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The discretization of convection-diffusion equations by implicit orsemi-implicit methods leads to a sequence of linear systems usually solved byiterative linear solvers such as GMRES. Many techniques bearing the name of\emph{recycling Krylov space methods} have been proposed to speed up theconvergence rate after restarting, usually based on the selection and retentionof some Arnoldi vectors.  After providing a unified framework for the description of a broad class ofrecycling methods and preconditioners, we propose an alternative recyclingstrategy based on a singular value decomposition selection of previoussolutions, and exploit this information in classical and new augmentation anddeflation methods. The numerical tests in scalar non-linearconvection-diffusion problems are promising for high-order methods.

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