DOLFIN User Manual - FEniCS Project

More documents

Recommendations

Info

DOLFIN User ManualHoffman, Jansson, Logg, WellsA.3.4Alignment of edgesDepending on the orientation of any given cell, an edge on the cell may bealigned or not aligned with the corresponding edge on the reference cell if thevertices of the cell are mapped to the reference cell. We define the alignmentof an edge with respect to a cell to be 0 if the edge is aligned with theorientation of the reference cell and 1 otherwise.Example 1: The alignment of the first edge (e 0 ) on a triangle is 0 if thefirst vertex of the edge is the second vertex (v 1 ) of the triangle.Example 2: The alignment of the second edge (e 1 ) on a tetrahedron is 0 ifthe first vertex of the edge is the third vertex (v 2 ) of the tetrahedron.If two cells share a common edge and the edge is aligned with one of the cellsand not the other, we must reverse the order in which the local nodes aremapped to global nodes on one of the two cells. As a convention, the orderis kept if the alignment is 0 and reversed if the alignment is 1.A.3.5Internal ordering on facesFor faces containing more than one node, the ordering of nodes is nestedgoing from the first to the third vertex and in each step going from the firstto the second vertex as in Figure A.6.A.3.6Alignment of facesThere are six different ways for a face to be aligned on a tetrahedron; there arethree ways to pick the first edge of the face, and once the first edge is picked,there are two ways to pick the second edge. To define an alignment of faces asan integer between 0 and 5, we compare the ordering of edges on a face withthe ordering of edges on the corresponding face on the reference tetrahedron.If the first edge of the face matches the first edge on the corresponding faceon the reference tetrahedron and also the second edge matches the secondedge on the reference tetrahedron, then the alignment is 0. If only the first94
DOLFIN User ManualHoffman, Jansson, Logg, Wellsv 2 fPSfrag replacements53 40 1 2v 0 fv 1 fFigure A.6: Internal ordering of nodes on faces.95
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:
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 25 and 26:
Chapter 3Linear algebra◮ Develope
Page 27 and 28:
Page 29 and 30:
Chapter 4The mesh◮ Developer’s
Page 31 and 32:
Page 33 and 34:
Chapter 5Functions◮ Developer’s
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43: Chapter 6Ordinary differential equa
Page 46 and 47: DOLFIN User ManualHoffman, Jansson,
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 88 and 89: v 2 v 0 = (0, 0)DOLFIN User ManualH
Page 105 and 106: Appendix CContributing codeIf you h
Page 109 and 110: Appendix DLicenseDOLFIN is licensed
show all

DOLFIN User Manual - FEniCS Project

Create successful ePaper yourself

Delete template?

Save as template?