Abstract

We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently developed parallelization technique to avoid communication bottleneck for the computation associated to the internal boundary nodes. Numerical results are given for a transputer network with up to 512 processors and a few workstation cluster. keywords: iterative methods for linear systems, parallel computing, preconditioning. AMS classification : 65F10, 65B99, 65N20. 1 Introduction We present here a parallel solver for linear systems arising from the discretization of second order two or three dimensional elliptic PDEs of the type \Gamma@ x a x @ x u \Gamma @ y a y @ y u (\Gamma @ z a z @ z u) = f in\Omega u = f 1 on \Gamma 1 ae @\Omega @u @n = f 2 on \Gamma 2 = @\Omega n\Gamma 1 (1:...