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Persistent URL http://purl.org/net/epubs/work/63164449
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Record Id 63164449
Title Multipreconditioning with directional sweeping methods for high-frequency Helmholtz problems
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Abstract We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present challenging sparse linear systems which are complex non-Hermitian and, due to the pollution effect, either very large or else still large but under-resolved in terms of the physics. These factors make finding general purpose, efficient and scalable solvers difficult and no one approach has become the clear method of choice. In this work we take inspiration from domain decomposition strategies known as sweeping methods, which have gained notable interest for their ability to yield nearly-linear asymptotic complexity and which can also be favourable for high-frequency problems. While successful approaches exist, such as those based on higher-order interface conditions, perfectly matched layers (PMLs), or complex tracking of wave fronts, they can often be quite involved or tedious to implement. We investigate here the use of simple sweeping techniques applied in different directions which can then be incorporated in parallel into a multipreconditioned GMRES strategy. Preliminary numerical results on a two-dimensional benchmark problem will demonstrate the potential of this approach.
Organisation STFC , SCI-COMP , SCI-COMP-CM
Keywords sweeping method , Helmholtz equation , preconditioning
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Language English (EN)
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Book Chapter or Section In Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1. Lecture Notes in Computational Science and Engineering 153 edited by A Sequeira, A Silvestre, SS Valtchev, J Janela, 168-176. Cham: Springer Nature Switzerland, 2025. doi:10.1007/978-3-031-86173-4_17 2025