Parameter estimates for the Relaxed Dimensional Factorization preconditioner and application to hemodynamics

We present new results on the Relaxed Dimensional Factorization (RDF) preconditioner for solving saddle point problems from incompressible flow simulations, first introduced in Benzi et al. (2011). This method contains a parameter α > 0, to be chosen by the user. Previous works provided an estimate of α in the 2D case using Local Fourier Analysis. A novel algebraic estimation technique for finding a suitable value of the RDF parameter in both the 2D and the 3D case with arbitrary geometries is proposed. This technique is tested on a variety of discrete saddle point problems arising from the approximation of the Navier-Stokes equations using a Marker-and-Cell scheme and a finite element one. We also show results for a large-scale problem relevant for hemodynamics simulation that we solve in parallel using up to 8196 cores.