A class of asynchronous parallel multisplitting blockwise relaxation methods

Abstract

By the principle of using sufficiently the delayed information and based on the technique of successively accelerated overrelaxation (AOR), we set up a class of asynchronous multisplitting blockwise relaxation methods for solving the large sparse blocked system of linear equations, which comes from the discretizations of many differential equations. These new methods are efficient blockwise variants of the asynchronous parallel matrix multisplitting relaxed iterations discussed by Bai et al. (Parallel Computing 21 (1995) 565–582), and they are very smart for implementations on the MIMD multiprocessor systems. Under reasonable restrictions on the relaxation parameters as well as the multiple splittings, we establish the convergence theories of this class of new methods when the coefficient matrices of the blocked systems of linear equations are block H-matrices of different types. A lot of numerical experiments show that our new methods are applicable and efficient, and have better numerical behaviours than their pointwise alternatives investigated by Bai et al.