Accelerating the iterative solution of convection–diffusion problems using singular value decomposition

Abstract

SummaryThe discretization of convection–diffusion equations by implicit or semi‐implicit methods leads to a sequence of linear systems usually solved by iterative linear solvers such as the generalized minimal residual method. Many techniques bearing the name of recycling Krylov space methods have been proposed to speed up the convergence rate after restarting, usually based on the selection and retention of some Arnoldi vectors. After providing a unified framework for the description of a broad class of recycling methods and preconditioners, we propose an alternative recycling strategy based on a singular value decomposition selection of previous solutions and exploit this information in classical and new augmentation and deflation methods. The numerical tests in scalar nonlinear convection–diffusion problems are promising for high‐order methods.