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Article Dans Une Revue Journal of Computational Physics Année : 2021

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

Résumé

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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hal-03235684 , version 1 (25-05-2021)

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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, 2021, 441, pp.110449. ⟨10.1016/j.jcp.2021.110449⟩. ⟨hal-03235684⟩
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