UFL Specification and User Manual 0.3 - FEniCS Project

More documents

Recommendations

Info

2.13.2 Action of a form on a function . . . . . . . . . . . . . . 502.13.3 Energy norm of a bilinear Form . . . . . . . . . . . . . 512.13.4 Adjoint of a bilinear Form . . . . . . . . . . . . . . . . 522.13.5 Linear and bilinear parts of a Form . . . . . . . . . . . 522.13.6 Automatic Functional Differentiation . . . . . . . . . . 532.13.7 Combining form transformations . . . . . . . . . . . . 572.14 Tuple Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 582.15 Form Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 Example Forms 613.1 The mass matrix . . . . . . . . . . . . . . . . . . . . . . . . . 613.2 Poisson’s equation . . . . . . . . . . . . . . . . . . . . . . . . 623.3 Vector-valued Poisson . . . . . . . . . . . . . . . . . . . . . . . 633.4 The strain-strain term of linear elasticity . . . . . . . . . . . . 643.5 The nonlinear term of Navier–Stokes . . . . . . . . . . . . . . 653.6 The heat equation . . . . . . . . . . . . . . . . . . . . . . . . 663.7 Mixed formulation of Stokes . . . . . . . . . . . . . . . . . . . 673.8 Mixed formulation of Poisson . . . . . . . . . . . . . . . . . . 683.9 Poisson’s equation with DG elements . . . . . . . . . . . . . . 693.10 Quadrature elements . . . . . . . . . . . . . . . . . . . . . . . 703.11 More Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 Internal Representation Details 754.1 Structure of a Form . . . . . . . . . . . . . . . . . . . . . . . . 754.2 General properties of expressions . . . . . . . . . . . . . . . . 764.2.1 operands . . . . . . . . . . . . . . . . . . . . . . . . . 764.2.2 reconstruct . . . . . . . . . . . . . . . . . . . . . . . 764.2.3 cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2.4 shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2.5 free indices . . . . . . . . . . . . . . . . . . . . . . . 774.2.6 index dimensions . . . . . . . . . . . . . . . . . . . . 774.2.7 str(u) . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2.8 repr(u) . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2.9 hash(u) . . . . . . . . . . . . . . . . . . . . . . . . . . 784.2.10 u == v . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.2.11 About other relational operators . . . . . . . . . . . . . 784.3 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4 Terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.5 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.6 Extending UFL . . . . . . . . . . . . . . . . . . . . . . . . . . 795 Algorithms 815.1 Formatting expressions . . . . . . . . . . . . . . . . . . . . . . 81
Page 1 and 2: UFL Specification and User Manual 0
Page 3 and 4: ContentsAbout this manual 111 Intro
Page 5: 2.8.10 skew . . . . . . . . . . . .
Page 9: B Installation 97B.1 Installing fro
Page 56 and 57:
UFL Specification and User Manual 0
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 93:
Bibliography[1] M. Alnæs and K.-A.
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118:
show all

UFL Specification and User Manual 0.3 - FEniCS Project

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?