A two-level preconditioning framework based on a Richardson iterative process

Thomas Dufaud (1)

1 SAGE - Simulations and Algorithms on Grids for Environment

A fully algebraic framework for constructing coarse spaces for multilevel preconditioning techniques is proposed. An issue of multilevel techniques is their application to linear system encountered in industrial applications which can be derived from non-elliptic PDEs. Drawing our inspiration from the Aitken-SVD methodology, dedicated to Schwarz methods, we proposed to construct an approximation space by computing the Singular Value Decomposition of a set of iterated solutions of the Richardson process associated to a given preconditioner.

Domaines: Analyse numérique [math.NA]

Thomas Dufaud. A two-level preconditioning framework based on a Richardson iterative process. Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi and Olof Widlund. Domain Decomposition Methods in Science and Engineering XXI, 98, Springer, 2014, Lecture Notes in Computational Science and Engineering. ⟨hal-00907504⟩