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Cache-aware multilevel Schur-complement-based preconditioning

J. Hollander (2016) Cache-aware multilevel Schur-complement-based preconditioning. Bachelor's Thesis, Mathematics.

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Sparse matrices arising from the numerical solution of partial differential equations often exhibit a fine-grained block structure, meaning that the sparsity pattern may contain many dense, or nearly dense, small submatrices. Algorithms recognizing such dense structures can take advantage of the improved data-locality on modern cache-based computer architectures. In this thesis we overview blocking techniques for sparse matrices and we discuss how to exploit them, improving the performance of modern multilevel Schur-complement-based iterative solvers. We propose novel compression strategies for the Schur-complement that may lead to better numerical stability, and we test their implementation in the Variable Block Algebraic Recursive Multilevel Solver (VBARMS) [Carpentieri et al., 2014], which is a Schur-complement based multilevel incomplete LU factorization preconditioner. The performed numerical experiments support our theoretical findings.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:13
Last Modified: 15 Feb 2018 08:13

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