UFL Specification and User Manual 0.3 - FEniCS Project

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UFL Specification and User Manual 0.3Martin S. Alnæs, Anders LoggChapter 5 explains many algorithms to work with UFL expressions, mostlyintended to aid developers of form compilers. The algorithms available includeshelper functions for easy and efficient iteration over expression trees,formatting tools to present expressions as text or images of different kinds,utilities to analyse properties of expressions or checking their validity, automaticdifferentiation algorithms, as well as algorithms to work with thecomputational graphs of expressions.14
Chapter 2Form LanguageUFL consists of a set of operators and atomic expressions that can be usedto express variational forms and functionals. Below we will define all theseoperators and atomic expressions in detail.UFLisbuiltontopof, orembeddedin, thehighlevellanguagePython. Sincethe form language is built on top of Python, any Python code is valid in thedefinition of a form (but not all Python code defines a multilinear form).In particular, comments (lines starting with #) and functions (keyword def,see section 2.12 below) are useful in the definition of a form. However, itis usually a good idea to avoid using advanced Python features in the formdefinition, to stay close to the mathematical notation.The entire form language can be imported in Python with the linefrom ufl import *whichisassumedinallexamplesbelowandcanbeomittedin.uflfiles. Thiscan be useful for experimenting with the language in an interactive Pythoninterpreter.15
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Page 3 and 4: ContentsAbout this manual 111 Intro
Page 5 and 6: 2.8.10 skew . . . . . . . . . . . .
Page 7 and 8: 4 Internal Representation Details 7
Page 9: B Installation 97B.1 Installing fro
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Bibliography[1] M. Alnæs and K.-A.
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