GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
ACM Transactions on Mathematical Software (TOMS)
Algebraic Two-Level Preconditioners for the Schur Complement Method
SIAM Journal on Scientific Computing
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
SchurRAS: A Restricted Version of the Overlapping Schur Complement Preconditioner
SIAM Journal on Scientific Computing
Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
Journal of Computational Physics
Optimized Multiplicative, Additive, and Restricted Additive Schwarz Preconditioning
SIAM Journal on Scientific Computing
Analysis of Patch Substructuring Methods
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
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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.