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Summary: RAL-TR-2002-026
NULL SPACE ALGORITHM AND SPANNING TREES IN
SOLVING DARCY'S EQUATION
Mario Arioli 1 and Gianmarco Manzini 2
ABSTRACT
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 eÆciency 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
application problems.
Keywords: Augmented systems, sparse matrices, mixed nite elements.
AMS(MOS) subject classi cations: 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
Atlas Centre
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