NULL SPACE ALGORITHM AND SPANNING TREES IN
SOLVING DARCY'S EQUATION
Mario Arioli 1 and Gianmarco Manzini 2
A Null Space algorithm is considered to solve the augmented system produced by the mixed
nite element approximation of Darcy's Law. The method is based on the combination
of a Gaussian factorisation technique for sparse matrices with an iterative Krylov solver.
The computational e∆ciency of the method relies on the use of spanning trees to compute
the Gaussian factorization without ll-in and on a suitable stopping criterion for the
iterative solver. We experimentally investigate its performance on a realistic set of selected
Keywords: Augmented systems, sparse matrices, mixed nite elements.
AMS(MOS) subject classications: 65F05, 65F10, 65F50.
Current reports available by anonymous ftp to ftp.numerical.rl.ac.uk in directory pub/reports.
1 M.Arioli@rl.ac.uk, Rutherford Appleton Laboratory,
2 Gianmarco.Manzini@ian.pv.cnr.it, IMATI - CNR, via Ferrata 1, 27100 Pavia, Italy
The work of second author was supported by EPSRC grant GR/R46427/01.
Computational Science and Engineering Department