of the master cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the master cell relative to the origo of the master cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod trimap() → ndarray

Returns a mapping used to transform the topology to triangles. This is only implemented here for standardization.

areas(*_, **__) → ndarray

Returns the areas of the cells as an 1d NumPy array.

to_triangles() → ndarray

Returns the topology as triangles.

class sigmaepsilon.mesh.cells.T6(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

A class to handle 6-noded triangles.

Example

>>> from sigmaepsilon.mesh import TriMesh, CartesianFrame, PointData, triangulate
>>> from sigmaepsilon.mesh.cells import T6 as CellData
>>> from sigmaepsilon.mesh.utils.topology.tr import T3_to_T6
>>> A = CartesianFrame(dim=3)
>>> coords, topo = triangulate(size=(800, 600), shape=(10, 10))
>>> coords, topo = T3_to_T6(coords, topo)
>>> pd = PointData(coords=coords, frame=A)
>>> cd = CellData(topo=topo)
>>> trimesh = TriMesh(pd, cd)
>>> trimesh.area()
480000.0

class Geometry

classmethod master_center() → ndarray

Returns the local coordinates of the center of the cell.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns local coordinates of the cell.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod trimap(subdivide: bool = True) → ndarray

Returns a mapper to transform topology and other data to a collection of triangular simplices.

to_triangles() → ndarray

Returns the topology as triangles.

class sigmaepsilon.mesh.cells.TET10(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

10-node isoparametric hexahedron.

class Geometry

classmethod master_center() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod tetmap(subdivide: bool = True) → ndarray

Returns a mapper to transform topology and other data to a collection of tetrahedral simplices.

class sigmaepsilon.mesh.cells.TET4(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

4-node isoparametric hexahedron.

class Geometry

classmethod master_center() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod tetmap() → ndarray

Returns a mapper to transform topology and other data to a collection of tetrahedral simplices.

to_tetrahedra(flatten: bool = True) → ndarray

Returns the topology as a collection of TET4 tetrahedra, represented as a 2d NumPy integer array, where the first axis runs along the tetrahedra, and the second along the nodes.

Only for 3d cells.

Parameters:

flatten (bool, Optional) – If True, the topology is returned as a 2d array. If False, the length of the first axis equals the number of cells in the block, the length of the second axis equals the number of tetrahedra per cell.

volumes() → ndarray

Returns the volumes of the cells in the database.

sigmaepsilon.mesh.cells.Tetra

alias of TET4

sigmaepsilon.mesh.cells.Tri

alias of T3

class sigmaepsilon.mesh.cells.W18(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

Polyhedra class for 18-noded biquadratic wedges.

class Geometry

classmethod master_center() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod tetmap() → ndarray

Returns a mapper to transform topology and other data to a collection of tetrahedral simplices.

class sigmaepsilon.mesh.cells.W6(*args, db: CellData[MeshDataLike, PointDataLike] | None = None, pointdata: PointDataLike | None = None, container: MeshDataLike | None = None, **kwargs)

Polyhedra class for 6-noded trilinear wedges.

class Geometry

classmethod master_center() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod master_coordinates() → ndarray

Returns the coordinates of the master element.

Return type:

numpy.ndarray

classmethod polybase() → Tuple[List]

Retruns the polynomial base of the master element.

Returns:

• list – A list of SymPy symbols.

• list – A list of monomials.

classmethod tetmap() → ndarray

Returns a mapper to transform topology and other data to a collection of tetrahedral simplices.

sigmaepsilon.mesh.cells.Wedge

alias of W6