A Unified Framework for Double Sweep Methods for the Helmholtz Equation
arXiv:2010.13563 · doi:10.1016/j.jcp.2023.112305
Abstract
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.
References in corpus (5)
- A rapidly converging domain decomposition method for the Helmholtz equation
- Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
- L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation
- An improved sweeping domain decomposition preconditioner for the Helmholtz equation
- Multidirectionnal sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems