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

Manuel Baumann, Martin B. van Gijzen

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)316-332
Number of pages17
JournalApplied Numerical Mathematics
Volume135
DOIs
Publication statusPublished - 2019

Keywords

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

Fingerprint

Dive into the research topics of 'An efficient two-level preconditioner for multi-frequency wave propagation problems'. Together they form a unique fingerprint.

Cite this