Abstract
We present a procedure for creating effective block Jacobi preconditioners for solving large sparse linear systems using Krylov subspace methods. Such preconditioners are constructed using two techniques. The first is a reordering scheme based on weighted graph partitioning which strengthens the block diagonal structure of the coefficient matrix while simultaneously accommodating load balancing on distributed memory architectures. The second technique is the factorization of the resulting diagonal blocks, or the factorization of slightly perturbed diagonal blocks to guard against possible singularity. Focusing on a set of linear systems arising in several computational fluid dynamics applications, we demonstrate the effectiveness of our enhanced block Jacobi preconditioners. Compared to a well-known sparse direct linear system solver, our parallel solver (block Jacobi preconditioned Krylov subspace method) proves to be equally robust and achieves appreciable speed improvements on a distributed memory parallel computing platform.
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Notes
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Note that a symmetric reordering preserves the maximum product traversal property.
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- 4.
Given the poor performance of ILUTP in Table 2 when ρ = 10−4, we did not include ILUTP for ρ = 10−10.
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Acknowledgements
This work was supported by the Army Research Office, ARO grant number 7W911NF-11-1-0401.
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Zhu, Y., Sameh, A.H. (2016). How to Generate Effective Block Jacobi Preconditioners for Solving Large Sparse Linear Systems. In: Bazilevs, Y., Takizawa, K. (eds) Advances in Computational Fluid-Structure Interaction and Flow Simulation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40827-9_18
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DOI: https://doi.org/10.1007/978-3-319-40827-9_18
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