Distributed Schur complement solvers for real and complex block-structured CFD problems

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 with block-structured grids for solving the Navier-Stokes equations results in large, sparse real or complex systems of linear equations. For the parallel iterative solution of these equation systems, FGMRes with Distributed Schur Complement (DSC) preconditioning for real or complex matrix problems has been integrated into TRACE. The DSC preconditioner replaces the original block-local preconditioning methods in the simulation system. Numerical and performance 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.