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Adaptive Block FSAI (ABF) is a novel preconditioner which has proved efficient for the parallel solution of symmetric positive definite (SPD) linear systems and eigenproblems. A possible drawback stems from its reduced strong scalability, as the iteration count to converge for a given problem tends to grow with the number of processors used. The preliminary use of graph partitioning techniques can help improve the preconditioner quality and scalability. According to the specific theoretical properties of Block FSAI, different partitionings are selected and tested in a set of matrices arising from SPD engineering applications. The results show that using an appropriate graph partitioning technique with ABF may play an important role to increase the preconditioner efficiency and robustness, allowing for its effective use also in massively parallel simulations. [ABSTRACT FROM AUTHOR]

Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward because of their inherent sequentiality. The present paper describes a novel parallel inexact constraint preconditioner (ParICP) for the efficient solution of linear algebraic systems arising from the FE discretization of the coupled poro-elasticity equations. The ParICP implementation is based on the use of the block factorized sparse approximate inverse incomplete Cholesky preconditioner, which is a very recent and effective development for the parallel preconditioning of symmetric positive definite matrices. The ParICP performance is experimented with in real 3D coupled consolidation problems, proving a scalable and efficient implementation of the constraint preconditioning for high-performance computing. ParICP appears to be a very robust algorithm for solving ill-conditioned large-size coupled models in a parallel computing environment. [ABSTRACT FROM AUTHOR]