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

2018/07/25 by Giuseppe Pitton, Pitton, Giuseppe, Luca Heltai +1
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1807.09467

openalex publication_date 2018/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The discretization of convection-diffusion equations by implicit or\nsemi-implicit methods leads to a sequence of linear systems usually solved by\niterative linear solvers such as GMRES. Many techniques bearing the name of\n\recycling Krylov space methods have been proposed to speed up the\nconvergence rate after restarting, usually based on the selection and retention\nof some Arnoldi vectors.\n After providing a unified framework for the description of a broad class of\nrecycling methods and preconditioners, we propose an alternative recycling\nstrategy based on a singular value decomposition selection of previous\nsolutions, and exploit this information in classical and new augmentation and\ndeflation methods. The numerical tests in scalar non-linear\nconvection-diffusion problems are promising for high-order methods.\n

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