UFL Specification and User Manual 0.3 - FEniCS Project

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UFL Specification and User Manual 0.3Martin S. Alnæs, Anders LoggEnumeration and list indicesThroughout this manual, elements x i of sets {x i } of size n are enumeratedfrom i = 0 to i = n − 1. Derivatives in R n are enumerated similarly:∂ ∂ ∂∂x 0,∂x 1,...,∂x n−1.ContactComments, corrections and contributions to this manual are most welcomeand should be sent toufl-dev@fenics.org12
Chapter 1IntroductionThe Unified Form Language (UFL) is a domain specific language for definingdiscrete variational forms and functionals in a notation close to pen-andpaperformulation.UFL [2] is part of the FEniCS project [4], and is usually used in combinationwith other components from this project to compute solutions to partialdifferential equations. The form compilers FFC [6] and SFC [1] use UFL astheir end-user interface, producing implementations of the UFC [3] interfaceas their output. See the DOLFIN manual [5] for more details about usingUFL in an integrated problem solving environment.This manual is intended for different audiences. If you are an end user and allyouwanttodoistosolveyourPDEswiththeFEniCSframework, Chapters2and 3 are for you. These two chapters explain how to use all operatorsavailable in the language and present a number of examples to illustrate theuse of the form language in applications. The rest of the chapters containmore technical details intended for developers who need to understand whatis happening behind the scenes and modify or extend UFL in the future.Chapter 4 details the implementation of the language, in particular how expressionsare represented internally by UFL. This can also be useful knowledgeto understand error messages and debug errors in your form files.13
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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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UFL Specification and User Manual 0.3 - FEniCS Project

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