from typing import Tuple, List
from functools import partial
import numpy as np
from numpy import ndarray
import sympy as sy
from ..geometry import PolyCellGeometry3d
from ..data.polycell import PolyCell
from ..utils.cells.h27 import (
shp_H27_multi,
dshp_H27_multi,
shape_function_matrix_H27_multi,
monoms_H27,
)
from ..utils.numint import Gauss_Legendre_Hex_Grid
[docs]
class H27(PolyCell):
"""
Class for 27-node triquadratic hexahedra.
::
top
7---14---6
| | |
15--25--13
| | |
4---12---5
middle
19--23--18
| | |
20--26--21
| | |
16--22--17
bottom
3---10---2
| | |
11--24---9
| | |
0----8---1
"""
label = "H27"
[docs]
class Geometry(PolyCellGeometry3d):
number_of_nodes = 27
vtk_cell_id = 29
shape_function_evaluator = shp_H27_multi
shape_function_matrix_evaluator = shape_function_matrix_H27_multi
shape_function_derivative_evaluator = dshp_H27_multi
monomial_evaluator = monoms_H27
quadrature = {
"full": partial(Gauss_Legendre_Hex_Grid, 3, 3, 3),
"geometry": "full",
}
[docs]
@classmethod
def polybase(cls) -> Tuple[List]:
"""
Retruns the polynomial base of the master element.
Returns
-------
list
A list of SymPy symbols.
list
A list of monomials.
"""
locvars = r, s, t = sy.symbols("r s t", real=True)
monoms = [
1,
r,
s,
t,
s * t,
r * t,
r * s,
r * s * t,
r**2,
s**2,
t**2,
r**2 * s,
r * s**2,
r * t**2,
r**2 * t,
s**2 * t,
s * t**2,
r**2 * s * t,
r * s**2 * t,
r * s * t**2,
r**2 * s**2,
s**2 * t**2,
r**2 * t**2,
r**2 * s**2 * t**2,
r**2 * s**2 * t,
r**2 * s * t**2,
r * s**2 * t**2,
]
return locvars, monoms
[docs]
@classmethod
def master_coordinates(cls) -> ndarray:
"""
Returns local coordinates of the cell.
Returns
-------
numpy.ndarray
"""
return np.array(
[
[-1.0, -1.0, -1],
[1.0, -1.0, -1.0],
[1.0, 1.0, -1.0],
[-1.0, 1.0, -1.0],
[-1.0, -1.0, 1.0],
[1.0, -1.0, 1.0],
[1.0, 1.0, 1.0],
[-1.0, 1.0, 1.0],
[0.0, -1.0, -1.0],
[1.0, 0.0, -1.0],
[0.0, 1.0, -1.0],
[-1.0, 0.0, -1.0],
[0.0, -1.0, 1.0],
[1.0, 0.0, 1.0],
[0.0, 1.0, 1.0],
[-1.0, 0.0, 1.0],
[-1.0, -1.0, 0.0],
[1.0, -1.0, 0.0],
[1.0, 1.0, 0.0],
[-1.0, 1.0, 0.0],
[-1.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 0.0],
]
)
[docs]
@classmethod
def master_center(cls) -> ndarray:
"""
Returns the local coordinates of the center of the cell.
Returns
-------
numpy.ndarray
"""
return np.array([0.0, 0.0, 0.0])