Mathematics – Numerical Analysis
Scientific paper
2011-05-16
Numerical Linear Algebra with Applications, v19, i2, p232-252, (2012)
Mathematics
Numerical Analysis
Scientific paper
10.1002/nla.1806
This paper analyzes the Krylov convergence rate of a Helmholtz problem preconditioned with Multigrid. The multigrid method is applied to the Helmholtz problem formulated on a complex contour and uses GMRES as a smoother substitute at each level. A one-dimensional model is analyzed both in a continuous and discrete way. It is shown that the Krylov convergence rate of the continuous problem is independent of the wave number. The discrete problem, however, can deviate significantly from this bound due to a pitchfork in the spectrum. It is further shown in numerical experiments that the convergence rate of the Krylov method approaches the continuous bound as the grid distance $h$ gets small.
Reps Bram
Vanroose Wim
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