This module provides a simple lazy evaluator of algebraic expressions over FEniCS functions. Expressions are defined in the UFL language. They can be evaluated provided that the function spaces of each Function type arguments are of the tensor product form V x V ... x V. The expression then results in a Function in some appropriate tensor product space with V. In general coefficients of the function for expression (op u v) are computed as (op U V) where U, V are coefficient vectors of the arguments. This approach means that the result is exact iff op is linear; otherwise there is an interpolation error.

from dolfin import *
from xcalc import Eval

mesh = UnitSquareMesh(5, 5)
T = TensorFunctionSpace(mesh, 'CG', 1)

A = interpolate(Expression((('x[0]', 'x[1]'),
                                    ('2*x[0]+x[1]', 'x[0]+3*x[1]')), degree=1), T)
expr = tr(sym(A) + skew(A))
me = Eval(expr)  # Function in VectorFunctionSpace(mesh, 'CG', 1)
                 # Exact due to linearity

Functions can be grouped into TempSeries (avoiding name collision with FEniCS's native TimeSeries). Same algebraic operations over these objects are supported as with normal functions with the exception of __getitem__ which is now understood as accessing the individual functions in the series. TempSeries are collapsed into functions by time-averaging operations such as mean

from dolfin import *
from xcalc.tempseries import PVDTempSeries
from xcalc.operators import Mean

# Let there be a time series stored in pvd of function in V
mesh = UnitSquareMesh(3, 3)
V = FunctionSpace(mesh, 'CG', 1)
series = PVDTempSeries('pvd_test.pvd', V)

mean = Mean(series)  # Not a lazy node!

At the moment the interpreter supports most commonly used nodes in UFL except for

• differentiation nodes, e.g. grad (hence algebraic expressions)
• FEM specific nodes such as FacetNormal, jump, avg and so on
• nodes for ComponentTensor, IndexSum are only partially supported.

Currently MPI support is missing.

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

In addition to FEniCS stack h5py is needed if one wants to use XDMFTempSeries. After that, python setup.py install --user (or variants) is how to install this module.

1. This code is only compatible with fenics 2017.1.0 (maybe 2017.2.0 is OK, not sure)

• docker pull quay.io/fenicsproject/stable:2017.1.0
• docker run -ti -v $(pwd):/home/fenics/shared --name fenics_postprocess quay.io/fenicsproject/stable:2017.1.0
• exit
• docker start fenics_postprocess
• docker exec -ti fenics_postprocess /bin/bash -l (go into root mode to install packages)
• cd local/

2. Using pip install --no-binary=h5py h5py to install h5py. Otherwise it will fail.
3. For DMD analysis, do as following:

• pip install numpy scipy matplotlib future sphinx nose

• apt-get update

• apt-get install python-tk

  Then follow the instruction here.

Note: do step 2 and 3 in root mode. Possible problems see here.