v 2 v 0 = (0, 0)<strong>DOLFIN</strong> <strong>User</strong> <strong>Manual</strong>Hoffman, 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
<strong>DOLFIN</strong> <strong>User</strong> <strong>Manual</strong>Hoffman, 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
- Page 1 and 2:
DOLFIN User ManualFebruary 24, 2006
- Page 3 and 4:
ContentsAbout this manual 91 Introd
- Page 5 and 6:
DOLFIN User ManualHoffman, Jansson,
- Page 7:
DOLFIN User ManualHoffman, Jansson,
- Page 12 and 13:
DOLFIN User ManualHoffman, Jansson,
- Page 14 and 15:
DOLFIN User ManualHoffman, Jansson,
- Page 16 and 17:
DOLFIN User ManualHoffman, Jansson,
- Page 18 and 19:
DOLFIN User ManualHoffman, Jansson,
- Page 20 and 21:
DOLFIN User ManualHoffman, Jansson,
- Page 22 and 23:
DOLFIN User ManualHoffman, Jansson,
- Page 25 and 26:
Chapter 3Linear algebra◮ Develope
- Page 27 and 28:
DOLFIN User ManualHoffman, Jansson,
- Page 29 and 30:
Chapter 4The mesh◮ Developer’s
- Page 31 and 32:
DOLFIN User ManualHoffman, Jansson,
- Page 33 and 34:
Chapter 5Functions◮ Developer’s
- Page 35 and 36:
DOLFIN User ManualHoffman, Jansson,
- Page 37 and 38: DOLFIN User ManualHoffman, Jansson,
- Page 39 and 40: DOLFIN User ManualHoffman, Jansson,
- Page 41 and 42: DOLFIN User ManualHoffman, Jansson,
- Page 43: Chapter 6Ordinary differential equa
- Page 46 and 47: DOLFIN User ManualHoffman, Jansson,
- Page 48 and 49: DOLFIN User ManualHoffman, Jansson,
- Page 50 and 51: DOLFIN User ManualHoffman, Jansson,
- Page 53 and 54: Chapter 8Nonlinear solver◮ Develo
- Page 55: DOLFIN User ManualHoffman, Jansson,
- Page 58 and 59: DOLFIN User ManualHoffman, Jansson,
- Page 60 and 61: DOLFIN User ManualHoffman, Jansson,
- Page 62 and 63: DOLFIN User ManualHoffman, Jansson,
- Page 65 and 66: Chapter 10The log systemDOLFIN prov
- Page 67 and 68: DOLFIN User ManualHoffman, Jansson,
- Page 69 and 70: DOLFIN User ManualHoffman, Jansson,
- Page 71: DOLFIN User ManualHoffman, Jansson,
- Page 74 and 75: DOLFIN User ManualHoffman, Jansson,
- Page 76 and 77: DOLFIN User ManualHoffman, Jansson,
- Page 78 and 79: DOLFIN User ManualHoffman, Jansson,
- Page 80 and 81: DOLFIN User ManualHoffman, Jansson,
- Page 82 and 83: DOLFIN User ManualHoffman, Jansson,
- Page 85: Bibliography[1] Cygwin, 2005. http:
- Page 90 and 91: DOLFIN User ManualHoffman, Jansson,
- Page 92 and 93: DOLFIN User ManualHoffman, Jansson,
- Page 94 and 95: DOLFIN User ManualHoffman, Jansson,
- Page 96 and 97: DOLFIN User ManualHoffman, Jansson,
- Page 98 and 99: DOLFIN User ManualHoffman, Jansson,
- Page 100 and 101: DOLFIN User ManualHoffman, Jansson,
- Page 102 and 103: DOLFIN User ManualHoffman, Jansson,
- Page 105 and 106: Appendix CContributing codeIf you h
- Page 107 and 108: DOLFIN User ManualHoffman, Jansson,
- Page 109 and 110: Appendix DLicenseDOLFIN is licensed
- Page 111 and 112: DOLFIN User ManualHoffman, Jansson,
- Page 113 and 114: DOLFIN User ManualHoffman, Jansson,
- Page 115: DOLFIN User ManualHoffman, Jansson,
- Page 118: DOLFIN User ManualHoffman, Jansson,