Source code for fe_utils.reference_elements

import numpy as np


[docs]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 `d`-entity. """ #: 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()])
[docs] def point_in_entity(self, x, e): """ Return true if the point x lies on the entity e. :param x: The coordinate vector of the point. :param e: The (d, i) pair describing the entity. """ vertices = self.topology[e[0]][e[1]] # Offset from first vertex. dx = np.subtract(x, self.vertices[vertices[0]]) # Project onto space spanned by remaining vertices. for v in vertices[1:]: dv = np.subtract(self.vertices[v], self.vertices[vertices[0]]) dx -= dv * np.dot(dx, dv) / np.dot(dv, dv) return (np.round(dx, 12) == 0).all()
def __repr__(self): return self.name
#: A :class:`ReferenceCell` storing the geometry and topology of the interval [0, 1]. ReferenceInterval = ReferenceCell(vertices=[[0.], [1.]], 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.], [1., 0.], [0., 1.]], 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")