We present a parallel iterative solver for discrete second order ellip
tic PDEs. It is based on the conjugate gradient algorithm with incompl
ete factorization preconditioning, using a domain decomposed ordering
to allow parallelism in the triangular solves, and resorting to some s
pecial recently developed parallelization technique to avoid communica
tion bottle-neck for the computation associated to the internal bounda
ry nodes. Numerical results are given for a transputer network with up
to 512 processors and a few workstation cluster.