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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2024

Quasi-local and frequency robust preconditioners for the Helmholtz first-kind integral equations on the disk

Résumé

We propose preconditioners for the Helmholtz scattering problems by a planar, disk-shaped screen in $\R^3$. Those preconditioners are approximations of the square-roots of some partial differential operators acting on the screen. Their matrix-vector products involve only a few sparse system resolutions and can thus be evaluated cheaply in the context of iterative methods. For the Laplace equation (i.e. for the wavenumber $k=0$) with Dirichlet condition on the disk and on regular meshes, we prove that the preconditioned linear system has a bounded condition number uniformly in the mesh size. We further provide numerical evidence indicating that the preconditioners also perform well for large values of $k$ and on locally refined meshes.
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Dates et versions

hal-04450758 , version 1 (24-04-2024)

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François Alouges, Martin Averseng. Quasi-local and frequency robust preconditioners for the Helmholtz first-kind integral equations on the disk. ESAIM: Mathematical Modelling and Numerical Analysis, 2024, 58 (2), pp.793-831. ⟨10.1051/m2an/2023105⟩. ⟨hal-04450758⟩
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