On Mon, Jul 13, 2009 at 12:11 PM, <alejandro.marti...@utoronto.ca> wrote: > Hi John: > I'm currently working on a problem that might be implemented with libMesh. > It requires a change of variables from global to local coordinates. The > nodes have to be inputed in the mapping equation in a certain order so that > the jacobian is not negative. > Can you recommend a reference that explains why this is tha case?
Sure, I usually think of this in terms of cross products. Wikipedia explains this well for the (positive) area of a 2D parallelogram. http://en.wikipedia.org/wiki/Cross_product#Geometric_meaning The area is defined to be positive according to the usual "right-hand rule" convention. The 2D elements in LibMesh follow this convention. Also, any finite element book which is in print today should explain it. > The numbering is based on convention and is dependent on the library. > Do you know what convention libMesh uses for this? Generally counter-clockwise node numbering for 2D elements. All the element's numbering schemes can be seen in their respective header files, e.g. include/geom/face_tri3.h. > Do you have any paper about libMesh that adresses this issue? There is a libmesh paper, but it doesn't really address these issues. Other than the libmesh-users mailing list (where I copied this message) you should also check out an introductory FEM text. -- John ------------------------------------------------------------------------------ Enter the BlackBerry Developer Challenge This is your chance to win up to $100,000 in prizes! For a limited time, vendors submitting new applications to BlackBerry App World(TM) will have the opportunity to enter the BlackBerry Developer Challenge. See full prize details at: http://p.sf.net/sfu/Challenge _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
