Parallel Segregated Schur Complement Methods for Fluid Density Functional Theories

Numerical formulations of density functional theories for inhomogeneous fluids (Fluid-DFTs) require the solution of large systems of equations with many degrees of freedom (DOFs) per node on a computational grid. Historically solvers for these problems have used simple Picard iterations across DOFs or, more recently, fully-coupled general algebraic techniques. In this paper we look at Fluid-DFTs from a fresh perspective, retaining a fully-coupled formulation but segregating variables for the purpose of introducing Schur complement formulations and specialized preconditioners. By viewing Fluid-DFTs from this perspective, we develop a mathematical framework and a collection of solution algorithms that have a dramatic impact on the robustness, performance and scalability of the implicit equations generated by Fluid-DFTs.