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Several ways to achieve robustness when solving wave propagation problems

Niall Bootland 1 Victorita Dolean 2, 1 Pierre Jolivet 3, 4 Frédéric Nataf 5 S. Operto 6 Pierre-Henri Tournier 5 
3 IRIT-APO - Algorithmes Parallèles et Optimisation
IRIT - Institut de recherche en informatique de Toulouse
5 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillatory nature of solutions, meaning that the number of degrees of freedom after discretisation increases drastically with the wave number, giving rise to large complex-valued problems to solve. Additional difficulties occur when the problem is defined in a highly heterogeneous medium, as is often the case in realistic physical applications. For time-discretised problems of Maxwell type, the main challenge remains the significant kernel in curl-conforming spaces, an issue that impacts on the design of robust preconditioners. This has already been addressed theoretically for a homogeneous medium but not yet in the presence of heterogeneities. In this review we provide a big-picture view of the main difficulties encountered when solving wave propagation problems, from the first step of their discretisation through to their parallel solution using two-level methods, by showing their limitations on a few realistic examples. We also propose a new preconditioner inspired by the idea of subspace decomposition, but based on spectral coarse spaces, for curl-conforming discretisations of Maxwell's equations in heterogeneous media.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03837294
Contributor : Frédéric Nataf Connect in order to contact the contributor
Submitted on : Thursday, November 3, 2022 - 10:04:45 AM
Last modification on : Thursday, November 17, 2022 - 9:42:49 AM

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Distributed under a Creative Commons Attribution 4.0 International License

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  • HAL Id : hal-03837294, version 1
  • ARXIV : 2103.06025

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Niall Bootland, Victorita Dolean, Pierre Jolivet, Frédéric Nataf, S. Operto, et al.. Several ways to achieve robustness when solving wave propagation problems. 2022. ⟨hal-03837294⟩

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