An efficient two-level preconditioner for multi-frequency wave propagation problems

An efficient two-level preconditioner for multi-frequency wave propagation problems

Baumann, M.M. (TU Delft Numerical Analysis)
van Gijzen, M.B. (TU Delft Numerical Analysis)

2019

We consider wave propagation problems that are modeled in the frequency-domain, and that need to be solved simultaneously for multiple frequencies within a fixed range. For this, a single shift-and-invert preconditioner at a so-called seed frequency is applied. The choice of the seed is crucial for the performance of preconditioned multi-shift GMRES and is closely related to the parameter choice for the Complex Shifted Laplace preconditioner. Based on a classical GMRES convergence bound, we present an analytic formula for the optimal seed parameter that purely depends on the original frequency range. The new insight is exploited in a two-level preconditioning strategy: A shifted Neumann preconditioner with minimized spectral radius is additionally applied to multi-shift GMRES. Moreover, we present a reformulation of the multi-shift problem to a matrix equation solved with, for instance, global GMRES. Here, our analysis allows for rotation of the spectrum of the linear operator. Numerical experiments for the time-harmonic visco-elastic wave equation demonstrate the performance of the new preconditioners.

Frequency-domain formulation
Multi-shift GMRES
Preconditioner design
Shift-and-invert preconditioner
Visco-elastic wave equation

http://resolver.tudelft.nl/uuid:4e28fbc1-0102-42bc-9866-1ce7bdf71335

https://doi.org/10.1016/j.apnum.2018.08.020

2021-11-02

0168-9274

Applied Numerical Mathematics, 135, 316-332

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2019 M.M. Baumann, M.B. van Gijzen