An a posteriori-based adaptive preconditioner for controlling a local algebraic error norm

• Published in: BIT Vol. 61; no. 1; pp. 209 - 235
• Main Authors: Anciaux-Sedrakian, A., Grigori, L., Jorti, Z., Yousef, S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-03-2021; Springer Nature B.V; Springer Verlag
• Subjects: Adaptive systems; Algebra; Computational Mathematics and Numerical Analysis; Computer Science; Iterative methods; Iterative solution; Linear systems; Mathematics; Mathematics and Statistics; Numeric Computing; Partial differential equations; 65F10; Error’s growth rate; Fixed-point iteration; 65F08; 65N22; Adaptive preconditioner; Block partitioning
• ISSN: 0006-3835; 1572-9125
• DOI: 10.1007/s10543-020-00822-3

This paper introduces an adaptive preconditioner for iterative solution of sparse linear systems arising from partial differential equations with self-adjoint operators. This preconditioner allows to control the growth rate of a dominant part of the algebraic error within a fixed point iteration scheme. Several numerical results that illustrate the efficiency of this adaptive preconditioner with a PCG solver are presented and the preconditioner is also compared with a previous variant in the literature.