Source code for fe_utils.reference_elements

import numpy as np




class ReferenceCell(object):

    def __init__(self, vertices, topology, name):
        """An object storing the geometry and topology of the reference cell.

        :param vertices: a list of coordinate vectors corresponding to
          the coordinates of the vertices of the cell.
        :param topology: a dictionary of dictionaries such that topology[d][i]
          is the list of vertices incident to the `i`-th entity of dimension
          `d`.
        """

        #: The vertices making up each topological entity of the reference
        #: cell.
        self.topology = topology

        #: The list of coordinate veritices of the reference cell.
        self.vertices = np.array(vertices, dtype=np.double)

        self.name = name

        #: The geometric and topological dimension of the reference cell.
        self.dim = self.vertices.shape[1]

        if self.dim != len(topology) - 1:
            raise ValueError("Dimension mismatch between vertices and topology.")

        #: The number of entities of each dimension.
        self.entity_counts = np.array([len(d) for d in topology.values()])

    def __repr__(self):

        return self.name



#: A :class:`ReferenceCell` storing the geometry and topology of the
#: interval [0, 1].
ReferenceInterval = ReferenceCell(
    vertices=[[0.0], [1.0]],
    topology={0: {0: [0], 1: [1]}, 1: {0: [0, 1]}},
    name="ReferenceInterval",
)

#: A :class:`ReferenceCell` storing the geometry and topology of the triangle
#: with vertices [[0., 0.], [1., 0.], [0., 1.]].
ReferenceTriangle = ReferenceCell(
    vertices=[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]],
    topology={
        0: {0: [0], 1: [1], 2: [2]},
        1: {0: [1, 2], 1: [0, 2], 2: [0, 1]},
        2: {0: [0, 1, 2]},
    },
    name="ReferenceTriangle",
)