Efficient parallel implementation of the fully algebraic multiplicative Aitken-RAS preconditioning technique

This paper details the software implementation of the ARAS preconditioning technique (Dufaud T, Tromeur-Dervout D. Aitken’s acceleration of the Restricted Additive Schwarz preconditioning using coarse approximations on the interface. CR Math Acad Sci Paris 2010;348(13–14):821–4), in the PETSc framework. Especially, the PETSc implementation of interface operators involved in ARAS and the introduction of a two level of parallelism in PETSc for the RAS are described. The numerical and parallel implementation performances are studied on academic and industrial problems, and compared with the RAS preconditioning. For saving computational time on industrial problems, the Aitken’s acceleration operator is approximated from the singular values decomposition technique of the RAS iterate solutions.