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Accelerating the iterative solution of convection–diffusion problems using singular value decomposition
Author(s) -
Pitton G.,
Heltai L.
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2211
Subject(s) - mathematics , discretization , scalar (mathematics) , nonlinear system , singular value decomposition , convection–diffusion equation , rate of convergence , mathematical optimization , iterative method , generalized minimal residual method , convergence (economics) , linear system , krylov subspace , diffusion , initial value problem , algorithm , computer science , mathematical analysis , geometry , key (lock) , physics , computer security , quantum mechanics , economics , thermodynamics , economic growth
Summary The 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.