  In this article, we present a parallel recursive algorithm based on
multi-level domain decomposition that can be used as a precondtioner to a
Krylov subspace method to solve sparse linear systems of equations arising from
the discretization of partial differential equations (PDEs). We tested the
effectiveness of the algorithm on several PDEs using different number of
sub-domains (ranging from 8 to 32768) and various problem sizes (ranging from
about 2000 to over a billion degrees of freedom). We report the results from
these tests; the results show that the algorithm scales very well with the
number of sub-domains.
