The Helmholtz-Hodge Decomposition (HHD) is a well-known technique used to decompose optical-flow vector fields into Divergence-free and Rotational-free fields. Such decomposition may be used to quantitatively assess the heart muscle profile in MRI images. The HHD is evaluated in image analysis in a discrete approach by applying the Finite Element Method resulting in an ill-conditioned linear system that can be solved by imposing zero-valued boundary conditions, which in turn induces significant errors in the solution given that the true value of the boundary conditions are not known. In this paper, the authors explore the use of iterative solvers based on Krylov Subspaces in order to avoid applying boundary conditions. With this approach, a mean squared error \(\varepsilon _{RMS} = 10^{-3}\) was obtained, while the mean squared error of the regular approach was \(\varepsilon _{RMS} = 10^{-1}\) .