A Unified Framework for Double Sweep Methods for the Helmholtz Equation

Nacime Bouziani (1) , Frédéric Nataf (2, 3) , Pierre-Henri Tournier (2, 3)

1 Department of Mathematics [Imperial College London]
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We consider sweeping domain decomposition preconditioners to solve the Helmholtz equation in the case of stripwise domain decomposition with or without overlaps. We unify their derivation and convergence studies by expressing them as Jacobi, Gauss-Seidel, and Symmetric Gauss-Seidel methods for different numbering of the unknowns. The proposed framework enables theoretical comparisons between the double sweep methods in [Nataf and Nier (1997), Vion and Geuzaine (2018)] and those in [Stolk (2013, 2017), Vion and Geuzaine (2014)]. Additionally, it facilitates the introduction of a new sweeping algorithm. We provide numerical test cases to assess the validity of the theoretical studies.

Domaines: Analyse numérique [math.NA]

Nacime Bouziani, Frédéric Nataf, Pierre-Henri Tournier. A Unified Framework for Double Sweep Methods for the Helmholtz Equation. Journal of Computational Physics, 2023, 490, pp.112305. ⟨10.1016/j.jcp.2023.112305⟩. ⟨hal-02964033v4⟩