Recently a variety of studies have shown the importance of including non-locality in the description of reactions. The goal of this work is to revisit the phenomenological approach to determining non-local optical potentials from elastic scattering. We perform a χ 2 analysis of neutron elastic scattering data off 40 Ca, 90 Zr and 208 Pb at energies E ≈ 5 − 40 MeV, assuming a Perey and Buck [1] or Tian, Pang, and Ma [2] non-local form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parameterization. Independently of the starting point in the minimization procedure, an energy dependence in the imaginary depth is required for a good description of the data across the included energy range. We present two parameterizations, both of which represent an improvement over the original potentials for the fitted nuclei as well as for other nuclei not included in our fit. Our results show that, even when including the standard Gaussian non-locality in optical potentials, a significant energy dependence is required to describe elastic-scattering data.

\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . We consider the numerical solution of discrete Oseen problems. We propose a new approach that consists of first applying a simple algebraic transformation to the linear system, which is afterwards preconditioned with an aggregation-based algebraic two-grid method. An algebraic analysis is provided, which proves uniform convergence in norm with respect to problem parameters if a few constants can be uniformly bounded. A further analysis of these constants shows that they can be bounded in the case of a constant convection field, provided that the coarsening of the pressure unknowns is also driven by the convection field. This makes the method essentially different from a similar method developed for Stokes equations which initially inspired the present work. Technically, this means that one has to either use point-based coarsening, or that an auxiliary convection-diffusion matrix has to be built on the pressure space to guide the coarsening, which makes the method only semialgebraic. Using this ingredient, promising results are obtained, showing that the number of iterations is, in practice, uniformly bounded with respect to both the mesh size and the Reynolds number even for challenging recirculating convection fields or in presence of outflow boundary conditions. \bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs . algebraic multigrid, linear systems, convergence analysis, Oseen, Navier--Stokes \bfM \bfS \bfC \bfc \bfo \bfd \bfe \bfs . 65N22, 65F10 \bfD \bfO \bfI .

We consider numerical solution of finite element discretizations of the Stokes problem. We focus on the transform-then-solve approach, which amounts to first apply a specific algebraic transformation to the linear system of equations arising from the discretization, and then solve the transformed system with an algebraic multigrid method. The approach has recently been applied to finite differences discretizations of the Stokes problem with constant viscosity, and has recommended itself as a robust and competitive solution method. In this work, we examine the extension of the approach to standard finite element discretizations of the Stokes problem, including problems with variable viscosity. The extension relies, on one hand, on the use of the successive over-relaxation method as a multigrid smoother for some finite element schemes. On the other hand, we present strategies that allow us to limit the complexity increase induced by the transformation. Numerical experiments show that our method is competitive compared to a state-of-the-art solver based on a block diagonal preconditioner and MINRES, and suggest that the transform-thensolve approach is also more robust. In particular, for problems with variable viscosity, the transform-then-solve approach demonstrates significant speed-up with respect to the block diagonal preconditioner.