Block ILP~(-1)U (0) Preconditioning for a GMRES based Euler/Navier-Stokes solver

摘要

Approximate factorisations such as the incomplete LP~(-1)U factorisation are notoriously sequential. We present the results of some experiments with a block-version of the ILP~(-1)U (0) factorisation preconditioning technique. Parallelisation of this Block ILP~(-1)U (0) factorisation preconditioner is straightforward: all blocks can be handled in parallel. Within the framework of an Euler/Navier-Stokes solver, we have studied the effect of introducing more blocks on the initial and the asymptotic convergence rate of a GMRES solver. The main result is that the introduction of more blocks does not lead to severe convergence degradation. Thus a high parallel efficiency can be achieved.