Computing the solution of linear systems of equations is invariably the most time consuming task in the numerical solutions of PDEs in many fields of computational science. In this study, we focus on the numerical simulation of cardiovascular hemodynamics with rigid and deformable walls, discretized in space and time through the variational multi-scale finite element method. We focus on three approaches: the problem agnostic generalized minimum residual (GMRES) and stabilized bi-conjugate gradie...