DOLFIN User Manual - FEniCS Project

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v 2 v 0 = (0, 0)DOLFIN User ManualHoffman, Jansson, Logg, Wellsx 1PSfrag replacementsv 1 = (1, 0)v 2 = (0, 1)v 0 v 1x 0Figure A.1: Physical coordinates of the reference triangle.v 2 e 0PSfrag replacementse 1 e 2v 0 v 1Figure A.2: Ordering of mesh entities (vertices and edges) for the referencetriangle.88
DOLFIN User ManualHoffman, Jansson, Logg, WellsA.2 The reference tetrahedronThe reference tetrahedron (Figure A.3) is defined by the following four vertices:v 0 = (0, 0, 0),v 1 = (1, 0, 0),v 2 = (0, 1, 0),v 4 = (0, 0, 1).(A.3)The faces of the reference tetrahedron are ordered following the conventionthat face f i should be opposite to vertex v i for i = 0, 1, 2, 3, with the verticesof each face ordered to give a counter-clockwise orientation of each face asseen from the outside of the tetrahedron and the first vertex of face f i givenby vertex v i+1 mod 4 :f 0 : (v 1 , v 3 , v 2 ),f 1 : (v 2 , v 3 , v 0 ),f 2 : (v 3 , v 1 , v 0 ),f 3 : (v 0 , v 1 , v 2 ).(A.4)The edges of the reference tetrahedron are ordered following the conventionthat edges e 0 , e 1 , e 2 should correspond to the edges of the reference triangle.Edges e 3 , e 4 , e 5 all ending up at vertex v 3 are ordered based on their firstvertex:e 0 : (v 1 , v 2 ),e 1 : (v 2 , v 0 ),e 2 : (v 0 , v 1 ),e 3 : (v 0 , v 3 ),e 4 : (v 1 , v 3 ),e 5 : (v 2 , v 3 ).(A.5)The ordering of vertices on faces implicitly defines an ordering of edges on89
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DOLFIN User ManualFebruary 24, 2006
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ContentsAbout this manual 91 Introd
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DOLFIN User ManualHoffman, Jansson,
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Chapter 3Linear algebra◮ Develope
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Chapter 4The mesh◮ Developer’s
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Chapter 5Functions◮ Developer’s
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Page 37 and 38: DOLFIN User ManualHoffman, Jansson,
Page 43: Chapter 6Ordinary differential equa
Page 53 and 54: Chapter 8Nonlinear solver◮ Develo
Page 55: DOLFIN User ManualHoffman, Jansson,
Page 65 and 66: Chapter 10The log systemDOLFIN prov
Page 85: Bibliography[1] Cygwin, 2005. http:
Page 105 and 106: Appendix CContributing codeIf you h
Page 109 and 110: Appendix DLicenseDOLFIN is licensed
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DOLFIN User Manual - FEniCS Project

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