UFL Specification and User Manual 0.3 - FEniCS Project

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UFL Specification and User Manual 0.3Martin S. Alnæs, Anders Logg5.3.1 Forward modeTODO: forward ad.py5.3.2 Reverse modeTODO: reverse ad.py5.3.3 Mixed derivativesTODO: ad.py5.4 Computational graphsThis section is for form compiler developers and is probably of no interest toend-users.An expression tree can be seen as a directed acyclic graph (DAG). To aidin the implementation of form compilers, UFL includes tools to build a linearized1 computational graph from the abstract expression tree.A graph can be partitioned into subgraphs based on dependencies of subexpressions,such that a quadrature based compiler can easily place subexpressionsinside the right sets of loops.5.4.1 The computational graphTODO: finish graph.py1 Linearized as in a linear datastructure, do not confuse this with automatic differentiation.88
UFL Specification and User Manual 0.3Martin S. Alnæs, Anders LoggTODOConsider the expressionf = (a+b)∗(c+d) (5.1)where a, b, c, d are arbitrary scalar expressions. The expression tree for flooks like this:TODO: Make figures.a b c d\ / \ /+ +\ /*In UFL f is represented like this expression tree. If a,b,c,d are all distinctFunction instances, the UFL representation will look like this:Function Function Function Function\ / \ /Sum Sum\ /ProductIf we instead have the expressionf = (a+b)∗(a−b) (5.2)the tree will in fact look like this, with the functions a and b only representedonce:Function Function89
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UFL Specification and User Manual 0
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ContentsAbout this manual 111 Intro
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2.8.10 skew . . . . . . . . . . . .
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4 Internal Representation Details 7
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B Installation 97B.1 Installing fro
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Page 93: Bibliography[1] M. Alnæs and K.-A.
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UFL Specification and User Manual 0.3 - FEniCS Project

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