2010/12/24 by Bram Reps, Reps, Bram, Wim Vanroose +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1012.5379
openalex publication_date 2010/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multigrid preconditioners and solvers for the indefinite Helmholtz equation\nsuffer from non-stability of the stationary smoothers due to the indefinite\nspectrum of the operator. In this paper we explore GMRES as a replacement for\nthe stationary smoothers of the standard multigrid method. This results in a\nrobust and efficient solver for a complex shifted or stretched Helmholtz\nproblem that can be used as a preconditioner. Very few GMRES iterations are\nrequired on each level to build a good multigrid method. The convergence\nbehavior is compared to a theoretically derived stable polynomial smoother. We\ntest this method on some benchmark problems and report on the observed\nconvergence behavior.\n