An inexact Krylov subspace method for response calculations in density functional theory

Kohn-Sham density functional theory (DFT) is today the most popular electronic structure theory in quantum chemistry. In this framework, Density Functional Perturbation Theory (DFPT) is pivotal for computing various quantities that physically represent the response of the ground state density to external perturbations. The key building block of these response calculations is the computationally intensive task of solving the Dyson equation. It involves the iterative solution of a large linear system, wherein each iteration necessitates solving multiple smaller linear systems. In this thesis, we propose an inexact Krylov subspace method to dynamically adjust the tolerance of the inner iteration to accelerate the computation. We study the theoretical properties of the proposed method and show its effectiveness in numerical experiments. Our strategy can save up to 40% of the cost-dominating Hamiltonian applications without compromising the accuracy of the returned solution.