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Local strategies for improving the conditioning of the plane-wave Ultra-Weak Variational Formulation

Abstract : Element-wise techniques based on SVD or QR Decomposition completely get rid of the usual ill-conditioning inherent to the plane-wave discretizations of the Ultra-Weak Variational Formulation (UWVF) for the Helmholtz equation. Associated preconditioning strategies lead to very low condition numbers of the corresponding linear system matrices, without any limitation on the number of plane waves per element. In addition, some of these procedures have the advantage of considerably reducing the size of the final system to be solved without altering the accuracy of the numerical solution.
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https://hal.inria.fr/hal-03235684
Contributor : Sébastien Tordeux Connect in order to contact the contributor
Submitted on : Tuesday, May 25, 2021 - 10:29:16 PM
Last modification on : Friday, May 13, 2022 - 7:40:32 PM
Long-term archiving on: : Thursday, August 26, 2021 - 8:58:51 PM

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Hélène Barucq, Abderrahmane Bendali, Julien Diaz, Sébastien Tordeux. Local strategies for improving the conditioning of the plane-wave Ultra-Weak Variational Formulation. Journal of Computational Physics, Elsevier, 2021, 441, pp.110449. ⟨10.1016/j.jcp.2021.110449⟩. ⟨hal-03235684⟩

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