## Non-stationary parallel multisplitting AOR methods.(English)Zbl 0858.65032

Authors’ abstract: Nonstationary parallel multisplitting iterative methods based on the accelerated overrelaxation (AOR) method are studied for the solution of nonsingular linear systems. Convergence of the synchronous and asynchronous versions of these methods is studied for $$H$$-matrices. Furthermore, computational results about these methods on both shared and distributed memory multiprocessors are discussed.
The numerical examples presented cover the nonstationary parallel multisplitting Gauss-Seidel and successive overrelaxation methods applied to the solution of the linear system yielded by a finite difference discretization of the two-dimensional Laplace equation on a rectangular domain under Dirichlet boundary conditions. These results show that non-stationary AOR-type methods (synchronous and asynchronous) are better than the corresponding standard parallel multisplitting AOR method. Moreover, asynchronous versions always behave better than the synchronous ones.
Reviewer: J.Zítko (Praha)

### MSC:

 65F10 Iterative numerical methods for linear systems 65Y05 Parallel numerical computation 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65N06 Finite difference methods for boundary value problems involving PDEs
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