We introduce a new two-level preconditioner for the efficient solution of large scale linear systems arising from the finite element (FE) discretization of parametrized unsteady Navier-Stokes (NS) equations. The proposed preconditioner combines a reduced basis (RB) solver, which plays the role of coarse component, with a fine grid preconditioner, in our numerical experiments a SIMPLE preconditioner. The RB coarse component is iteration dependent and is built upon a new Multi Space Reduced Basis (MSRB) method, where a RB space is built through the proper orthogonal decomposition algorithm and is tailored to each step of the iterative method at hand. The resulting operator is used as preconditioner in the flexible GMRES method. The Krylov iterations employed to solve the resulting preconditioned system target small tolerances with a very small iteration count and in a very short time. We show in this poster how to address the well-posedness of the RB coarse components and the efficient construction of the resulting preconditioner by means of hyper-reduction techniques. Simulations are carried out to evaluate the performance of the proposed MSRB preconditioner in a large scale computational setting related to the NS equations in parametrized carotid bifurcations and compared to state of the art preconditioners.
|ScienceOpen disciplines:||Applied mathematics, Applications, Statistics, Data analysis, Mathematics, Mathematical modeling & Computation|
|Keywords:||High Performance Computing, Finite Element method, Reduced Basis method, Preconditioning techniques, Multi Space Reduced Basis, Computational Fluid Dynamics|