UFL Specification and User Manual 0.3 - FEniCS Project

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2.3.1 Basis functions . . . . . . . . . . . . . . . . . . . . . . 242.3.2 Coefficient functions . . . . . . . . . . . . . . . . . . . 252.4 Basic Datatypes . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.1 Literals and geometric quantities . . . . . . . . . . . . 272.5 Indexing and tensor components . . . . . . . . . . . . . . . . . 292.5.1 Defining indices . . . . . . . . . . . . . . . . . . . . . . 302.5.2 Taking components of tensors . . . . . . . . . . . . . . 322.5.3 Making tensors from components . . . . . . . . . . . . 332.5.4 Implicit summation . . . . . . . . . . . . . . . . . . . . 342.6 Basic algebraic operators . . . . . . . . . . . . . . . . . . . . . 342.7 Basic nonlinear functions . . . . . . . . . . . . . . . . . . . . . 352.8 Tensor Algebra Operators . . . . . . . . . . . . . . . . . . . . 362.8.1 transpose . . . . . . . . . . . . . . . . . . . . . . . . . 362.8.2 tr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.8.3 dot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.8.4 inner . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.8.5 outer . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.8.6 cross . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.8.7 det . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.8.8 dev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.8.9 sym . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.8.10 skew . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.8.11 cofac . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.8.12 inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.9 Differential Operators . . . . . . . . . . . . . . . . . . . . . . . 422.9.1 Basic spatial derivatives . . . . . . . . . . . . . . . . . 422.9.2 Compound spatial derivatives . . . . . . . . . . . . . . 432.9.3 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . 432.9.4 Divergence . . . . . . . . . . . . . . . . . . . . . . . . . 442.9.5 Curl and rot . . . . . . . . . . . . . . . . . . . . . . . . 452.9.6 Variable derivatives . . . . . . . . . . . . . . . . . . . . 452.9.7 Functional derivatives . . . . . . . . . . . . . . . . . . 462.10 DG operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.10.1 Restriction: v(’+’) and v(’-’) . . . . . . . . . . . . . 472.10.2 Jump: jump(v) . . . . . . . . . . . . . . . . . . . . . . 472.10.3 Average: avg(v) . . . . . . . . . . . . . . . . . . . . . 482.11 Conditional Operators . . . . . . . . . . . . . . . . . . . . . . 482.11.1 Conditional . . . . . . . . . . . . . . . . . . . . . . . . 482.11.2 Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 492.12 User-defined operators . . . . . . . . . . . . . . . . . . . . . . 492.13 Form Transformations . . . . . . . . . . . . . . . . . . . . . . 502.13.1 Replacing arguments of a Form . . . . . . . . . . . . . 50
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Page 3: ContentsAbout this manual 111 Intro
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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