3 ms·
As far as I know the reason why square lattices are preferred over hex lattices is that they can easily generalized to 3D, ... . If you invest lots of time thin
by wolfgke 12y ago
As far as I know the reason why square lattices are preferred over hex lattices is that they can easily generalized to 3D, ... . If you invest lots of time thinking about good, say, FEM or Finite Volume algorithms, you want to have results that can easily generalized afterwards.
- theoh 12y agoActually there is a simple 3D analog of the hexagonal grid, which occurs in crystal structures. Somewhat interestingly there are two variants, known in crystallography as Face-Centred Cubic and Hexagonal Close Packing. http://en.m.wikipedia.org/wiki/Close-packing_of_equal_spheres http://en.m.wikipedia.org/wiki/Close-packing_of_equal_sphere... In higher dimensions there are applications to broadband coding (you want the densest possible constellation). http://mathworld.wolfram.com/HyperspherePacking.html http://mathworld.wolfram.com/HyperspherePacking.html
- theoh 12y agoThough perhaps more relevant to FEM is the tetrahedral mesh...
- wolfgke 12y agoBoth types are important. The math is indeed more complicated for square meshes, but you can use the fact that the basis functions (is this the proper English translation of the German "Basisfunktionen"?) on square elements have more degrees of freedom to sometimes get better approximations. Disclosure: I heard some advanced lectures about FEM intended for students who intended to write a diploma thesis about this topic.