Source code for polymesh.cells.t6

# -*- coding: utf-8 -*-
from typing import Tuple, List
import numpy as np
from numpy import ndarray
from sympy import symbols

from ..utils.utils import cells_coords
from ..polygon import QuadraticTriangle as Triangle
from ..utils.cells.t6 import (
    shp_T6_multi,
    dshp_T6_multi,
    areas_T6,
    shape_function_matrix_T6_multi,
    monoms_T6,
)
from ..utils.cells.gauss import Gauss_Legendre_Tri_3a


class T6(Triangle):
    """
    A class to handle 6-noded triangles.

    See Also
    --------
    :class:`~polymesh.polygon.Triangle`
    """

    shpfnc = shp_T6_multi
    shpmfnc = shape_function_matrix_T6_multi
    dshpfnc = dshp_T6_multi
    monomsfnc = monoms_T6

    quadrature = {
        "full": Gauss_Legendre_Tri_3a(),
    }

    @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 = symbols("r s", real=True)
        monoms = [1, r, s, r**2, s**2, r * s]
        return locvars, monoms

    @classmethod
    def lcoords(cls) -> ndarray:
        """
        Returns local coordinates of the cell.

        Returns
        -------
        numpy.ndarray
        """
        return np.array(
            [[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [0.5, 0.0], [0.5, 0.5], [0.0, 0.5]]
        )

    @classmethod
    def lcenter(cls) -> ndarray:
        """
        Returns the local coordinates of the center of the cell.

        Returns
        -------
        numpy.ndarray
        """
        return np.array([[1 / 3, 1 / 3]])

    def areas(self) -> ndarray:
        """
        Returns the areas of the triangles of the block.

        Returns
        -------
        numpy.ndarray
        """
        coords = self.source_coords()
        topo = self.topology().to_numpy()
        ecoords = cells_coords(coords[:, :2], topo)
        qpos, qweight = self.quadrature["full"]
        return areas_T6(ecoords, qpos, qweight)