Tutorial#
Here I use the example CR CR_P_Laplacian.
from crikit.cr.ufl import CR_P_Laplacian
from fenics import *
mesh = UnitSquareMesh(4,4)
V = FunctionSpace(mesh, 'P', 1)
u = Function(V)
cr = CR_P_Laplacian(Constant(2))
This CR is made to take a scalar function and its gradient as input, so we can run it like so:
input_point = (u, grad(u))
output_point = cr(input_point)
The source and target properties track the source and target Spaces of the point map.
assert cr.source.is_point(input_point)
assert cr.target.is_point(output_point)
Since this is a UFL CR, it can directly be used in a UFL form.
v = TestFunction(V)
F = (dot(output_point, grad(v)) - v)*dx
u = solve(F == 0, u, DirichletBC(V, Constant(0), lambda x, on_boundary: on_boundary))
Wrapping it all together into one code block:
from crikit.cr.ufl import CR_P_Laplacian
from fenics import *
mesh = UnitSquareMesh(4,4)
V = FunctionSpace(mesh, 'P', 1)
u = Function(V)
cr = CR_P_Laplacian(Constant(2))
input_point = (u, grad(u))
output_point = cr(input_point)
v = TestFunction(V)
F = (dot(output_point, grad(v)) - v)*dx
u = solve(F == 0, u, DirichletBC(V, Constant(0), lambda x, on_boundary: on_boundary))