from typing import Tuple, List
import numpy as np
from numpy import ndarray
from sympy import symbols
from ..geometry import PolyCellGeometry3d
from ..data.polycell import PolyCell
from ..utils.cells.tet10 import (
monoms_TET10,
)
from ..utils.numint import Gauss_Legendre_Tet_4
[docs]
class TET10(PolyCell):
"""
Class for 10-node tetrahedra.
"""
label = "TET10"
[docs]
class Geometry(PolyCellGeometry3d):
number_of_nodes = 10
vtk_cell_id = 24
monomial_evaluator = monoms_TET10
quadrature = {
"full": Gauss_Legendre_Tet_4,
"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 = symbols("r s t", real=True)
monoms = [1, r, s, t, r * s, r * t, s * t, r**2, s**2, t**2]
return locvars, monoms
[docs]
@classmethod
def master_coordinates(cls) -> ndarray:
return np.array(
[
[-1 / 3, -1 / 3, -1 / 3],
[2 / 3, -1 / 3, -1 / 3],
[-1 / 3, 2 / 3, -1 / 3],
[-1 / 3, -1 / 3, 2 / 3],
[1 / 6, -1 / 3, -1 / 3],
[1 / 6, 1 / 6, -1 / 3],
[-1 / 3, 1 / 6, -1 / 3],
[-1 / 3, -1 / 3, 1 / 6],
[1 / 6, -1 / 3, 1 / 6],
[-1 / 3, 1 / 6, 1 / 6],
]
)
[docs]
@classmethod
def master_center(cls) -> ndarray:
return np.array([[0.0, 0.0, 0.0]], dtype=float)
[docs]
@classmethod
def tetmap(cls, subdivide: bool = True) -> np.ndarray:
if subdivide:
raise NotImplementedError
else:
return np.array([[0, 1, 2, 3]], dtype=int)