def __init__(self, mesh, element, continuity="C0"):
if isinstance(element, HermiteElement):
self.dofmap = HermiteDofMap(mesh, element)
elif isinstance(element, LagrangeElement):
assert continuity
if continuity == "L2":
self.dofmap = DGDofMap(mesh, element)
else:
self.dofmap = CGDofMap(mesh, element)
self.element = element
self.mesh = mesh
self.dim = len(set(sum((dofs for dofs in self.dofmap.dofmap.values()), [])))
class FunctionSpace(object):
"""Finite element function space ever mesh."""
def __init__(self, mesh, element, continuity="C0"):
if isinstance(element, HermiteElement):
self.dofmap = HermiteDofMap(mesh, element)
elif isinstance(element, LagrangeElement):
assert continuity
if continuity == "L2":
self.dofmap = DGDofMap(mesh, element)
else:
self.dofmap = CGDofMap(mesh, element)
self.element = element
self.mesh = mesh
self.dim = len(set(sum((dofs for dofs in self.dofmap.dofmap.values()), [])))
def interpolate(self, f):
"""Interpolate f to V creating a new function."""
vector = np.zeros(self.dim)
# Fill the vector L_global(f)
for cell in Cells(self.mesh):
global_dofs = self.dofmap.cell_dofs(cell.index)
dof_values = self.element.eval_dofs(f, cell)
vector[global_dofs] = dof_values
# Now make the function
return Function(self, vector)
@property
def vertex_to_dof_map(self):
"""Item i of this map is the dof index of dof at vertex i."""
return self.dofmap._vertex_to_dofmap
from dofmap import CGDofMap, DGDofMap, HermiteDofMap
from function_space import FunctionSpace
from lagrange_element import LagrangeElement
from hermite_element import HermiteElement
import numpy as np
# CG ---------
# Element
x = Symbol('x')
poly_set = [S(1), x, x**2, x**3]
dof_set = np.array([-1, -0.5, 0.5, 1])
element = LagrangeElement(poly_set, dof_set)
# Mesh
mesh = IntervalMesh(a=-1, b=1, n_cells=2)
# Dofmap
dofmap = CGDofMap(mesh, element)
assert dofmap.dofmap[0] == [0, 1, 2, 3]
assert dofmap.dofmap[1] == [1, 4, 5, 6]
# Space
V = FunctionSpace(mesh, element)
assert V.dim == 7
assert dofmap.tabulate_facet_dofs(1) == [1]
# Interpolation
mesh = IntervalMesh(a=-1, b=1, n_cells=10)
V = FunctionSpace(mesh, element)
# Function: expr
x = Symbol('x')
f = Expression(x)
f = V.interpolate(f)
# As pure function
g = V.interpolate(f)
