Preconditioning techniques for almost symmetric operator equations in Newton-NEPv

 

This talk aims at presenting different techniques to accelerate the convergence of Krylov subspace solvers for the correction equation in Newton’s method for nonlinear eigenvector problems (NEPv). While this operator equation is generally unsymmetric, its structure allows a splitting into symmetric and nonsymmetric parts which can be used to derive efficient direct and iterative preconditioners. We will show how to obtain that splitting of the update equation, discuss a selection of preconditioning techniques present in the literature and adapt them to the particular problem. Some numerical comparisons on a discrete Kohn-Sham example complete the talk.