Parallel solution of large sparse SPD linear systems based on overlapping domain decomposition

Abstract

We present a parallel iterative solver for large sparse symmetric positive definite (SPD) linear systems based on a new theory describing the convergence ofthe Preconditioned Conjugate Gradient (PCG) method and a proper combination ofa dvanced preconditioning strategies. Formally, the preconditioning can be interpreted as a special (nearly optimum from the viewpoint of the new PCG theory) version of overlapping domain decomposition with incomplete Cholesky solutions over subdomains. The estimates ofpa rallel efficiency are given as well as the results ofn umerical experiments for the serial and parallel versions oft he solver.