Scalable Distributed Schur Complement Preconditioning for Real and Complex CFD Problems on Many-Core Architectures

Abstract

At the German Aerospace Center, the parallel simulation system TRACE (Turbo-machinery Research Aerodynamic Computational Environment) has been developed for the calculation of internal turbo-machinery flows. The finite volume approach requires the parallel, iterative solution of large, sparse real or complex systems of linear equations. For convergence acceleration of the iteration, scalable Distributed Schur Complement (DSC) preconditioners for real or complex matrix problems have been integrated into TRACE and replace the original block-local preconditioning methods. Numerical, performance and scalability results of DSC methods are presented for typical TRACE problems on many-core architectures together with an analysis of the pros and cons of the complex problem formulation. The DSC preconditioned iterative solvers for the complex problem formulation distinctly outperform the solvers for the real formulation. Reasons are that the complex formulation results in lower problem order, more advantageous matrix structure, has higher data locality and a better ratio of computation to memory access.