[petsc-users] Direct solver for 3D-FEM

[Thomas Witkowski]

Could one of you explain me why direct solvers (I make use of UMFPACK) 
seems to work quite bad for 3D-FEM? For a small test case, I take a 
unite square/box and refine it globally (bisectioning of 
triangle/tetrahedrons). I solve a six order PDE  (that leads to 
symmetric but indefinite matrices) on it. In 2D the resulting system has 
49.923 rows with 808.199 non zeros, UMFPACK solves the system within 2.8 
seconds. For 3D I've refine the box such that the resulting matrix has 
more or less the same number of non zeros, in this case 898.807 on 
27.027 rows. UMFPACK needs 32 seconds to solve it, so more than 10 time 
as for the 2D case. Even if I make use of fourth order Lagrange 
functions for the 2D case, which leads to much denser matrices (49.923 
rows and 2.705.927 non zeros), UMFPACK solves it within 3.2 seconds. Is 
there any good reason for it?

Thomas