Extend preflattening to non-ideal mixtures and PDE-derived nonlinear systems

Extend the preflattening approach, combined with nonlinear elimination and threshold-free bad-subset selection, to non-ideal chemical mixtures and to nonlinear systems arising from the discretization of partial differential equations.

Background

The paper introduces preflattening as a nonlinear analogue of preconditioning, using the flatness number or an upper bound of it to select changes of variables that make nonlinear algebraic systems more favorable for Newton's method. For ideal chemical-equilibrium systems, the authors combine this strategy with nonlinear elimination and the double above-average norms of columns rule for selecting variables to eliminate.

The reported numerical experiments are restricted to ideal mixtures and demonstrate substantial acceleration for the H₂O, NaCl, and Seawater test cases. The authors explicitly identify extension to non-ideal mixtures and to nonlinear systems generated by PDE discretizations as work not addressed in the paper.