Massively parallel preconditioners for the sparse conjugate gradient method

Abstract

We study the conjugate gradient method to solve large sparse linear systems with two ways of preconditioning: the polynomial and the ILU preconditionings. A parallel version is evaluated on the Connection Machine 2 (CM-2) with large sparse matrices. Results show that we must find a tradeoff between high performance (in terms of Mflops) and fast convergence. We first conclude that to find efficient methods on massively parallel computers, especially when irregular structures were used, parallelising usual algorithms is not always the most efficient way. Then, we introduce the new massively parallel hybrid polynomial-/ILUTmp(l, ε, d) preconditioning for distributed memory machines using a data parallel programming model.