hello
I am estimating the optimal bandwidth for the FEM matrix over an NxNxN uniform grid. The band width is related to the numbering scheme.
My questions are:
- what is the optimal bandwidth for an NxNxN grid meshed by tetrahedron elements in terms of N?
- what's the numbering scheme corresponding to this optimal bandwidth?
- what's the asymptotic form of the optimal bandwidth w.r.t. N?
I have read some books on the BW reduction for FEM matrices, but they addressed to more general unstructual meshes. I just wondering whether there are simple analytical relation which has been discovered for this simple uniform grid?
Once I saw some discussion on the complexities of 3D FEM, I remember (if correctly) the asymptotic form for the complexity of solving the matrix equation by direct method is O(P^2) (P is the total num of unknown, in this case, P=N^3). If the matrix is solved by Cholesky decomp, the estimated bandwidth should be on the scale of sqrt(P)=N^(3/2), how can I get this bandwidth in this NxNxN grid?
references or hint would be appreciated.
thank you.
Qianqian