ulfy

This package translates UFL expressions to SymPy expressions which can then be compiled to instances of DOLFIN Expressions. A typical use case is when one wants to prepare a manufactured solution for their FEniCS solver.

from dolfin import *
from ulfy import Expression
import sympy as sp
x, y, z, t = sp.symbols('x y z t')
f = 3*x*y + x**2 + 2*y**2 + t**3
mesh = UnitSquareMesh(64, 64)
V = FunctionSpace(mesh, 'CG', 2)
v = Function(V)
e = v - 3*v**2 + v.dx(0)  # UFL
e = Expression(e, subs={v: f}, degree=4)  # to DOLFIN

Rationale

Assuming you started with SymPy you will most likely write some small ad-hoc vector calculus module to deal with grad, div, etc to get the desired right hand side. If you are like me you will end up writing such module for each solver and that is no fun. Alternatively, you can build the right hand side as an UFL expression, however, to use it with errornorm the expression needs to be projected (as UFL expressions cannot be interpolated) and this involves a solve of a linear system. Your third (and best ) option is to use ulfy and translate UFL expression, e.g. -div(grad(u)) (for the right hand side of Poisson problem) to the DOLFIN expression. Note that expressions such as u+u can be handled by DOLFIN; Expression('u+u', u=u, degree=1).

What works

At the moment ulfy supports most commonly used nodes in UFL, (see the here for examples). Nodes for ComponentTensor and IndexSum are only partially supported. More precisely, let
A=Costant(((1, 2), (3, 4))). Then as_matrix(A[i, j], [j, i]) will not work but A*A is fine. There is no support for FEM
specific nodes such as FacetNormal, jump, avg and so on.

Other alternatives

Expressions that represent UFL expressions (without substituting SymPy expressions for terminals) can compiled with
ufl-interpreter. This allows you to evaluate the UFL expressions which
DOLFIN uses (e.g. to assemble forms) in arbitrary point in the finite element mesh.

FEniCS compatibility

This package is CI tested against FEniCS packages for ubuntu 16.04 LTS