PARALLEL GMRES AND DOMAIN DECOMPOSITION
K. Dekker · Research Repository (Delft University of Technology) · 2000
Solution of large linear systems encountered in computational fluid dynamics often leads to some form of domain decomposition, especially when it is desired to use parallel machines.To solve such problems we introduce a partitioned modification of GMRES, which has the property of minimising the the norm of the residual vector over a Krylov subspace of larger dimension than the one in GMRES.We prove that the new method converges faster than GMRES, if the subdomain problems are solved exactly.Moreover, less communication is required in the computation of inner products in a modified Gram-Schmidt orthogonalisation process, which makes the method suitable for parallel computing.The additional computational work is negligible, as a resulting least squares can be solved efficiently using Givens rotations.Numerical experiments for two fundamental test problems show that the new method requires about 30% less iterations than GMRES.