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

Giuseppe Pitton; Luca Heltai

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arXiv · 1807.09467

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

Giuseppe Pitton·Luca Heltai

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Abstract

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 GMRES. Many techniques bearing the name of \emph{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 non-linear convection-diffusion problems are promising for high-order methods.

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Giuseppe Pitton, Luca Heltai. 2018-07-25. Accelerating the iterative solution of convection-diffusion problems using singular value decomposition. https://arxiv.org/abs/1807.09467

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