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Enhanced Block FSAI Preconditioning Using Domain Decomposition Techniques

Adaptive block factorized sparse approximate inverse (FSAI) (ABF) is a novel algebraic preconditioner for the cost-effective parallel solution of symmetric positive definite linear systems. However, a main drawback stems from its reduced scalability, as the iteration count to convergence tends to grow when the number of processors increases. A domain decomposition Schur complement approach can enhance both the ABF performance and scalability. It is demonstrated that the enhanced ABF preconditioner is superior to the native block FSAI, reducing at the same time the construction and communication computational burden. Numerical results from different large size applications show that the proposed algorithm can improve significantly the preconditioner, allowing for its efficient use in massively parallel simulations as well.