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MiroK / fenics-calc

Calculator over FEniCS functions
MIT License
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fenics

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fenics-calc

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. 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(abs(series))  # A lazy node!

What works and what does not

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

Limitations

In order for Eval to be successfull operations on the dofs must translate nicely to numpy. Among other things this means that the spaces where the expression terminals are defined must be collapseable to scalars (in order to access components). This rules out vector-valued elements such as Raviart-Thomas

from dolfin import *
from xcalc import Eval

mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, 'RT', 1)

x = Function(V)
y = Function(V)

 Eval(inner(x, y))  # Fails - what is the scalar space here?
 Eval(as_vector((x[0], y[1])))  # Fails - same reason
 Eval(2*x + y)  # Fails - handled internally as 2*as_vector((x[0], x[1])) + y
 Eval(dot(outer(x, y), x))  # Fails - numpy eval of the mat is array of length 2
                            #         numpy eval of the vec is single number
                            #         numpy op produces array of 2 where 1 is expected

FEniCS compatibility

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

Dependencies and installation

In addition to FEniCS stack h5py is needed if one wants to use XDMFTempSeries. Dynamic mode decomposition of series relies on PyDMD module. After that, python setup.py install --user (or variants) is how to install this module.