A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations
The authors present an algorithm of the restarted and preconditioned GMRES\((c)\) method with a restart \(c\). They describe the parallelisation of the GMRES\((c)\) and its implementation on distributed-memory architectures, using both networks of transputers and networks of workstations under the PVM message-passing system. The considered test systems of linear equations are derived from five-point finite difference approximations of convection-diffusion equations on the unit square. A theoretical model of the computation and communication phases is presented which allows us to describe for which values of the parameter \(c\) our implementation executes efficiently. The results show that for reasonably large discretisation grids the implementations are effective on a large number of processors.
five-point finite difference approximations
scientific article; zbMATH DE number 784496
scientific article