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SolverGMRES: Implement classical Gram-Schmidt with delayed reorthogonalization #16749

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Mar 19, 2024
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SolverGMRES: Implement classical Gram-Schmidt with delayed reorthogonalization #16749

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SolverGMRES: Implement classical Gram-Schmidt with delayed reorthogon…
kronbichler Mar 13, 2024
4e9130b
New test cases
kronbichler Mar 13, 2024
d4b8132
Clean up orthogonalization process by separate class
kronbichler Mar 14, 2024
16f9a00
Fix unnecessary allreduce
kronbichler Mar 15, 2024
b54285f
Change variable name 'dim' -> 'n'
kronbichler Mar 19, 2024
2fad716
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kronbichler Mar 19, 2024
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15 changes: 14 additions & 1 deletion doc/doxygen/references.bib
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Expand Up @@ -2391,4 +2391,17 @@ @article{Shephard1984
author = {Mark S. Shephard},
title = {Linear multipoint constraints applied via transformation as part of a direct stiffness assembly process},
journal = {International Journal for Numerical Methods in Engineering}
}
}

@article{Bielich2022,
title = {Low-synch {G}ram--{S}chmidt with delayed reorthogonalization for {K}rylov solvers},
volume = {112},
url = {https://doi.org/10.1016/j.parco.2022.102940},
DOI = {10.1016/j.parco.2022.102940},
journal = {Parallel Computing},
publisher = {Elsevier},
author = {Bielich, Daniel and Langou, Julien and Thomas, Stephen and Świrydowicz, Kasia and Yamazaki, Ichitaro and Boman, Erik G.},
year = {2022},
pages = {102940}
}

16 changes: 15 additions & 1 deletion include/deal.II/lac/orthogonalization.h
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Expand Up @@ -39,7 +39,21 @@ namespace LinearAlgebra
* is less stable in terms of roundoff error propagation, requiring
* additional re-orthogonalization steps more frequently.
*/
classical_gram_schmidt
classical_gram_schmidt,
/**
* Use classical Gram-Schmidt algorithm with two orthogonalization
* iterations and delayed orthogonalization using the algorithm described
* in @cite Bielich2022. This approach works on multi-vectors with a
* single global reduction (of multiple elements) and is more efficient
* than the modified Gram-Schmidt algorithm. At the same time, it
* unconditionally performs the second orthogonalization step, making it
* more stable than the classical Gram-Schmidt variant. For deal.II's own
* vectors, there is no additional cost compared to the classical
* Gram-Schmidt algorithm, because the second orthogonalization step is
* done on cached data. For these beneficial reasons, this is the default
* algorithm in the SolverGMRES class.
*/
delayed_classical_gram_schmidt
};
} // namespace LinearAlgebra

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