Adaptive preconditioners for nonlinear systems of equations (Q818192)

The authors propose an adaptive preconditioning technique, based on the Krylov method, for sequences of linear systems arising from systems of nonlinear equations. The preconditioners used here are guaranteed to shift eingenvalues to one, while preserving positivity, in case of positive-definite matrices. In particular, domain decomposition methods for nonlinear problems lend themselves to this adaptive technique. Numerical experiments drawn from domain decomposition techniques and fluid flow applications are used to validate the increased efficiency of proposed algorithm.