# Parallel Matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks

@article{Bergamaschi2022ParallelMP, title={Parallel Matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks}, author={Luca Bergamaschi and Massimiliano Ferronato and Giovanni Isotton and Carlo Janna and {\'A}ngeles Mart{\'i}nez}, journal={ArXiv}, year={2022}, volume={abs/2208.01339} }

. We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive deﬁnite linear systems.We discuss the selection of a scaling parameter aimed at avoiding unwanted clustering of eigenvalues of the preconditioned matrices at the extrema of the spectrum. We use this preconditioned framework to solve a 3 × 3 block system arising in the simulation of ﬂuid ﬂow in large-size discrete…

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