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Adaptive solution of linear systems of equations based on a posteriori error estimators

Ani Anciaux-Sedrakian 1 Laura Grigori 2 Zakariae Jorti 1, 2 Jan Papež 2 Soleiman Yousef 1
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : In this paper, we discuss a new adaptive approach for iterative solution of sparse linear systems arising from partial differential equations (PDEs) with self-adjoint operators. The idea is to use the a posteriori estimated local distribution of the algebraic error in order to steer and guide the solve process in such way that the algebraic error is reduced more efficiently in the consecutive iterations. We first explain the motivation behind the proposed procedure and show that it can be equivalently formulated as constructing a special combination of preconditioner and initial guess for the original system. We present several numerical experiments in order to identify when the adaptive procedure can be of practical use.
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Submitted on : Thursday, June 25, 2020 - 5:20:45 PM
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Ani Anciaux-Sedrakian, Laura Grigori, Zakariae Jorti, Jan Papež, Soleiman Yousef. Adaptive solution of linear systems of equations based on a posteriori error estimators. Numerical Algorithms, Springer Verlag, 2020, 84, pp.331-364. ⟨10.1007/s11075-019-00757-z⟩. ⟨hal-02425391⟩

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