Multidirectionnal sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems

Abstract

This paper explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission conditions and cross-point treatments, which cannot scale without an efficient preconditioning technique when the number of subdomains increases. With the proposed approach, existing sweeping preconditioners, such as the symmetric Gauss-Seidel and parallel double sweep preconditioners, can be applied to checkerboard partitions with different sweeping directions (e.g. horizontal and diagonal). Several directions can be combined thanks to the flexible version of GMRES, allowing for the rapid transfer of information in the different zones of the computational domain, then accelerating the convergence of the final iterative solution procedure. Several two-dimensional finite element results are proposed to study and to compare the sweeping preconditioners, and to illustrate the performance on cases of increasing complexity.

References in corpus (1)

• A comparison of coarse spaces for Helmholtz problems in the high frequency regime

Cited by in corpus (5)

• Schwarz methods by domain truncation
• A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems
• A Unified Framework for Double Sweep Methods for the Helmholtz Equation
• Can DtN and GenEO coarse spaces be sufficiently robust for heterogeneous Helmholtz problems?
• Multipreconditioning with directional sweeping methods for high-frequency Helmholtz problems